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Subject to daytime heating and nighttime cooling, a horizontal temperature gradient is generated in nearshore waters owing to the gradually deepening topography offshore. The resulting natural convection has significant biological and environmental implications. The present investigation is concerned with natural convection in a reservoir model induced by a periodically varying surface temperature. A hybrid of semi-analytical approach coupled with scaling analysis and numerical simulation is adopted to characterize the periodic flow. The present scaling focuses on the long period scenario for which a quasi-steady state is reached within a thermal forcing cycle. This is the case in natural water bodies under typical field conditions. Compared to the previously reported constant heating or cooling cases, the present scaling analysis is more complex and the developed scales depend on the period of the thermal forcing. Two critical functions of the Rayleigh number have been derived to identify the distinctness and stability of the thermal boundary layer. Distinct subregions are identified, and the scales of flow velocity and phase lag are derived for different subregions. These scaling results are verified by numerical simulations. Numerical results show that the flow response varies significantly with the length of period. For short periods, the large scale flow never reverses from cooling-induced flow. For the long period scenario, flow reversal occurs, with much more intense flow during the cooling phase than during the heating phase. The phase lag of flow response decreases with increasing period length. Finally, the present scaling results are applied to field situations, which agree well with field observations.

The K-type transition of a natural convection boundary layer of Ra = 9.8 × 109 is studied by PIV (Particle Image Velocimetry) measurements. To excite the transition, Tollmien-Schlitchting (TS) and oblique waves of the same frequency are introduced into the upstream boundary layer in the form of velocity perturbations. It is found that resonant interactions between the characteristic frequency of the natural convection boundary layer and the superimposed TS and oblique waves are present, which trigger the K-type transition of the boundary layer. The typical aligned Λ-shaped flow structures characterising the K-type transition present in the transition of Blasius boundary layers are also observed in the present natural convection boundary layers. They occur when the primary instability grows to a certain extent. The appearance of the spanwise mode characterised by the aligned Λ-shaped flow structures is found to be an ‘abrupt’ process, although the development of the three-dimensionality in the natural convection boundary layer is found to be a ‘gradual’ process. A peak in the typical profile of the Root-Mean-Square (RMS) of the amplitude of streamwise velocity is also noted around the transition point, beyond which distinct three-dimensional Λ-shaped flow structures are observed. The transition point has been determined consistently using different approaches. A Bicoherence analysis suggests that the interaction between the external excitation frequency and the characteristic frequency of the boundary layer is responsible for the production of new harmonic frequencies and resonance groups. The PIV measurements have been extended to a range of perturbation frequencies for the boundary layer, and the dependence of the K-type transition on the perturbation frequency is discussed.

The K-type and H-type transitions of a natural convection boundary layer of a fluid of Prandtl number 7 adjacent to an isothermally heated vertical surface are investigated by means of three-dimensional direct numerical simulation (DNS). These two types of transitions refer to different flow features at the transitional stage from laminar to turbulence caused by two different types of perturbations. To excite the K-type transition, superimposed Tollmien–Schlichting (TS) and oblique waves of the same frequency are introduced into the boundary layer. It is found that a three-layer longitudinal vortex structure is present in the boundary layer undergoing the K-type transition. The typical aligned $\wedge$-shaped vortices characterizing the K-type transition are observed for the first time in pure natural convection boundary layers. For exciting the H-type transition, superimposed TS and oblique waves of different frequencies, with the frequency of the oblique waves being half of the frequency of the TS waves, are introduced into the boundary layer. Unlike the three-layer longitudinal vortex structure observed in the K-type transition, a double-layer longitudinal vortex structure is observed in the boundary layer undergoing the H-type transition. The successively staggered $\wedge$-shaped vortices characterizing the H-type transition are also observed in the downstream boundary layer. The staggered pattern of $\wedge$-shaped vortices is considered to be caused by temporal modulation of the TS and oblique waves. Interestingly the flow structures of both the K-type and H-type transitions observed in the natural convection boundary layer are qualitatively similar to those observed in Blasius boundary layers. However, an analysis of turbulence energy production suggests that the turbulence energy production by buoyancy rather than Reynolds stresses dominates the K-type and H-type transitions. In contrast, the turbulence energy production by Reynolds stresses is the only factor contributing to the transition in Blasius boundary layers.

This investigation is motivated by interest in the mixing caused by the absorption of solar radiation in the near-shore regions of lakes. In the daytime, incoming solar radiation is absorbed by the water following Beer’s law. In the near-shore region where the water depth is less than the penetration depth of solar radiation, the residual radiation reaches the bottom and is absorbed and re-emitted back into the water body as a bottom heat flux, resulting in an adverse temperature gradient which may become unstable. In this laboratory-scale experimental study, this situation is modelled with a water-filled, open top tank with a black bottom subjected to radiative heating from a halogen theatre spotlight. Concurrent shadowgraph and Particle Image Velocimetry (PIV) are utilised for simultaneous visualisation of the temperature field and flow measurements. Initially, there is no motion and two distinct thermal boundary layers simultaneously grow from the water surface and from the bottom boundary. The bottom boundary layer becomes unstable at a certain thickness, and rising plumes are formed. The plumes transfer heat and cause circulation and vertical mixing in the water body. Subsequently the plumes disappear as the bottom boundary layer is dismantled, the bottom boundary layer is re-established, and the plumes re-formed. This paper will focus on characterising the first and the second stages. Accordingly, the onset of convection, plume rise height, and plume rise velocity are investigated through analysis of the PIV and shadowgraph images and compared with previously published scaling.

We report the first definitive Nusselt number scale of thermal boundary layers from curved surfaces characterized by the proposed non-dimensional curvature parameter ξ = R 0/(H Ra −1/4), where R 0 denotes the radius of a curved surface, H denotes the corresponding finite height, and Ra denotes the global Rayleigh number of a virtual reference thermal boundary layer on a vertical flat surface. The Nusselt number scale is given by Nu ∼ ξ −1/5 Ra 1/4 in which Nu ∼ Ra 1/4 is the scale for the flat surface case, revealing that curved thermal boundary layers could present times-of-magnitude larger heat flux with the curvature parameter being ξ ≪ 1. The velocity and thickness scales are also given by V s ∼ R 0 2 / 5 R a 3 / 5 H 7 / 5 κ and Δ T ∼ R 0 1 / 5 H 4 / 5 R a 1 / 5 .

The ‘natural transition’ of a natural convection boundary layer adjacent to an isothermally heated vertical surface is investigated by means of three-dimensional direct numerical simulation (DNS). In order to trigger ‘natural transition’ numerically, spatially and temporally random perturbations are introduced into the upstream boundary layer. The propagation of the random perturbations in the streamwise direction is observed. It is found that there exist two competing wavenumbers of spanwise vortical structures, one large and the other small. The large wavenumber dominates in the upstream boundary layer, whereas the small wavenumber dominates in the downstream boundary layer. The streamwise evolution of the mean (time-averaged) streamwise vorticity observed at planes perpendicular to the heated surface in general reveals two- and three-layer longitudinal roll structures. Nonlinear processes in a transitioning natural convection boundary layer are also analysed using Bicoherence method. The transition route and mechanism are discussed based on the power spectra and Bicoherence spectra of the temperature time series obtained in the boundary layer. A spectrum filling process during the ‘natural transition’ to turbulence is also observed, which is qualitatively similar to that observed in Blasius boundary layers.

This paper considers linear and oscillatory behaviours of the natural convection boundary layer induced by the absorption of incoming radiation in response to constant and time-varying (ramp) thermal forcing. The considered configuration is relevant to the flow in littoral regions of lakes and reservoirs in response to the daytime thermal forcing due to solar radiation. The absorption of the incoming solar radiation is depth-dependent, following Beer’s law, whilst the residual radiation at the bottom bathymetry is absorbed and released back to the water body as a boundary flux. Therefore, a potentially unstable thermal boundary layer forms adjacent to the bottom bathymetry and the associated thermoconvective instability induces vertical mixing in the form of rising plumes (i.e. intermittent convection). The linear theory is applied to investigate the incipient evolution of the instability, and direct comparisons of linear and direct stability analyses are performed. The fastest growing mode and the corresponding temporal growth rate obtained via a quasi-static linear stability analysis are shown to be in excellent agreement with the results of the direct stability analysis based on numerical simulations of the flow. Further, the time and frequency scales of the unstable bottom thermal boundary layer are derived via a local Rayleigh number analysis. It is then demonstrated that the boundary layer response to the time-varying thermal forcing is in equilibrium with the forcing intensity at each instant of time.

The present study considers the early stage of the flow development in a water-filled, three-dimensional parallelepiped cavity subject to solar radiation. The thermal structure consists of an upper stable stratification due to internal heating, provided by the direct absorption of radiation, and a bottom potentially unstable boundary layer due to the absorption and re-emission of the residual radiation by the bottom boundary. The growth of the competing thermal layers and the stability properties of the bottom thermal boundary layer are investigated by means of a scaling analysis and a direct stability analysis based on three-dimensional numerical simulation. The scaling relations are benchmarked against the numerical simulation, and the effects of the normalised water depth, the Rayleigh number and the box aspect ratio on the thermal instability are studied.

This study focuses on the marginal stability of the natural convection flow induced by the absorption of radiation. Non-uniform internal heating associated with the absorption of radiation following Beer’s law and the absorption and re-emission of residual radiation by the bottom boundary wall lead to a nonlinear base temperature profile that evolves with time. A horizontal throughflow and lateral confinement are incorporated in the analysis, and two forms of convective instability, i.e. longitudinal and transverse rolls, are investigated. It is shown that the formation of longitudinal rolls, with their axes parallel to the throughflow direction, is not affected by the presence of the throughflow. For transverse rolls, with their axes perpendicular to the throughflow direction, however, the throughflow is shown to have a stabilising effect, with the critical Rayleigh number increasing with the increasing throughflow Reynolds number. It follows that longitudinal rolls are the preferred form of instability in laterally unconfined domains for any nonzero Reynolds number and in confined domains if the Reynolds number is greater than a critical value. The value of the critical Reynolds number, which separates the preferred mode of instability, is found to rapidly reduce with increasing lateral extent and approaches zero for a normalised lateral extent greater than 2.0. The lateral confinement is also shown to have a stabilising effect for both longitudinal and transverse rolls, with the critical Rayleigh number increasing with the reducing lateral extent. It is shown that the lateral confinement only substantially affects the wave number of the rolls with their axes parallel to the confining walls but not the rolls with their axes perpendicular to the confining walls.

This study considers the natural convection flow in a water body subjected to heating by solar radiation. The investigation into this type of natural convection flow has been motivated by the fact that it is known to play a crucial role in the daytime heat and mass transfer in shallow regions of natural water reservoirs and lakes, with a resultant impact on biological activity. An analytical solution for temperature in such an internally heated system shows that the temperature stratification consists of an upper stable stratification and a lower unstable stratification. One of the important consequences of such a nonlinear temperature stratification is the limitation of the mixing driven by rising thermal plumes with the penetration length scale of the plumes determining the lower mixed layer thickness. A theoretical analysis conducted in the present study suggests that in relatively deep waters, the lower mixed layer thickness is equal to the attenuation length of the radiation, which has important implications for water quality, including the transport of pollutants and nutrients in the water body. Scalings are also obtained for the quasi-steady boundary layer. The theoretical analysis is validated against numerical simulations.

Previous studies have revealed that heat transfer through a convective thermal boundary layer can be significantly enhanced by perturbing the thermal boundary layer to advance linear to nonlinear transition. It has also been demonstrated that the enhancement of heat transfer is mostly achieved in the nonlinear regime. In this study, the transition of the thermal boundary layer adjacent to an isothermally heated vertical surface is revisited by means of Bicoherence analysis, which is a statistical approach for identifying and quantifying quadratic wave interactions. The streamwise evolution of Bicoherence spectra suggests that the thermal boundary layer can be classified into three regimes: a linear flow regime, a transitional flow regime and a nonlinear flow regime. The positions of the transition from the transitional to nonlinear regimes in the thermal boundary layer at various Rayleigh numbers, perturbation frequencies and perturbation amplitudes are determined using Bicoherence analysis. It is found that in the nonlinear flow regime, the number of resonance groups fluctuates, which indicates the occurrence of coupling and decoupling of harmonics in the boundary layer. This process may be the mechanism responsible for the resonance induced enhancement of heat transfer.

In this study the natural convection flow adjacent to a finned sidewall of a differentially heated cavity is experimentally investigated using the shadowgraph technique. Two Perspex fins of different lengths are placed horizontally at different heights along each of the cavity sidewalls. It is revealed from the shadowgraph observation of the heated sidewall that similar horizontal hot intrusions form underneath the fins and the cavity ceiling at the early stage. In the transitional stage, the thermal flows bypassing the fins are entrained towards the heated sidewall and a cavity-scale interior temperature stratification is gradually established. In the quasi-steady stage, regular oscillations are observed above the lower fin. The oscillation in the horizontal thermal flow above the lower fin results in strong mixing in the thermal boundary layer between the two fins and that downstream of the upper fin. As a consequence, heat transfer through the downstream thermal boundary layer is greatly enhanced. A corresponding numerical simulation is also conducted and a good agreement between the simulation and the experiment is achieved. It is further revealed numerically that the convective flow across the cavity is significantly enhanced due to the presence of the fins. The heat transfer is improved by up to 17.1% over the investigated Rayleigh number range. The dependency of the time averaged Nusselt number at the finned sidewall on the Rayleigh number has been quantified.

The flow behavior due to natural convection of air (with a Prandtl number less than 1) inside a solar chimney with an imposed heat flux on a vertical absorber wall is investigated by a scaling analysis and a corresponding numerical simulation. Three distinct flow regimes are identified, one with a distinct thermal boundary layer and the other two without a distinct thermal boundary layer, depending on the Rayleigh number. The two regimes without a distinct thermal boundary layer are further classified into low and medium Rayleigh number sub-regimes respectively. These sub-regimes are characterized by conduction dominance in which the thermal boundary layer grows to encompass the entire width of the channel before convection becomes important. Flow development in each of these flow regimes and sub-regimes is characterized through transient scaling, and scaling correlations are developed to describe the temperature, flow velocity and mass flow rate, which characterize the ventilation performance of the solar chimney. The scaling arguments are validated by the corresponding numerical data.

Nearshore natural convection induced by differential heating across shore has significant biological and environmental implications. The present investigation is concerned with convection in a wedge-shaped reservoir sidearm induced by isothermal heating at the water surface which increases linearly over a specified time period from an initial value to a final steady value (i.e. ramped heating), extending our previous report on convection induced by constant isothermal heating. A semi-analytical approach coupled with scaling analysis and numerical simulation is adopted to resolve the problem. It is revealed that the flow domain is composed of two distinct subregions, a conductive region nearshore which finally becomes isothermal and stationary, and a convective region offshore which eventually maintains a steady flow velocity. Different scenarios are revealed through the comparison between the ramp duration P and a characteristic time t c of the induced flow. For the conductive region, the characteristic time is the time for the thermal boundary layer formed at the surface to reach the full local depth. For the convective region, it is the steady state time when convection balances conduction. For a short ramp ( P t c ), no steady state is reached within the ramping stage. For a long ramp ( P > t c ), a quasi-steady state is reached for both subregions before the ramp finishes. For the conductive region, the quasi-steady state is characterized by a steady flow velocity and the same local temperature growth rate as the water surface. For the convective region, the quasi-steady state is characterized by a change in the growth rate of the velocity. Major time and velocity scales governing the flow development in both subregions are proposed by a semi-analytical solution coupled with scaling and verified by the numerical simulation. Implication of the present study for field situations is also discussed.

The instability characteristics and resonance of a natural convection boundary layer adjacent to an isothermally heated vertical surface are investigated using direct stability analyses. The detailed streamwise evolution of the boundary-layer frequencies is visualized via the power spectra of the temperature time series in the thermal boundary layer. It is found that the entire thermal boundary layer may be divided into three distinct regions according to the frequency profile, which include an upstream low-frequency region, a transitional region (with both low- and high-frequency bands) and a downstream high-frequency region. The high-frequency band in the downstream region determines the resonance characteristics of the thermal boundary layer, which can be triggered by a single-mode perturbation at frequencies within the high-frequency band. The single-mode perturbation experiments further reveal that the maximum resonance of the thermal boundary layer is triggered by a perturbation at the characteristic frequency of the boundary layer. For the boundary-layer flow at $\mathit{Ra}= 3. 6\times 1{0}^{10} $ and $\mathit{Pr}= 7$, a net heat transfer enhancement of up to 44 % is achieved by triggering resonance of the boundary layer. This significant enhancement of heat transfer is due to the resonance-induced advancement of the laminar–turbulent transition, which is found to be dependent on the perturbation frequency and amplitude. Evidence from different perspectives revealing the same position of the transition are provided and discussed. The outcomes of this investigation demonstrate the prospect of a resonance-based approach for enhancing heat transfer.

The present investigation is concerned with natural convection in a wedge-shaped domain induced by constant isothermal heating at the water surface. Complementary to the study of daytime heating by solar radiation relevant to nearshore regions of lakes and reservoirs previously reported by the same authors, this study focuses on sensible heating imposed by the atmosphere when it is warmer than the water body. A semi-analytical approach coupled with scaling analysis and numerical simulation is adopted to resolve the problem. Two flow regimes are identified depending on the comparison between the Rayleigh number and the inverse of the square of the bottom slope. For the lower Rayleigh number regime, the entire flow domain eventually becomes isothermal and stationary. For the higher Rayleigh number regime, the flow domain is composed of two distinct subregions, a conductive subregion near the shore and a convective subregion offshore. Within the conductive subregion, the maximum local flow velocity occurs when the thermal boundary layer reaches the local bottom, and the subregion eventually becomes isothermal and stationary. In the offshore convective subregion, a steady state is reached with a distinct thermal boundary layer below the surface and a steady flow velocity. The dividing position between the two subregions and the major time and velocity scales governing the flow development in both subregions are proposed by the scaling analysis and validated by corresponding numerical simulation.

We perform detailed numerical simulations of natural convection in a reservoir model induced by surface heating. The transient behaviour of the flow, including streamlines, isotherms, surface velocity profiles, volumetric flow rates, heat transfer rates, and temperature averaged over the local water depth are presented at different Rayleigh numbers. At an instantaneous time within the sloping bottom region, the surface velocity initially increases and then decreases with an increase of the offshore distance. Over a certain range of Rayleigh numbers, the location of the peak surface velocity may initially move in the offshore direction and then retract with the elapse of time. The point at which the rates of horizontal conduction and convection balance also retracts towards the tip region with the elapse of time. Some insight into understanding the mechanisms that drive the flow is provided according to the detailed transient behaviour of the flow.

The natural convection thermal boundary-layer adjacent to an inclined flat plate subject to sudden heating and a temperature boundary condition which follows a ramp function up until a specified time and then remains constant is investigated. The development of the flow from start-up to a steady state has been described based on scaling analyses and verified by numerical simulations. Different flow regimes based on the Rayleigh number are discussed with numerical results for both boundary conditions. For ramp heating, the boundary-layer flow depends on the comparison of the time at which the ramp heating is completed and the time at which the boundary layer completes its growth. If the ramp time is long compared with the steady-state time, the layer reaches a quasi-steady mode in which the growth of the layer is governed solely by the thermal balance between convection and conduction. On the other hand, if the ramp is completed before the layer becomes steady; the subsequent growth is governed by the balance between buoyancy and inertia, as for the case of instantaneous heating.

A fundamental study of the fluid dynamics inside an attic shaped triangular enclosure with cold upper walls and adiabatic horizontal bottom wall is reported in this study. The transient behaviour of the attic fluid which is relevant to our daily life is examined based on a scaling analysis. The transient phenomenon begins with the instantaneous cooling and the cooling with linear decreases of temperature up to some specific time (ramp time) and then maintain constant of the upper sloped walls. It is shown that both inclined walls develop a thermal boundary layer whose thicknesses increase towards steady state or quasi-steady values. A proper identification of the time scales, the velocity and the thickness relevant to the flow that develops inside the cavity makes it possible to predict theoretically the basic flow features that will survive once the thermal flow in the enclosure reaches a steady state. A time scale for the cooling-down of the whole cavity together with the heat transfer scales through the inclined walls has also been obtained through scaling analysis. All scales are verified by the numerical simulations.

In this study, a discussion of the fluid dynamics in the attic space is reported, focusing on its transient response to sudden and linear changes of temperature along the two inclined walls. The transient behaviour of an attic space is relevant to our daily life. The instantaneous and non-instantaneous (ramp) heating boundary condition is applied on the sloping walls of the attic space. A theoretical understanding of the transient behaviour of the flow in the enclosure is performed through scaling analysis. A proper identification of the timescales, the velocity and the thickness relevant to the flow that develops inside the cavity makes it possible to predict theoretically the basic flow features that will survive once the thermal flow in the enclosure reaches a steady state. A time scale for the heating-up of the whole cavity together with the heat transfer scales through the inclined walls has also been obtained through scaling analysis. All scales are verified by the numerical simulations.

Temperature measurements of the thermal flows in a differentially heated cavity with and without a fin on the sidewall were performed. The oscillatory behaviours in the transition from an initially isothermal state to an eventually stratified interior fluid ambient are characterized. It is revealed that, for the case without a fin, the amplitude of the oscillations in the thermal boundary layer increases as the stratification of the interior fluid increases. For the case with a fin, the temperature measurements show that the oscillations are induced by an unstable fluid layer above the fin. The spectral analysis reveals that the frequency properties of the oscillations are different between the cases with and without a fin.

Natural convection in calm near-shore waters induced by daytime heating or nighttime cooling plays a significant role in cross-shore exchanges with significant biological and environmental implications. Having previously reported an improved scaling analysis on the daytime radiation-induced natural convection, the authors present in this paper a detailed scaling analysis quantifying the flow properties at varying offshore distances induced by nighttime surface cooling. Two critical functions of offshore distance have been derived to identify the distinctness and the stability of the thermal boundary layer. Two flow scenarios are possible depending on the bottom slope. For the relatively large slope scenario, three flow regimes are possible, which are discussed in detail. For each flow regime, all the possible distinctive subregions are identified. Two different sets of scaling incorporating the offshore-distance dependency have been derived for the conduction-dominated region and stable-convection-dominated region respectively. It is found that the scaling for flow in the stable-convection-dominated region also applies to the time-averaged mean flow in the unstable region. The present scaling results are verified by numerical simulations.

This work incorporates scaling analysis to characterise unsteady boundary-layer development for thermo-magnetic convection of paramagnetic fluids with Prandtl numbers (Pr ) greater than one. Under consideration is a square cavity with a quiescent isothermal, Newtonian fluid placed in a micro-gravity condition (g≈0g≈0), and under a uniform vertical gradient magnetic field. A distinct magnetic convection boundary layer is produced by the sudden imposition of a higher temperature on the left-hand side vertical sidewall due to the effect of the magnetic body force generated on the paramagnetic fluid. This magnetic force is proportional to the magnetic susceptibility and the gradient of the square of the magnetic induction. According to Curie’s law, the magnetic susceptibility of a paramagnetic fluid is inversely proportional to the absolute temperature. Thermal convection of a paramagnetic fluid can therefore take place even in zero-gravity environments as a direct consequence of temperature differences occurring within the fluid placed within a magnetic field gradient. Scaling predictions presented here are verified by numerical simulations It is shown that the transient flow behaviour of the resulting boundary layer can be described by three stages: a start-up stage, a transitional stage and a steady state. Special attention in this work is paid to the dependency of the flow development upon the Prandtl number, varied over the range of 5–100, thus representing various fluids. Also, the effect of the magnetic momentum parameter, m, and the quantity γRa, upon the flow development obtained in numerical simulations confirms the accuracy of new scaling predictions for paramagnetic fluids.

Transient natural convection flows around a thin fin on the sidewall of a differentially heated cavity, which includes a lower intrusion under the fin, a starting plume bypassing the fin and a thermal flow entrained into the vertical thermal boundary layer downstream of the fin in a typical case, are investigated using a scaling analysis and direct numerical simulations. The obtained scaling relations show that the thickness and velocity of the transient natural convection flows around the fin are determined by different dynamic and energy balances, which can be either a buoyancy-viscous balance or a buoyancy-inertial balance, depending on the Rayleigh number, the Prandtl number and the fin length. A time scale of the transition from a buoyancy-viscous flow regime to a buoyancy-inertial flow regime is obtained. The major scaling relations quantifying the transient natural convection flows are also validated by direct numerical simulations. In general, there is a good agreement between the scaling predictions and the corresponding numerical results.

A scaling analysis is presented for the transient boundary layer established on a vertical wall following non-instantaneous heating in the form of an imposed wall temperature which increases linearly up to a prescribed steady value over a prescribed time. The scaling analysis is verified by comparison with numerical solutions of the full equations of motion and energy. The analysis reveals that, if the period of temperature growth on the wall is sufficiently long, the boundary layer reaches a quasi-steady state before the temperature growth is completed. In this mode the thermal boundary layer at first grows in thickness and then contracts with increasing time, and the fluid acceleration also changes character. If the wall temperature growth period is sufficiently short, the boundary layer commences differently, but after the wall temperature growth is completed, the boundary layer develops as though the start up had been instantaneous. In both cases, the ultimate steady state is the same as if the start up had been instantaneous; however the different transient nature may have implications for the stability of the boundary layer or of the subsequent development of the flow in a cavity of which the wall is one boundary.

The coupled thermal boundary layers adjacent to a partition in a differentially heated cavity are numerically investigated. The cavity is filled with water, which is initially quiescent but with an imposed temperature difference between the two sides of the vertical partition. The numerical results show that the development of natural convection flows in the partitioned cavity undergoes three main stages: an initial stage, a transitional stage and a steady stage. The transient features of the coupled thermal boundary layers adjacent to the partition as well as the overall natural convection flow in the partitioned cavity are described, and heat transfer through the coupled thermal boundary layers and the partitioned cavity is examined.

The present study is concerned with radiation-induced natural convection in a water-filled triangular enclosure with a sloping bottom, which is directly relevant to buoyancy-driven flows in littoral regions. An improved scaling analysis is carried out to reveal more detailed features of the flow than a previously reported analysis. Two critical functions of the Rayleigh number with respect to the horizontal position are derived from the scaling for identifying the distinctness and stability of the thermal boundary layer. Four flow scenarios are possible, depending on the bottom slope and the maximum water depth. For each flow scenario, the flow domain may be composed of multiple subregions with distinct thermal and flow features, depending on the Rayleigh number. The dividing points between neighbouring subregions are determined by comparisons of the critical functions of the Rayleigh number with the global Rayleigh number. Position-dependent scales have been established to quantify the flow properties in different subregions. The different flow regimes for the case with relatively large bottom slopes and shallow waters are examined in detail. The present scaling results are verified by numerical simulations.

The transition to a periodic flow induced by a thin fin on the sidewall of a differentially heated cavity is numerically investigated. The numerical results are compared with a previously reported experiment. It is demonstrated that the transient flow obtained numerically shows features consistent with the experimental flow. Based on the present numerical results, the temporal development and spatial structures of the thermal flow around the fin are described, and the separation of the thermal flow above the fin is discussed. It is found that the presence of the fin changes the flow regime and results in the transition of the thermal flow to a periodic flow. The present numerical results also indicate that the unstable temperature configuration above the fin results in intermittent plumes at the leeward side of the fin, which in turn induce strong oscillations of the downstream boundary layer flow. It is demonstrated that the oscillations of the boundary layer flow significantly enhance the heat transfer through the finned sidewall (by up to 23%).

The unsteady thermal flow around a thin fin on a sidewall of a differentially heated cavity is visualized using a shadowgraph technique and measured using fast-response thermistors. Experiments show that the transition of the unsteady thermal flow around the fin from initiation by sudden heating to a quasi-steady state undergoes a number of stages including the formation of a horizontal gravity current under the fin and a starting plume bypassing the fin, entrainment into the downstream thermal boundary layer, and separation and oscillations of the thermal flow above the fin. We present a series of flow visualization images to describe the transition of the unsteady thermal flow, and obtain the unsteady velocity scales of the fronts of the lower intrusion and starting plume as functions of the time and Rayleigh number, which are verified by the results of the flow visualization experiments. In the transition to the quasi-steady state, separation and oscillations of the thermal flow above the fin are observed. It is demonstrated that these oscillations, which are sensitive to the geometry of the fin, trigger instability of the downstream thermal boundary layer flow and thus enhance convection. It is found that the frequency of the oscillations is a linear function of the Rayleigh number.

The general characteristics of unsteady natural convection flow in a reservoir model cooled from the water surface are presented in this paper. Flow visualization was carried out using thermo-chromic liquid crystals, and quantitative temperature measurements were conducted using a PIT (particle image thermometry) technique. The experimental photographs clearly show different stages of the flow development including the growth of a thermal boundary layer below the water surface, the onset of convective instabilities, and further flow development. The present results indicate that the convective motions in reservoirs induced by night-time cooling have a significant impact on water quality and transport of nutrients and pollutants.

Natural convection in a differentially heated cavity with a square obstruction placed in the middle of the hot wall is investigated numerically. The results demonstrate that, firstly, the thermal boundary layer flow, blocked by the obstruction, forms a lower intrusion front, which then detaches from the hot wall, bypasses the obstruction, and reattaches to the thermal boundary layer. While the reattachment occurs, a complicated flow with circulations is induced, and the heat transfer through the hot wall is significantly enhanced.

A natural convection boundary layer undergoing natural transition to turbulence is investigated by particle image velocimetry (PIV) measurements for the first time. The boundary layer adjacent to an isothermally heated plate immersed in water is subjected to environmental noise, the transition of which is therefore regarded as a natural transition. Distinct stripe-like flow structures characterising the natural transition of the natural convection boundary layer are visualised for the first time by the PIV experiments. The spatial wavenumber and the frequency of the flow structures are further quantified by applying a two-dimensional Fourier transform to time series of the flow properties. A distinct transitional regime in the boundary layer is noted, in which the three-dimensionality of the flow grows exponentially in the streamwise direction. The characteristic frequency of the natural convection boundary layer is also obtained from the PIV measurements, which agrees well with a theoretical prediction reported previously.

The double layer structure of the thermal boundary layer in a side-heated cavity is investigated numerically and experimentally. Through comparing the flow visualizations with the numerical results, the mechanisms of the transition of the thermal boundary layer are discussed. The numerical results demonstrate that an upward thermal tongue leads to the double layer structure of the thermal boundary layer in the quasi-steady stage, which is observed in shadowgraph images.

The transient thermal boundary layer flow around a square obstruction placed at the middle of the hot wall in a differentially heated cavity is visualized using a shadowgraph technique. The results show that the thermal boundary layer flow, which is blocked by the obstruction, firstly forms an intrusion head under the obstruction (the lower intrusion head). Subsequently, the lower intrusion head bypasses the obstruction and reattaches to the down-stream boundary. During the reattachment process, a more complicated flow is induced, and eventually both the lower intrusion head and the thermal boundary layer destabilize. After the lower intrusion head is convected away, the thermal boundary layer flow re-stabilizes. At the quasi-steady state, the thermal boundary layer forms a double-layer structure, which is split into two sections by the obstruction. It is demonstrated that both the transient processes and the quasi-steady state flow structures of the thermal boundary layer are significantly altered by the obstruction in comparison with the case without the obstruction.

The transition of the thermal boundary layer from start-up to a quasi-steady state in a side-heated cavity is observed using a shadowgraph technique. Three stages of the transition, including an initial growth stage, an entrainment development stage and a quasi-steady stage, are demonstrated. A significant feature of the transition revealed from the present flow visualisation is the formation of a double-layer structure along the sidewall at the entrainment development stage. It is believed that the reverse flow in the double-layer structure is the likely cause responsible for the unstable travelling waves at the quasi-steady state.

This study considers the convective instability of a water-filled shallow wedge with an absorptive bottom subject to solar radiation. Previous studies have revealed that a thermal boundary layer develops along the sloping bottom due to the absorption of penetrative radiation there, and this boundary layer is potentially unstable to the Rayleigh–Benard instability. The stability properties of the thermal boundary layer are determined in the present study by perturbing the three-dimensional numerical solution. The result of the direct stability analysis has confirmed previous scaling with respect to the convective instability. Additional features of the thermal layer instability have also been revealed from the direct stability analysis.

The natural convection in a reservoir sidearm induced by solar radiation is visualised using a shadowgraph technique. The flow visualisation reveals three stages of the flow development, namely an initial growth stage, a transitional stage and a quasi-steady stage. At the initial growth stage, a distinct thermal boundary layer grows rapidly along the sloping bottom. The transitional stage is characterised by the onset of convective instability in a form of rising plumes. At the quasi-steady state, the mean temperature across the enclosure increases steadily in time and the flow is sighted with quasi-regular presence of instabilities with reduced intensities.

In this study, the Navier-Stokes equations and the pressure Poisson equation for two-dimensional time-dependent viscous flows are solved with a finite difference method in a curvilinear coordinate system. With this numerical procedure, the vortex shedding flow past a circular cylinder near a wall is investigated. The flow is calculated for a broad range of gap ratios for different Reynolds numbers ranging from 80 to 1000. Based on the numerical solutions, the vortex shedding is observed using various methods, and the mechanism for the vortex shedding suppression at small gap ratios is analyzed. The critical gap ratio at which the vortex shedding is suppressed is identified at different Reynolds numbers.

The hydrodynamic forces and vortex shedding of a smooth circular cylinder immersed in different boundary layers were experimentally investigated at Reynolds numbers from 1.30×104 to 1.45×104. The effects of the bed proximity, the thickness of the boundary layer, and the velocity gradient in the boundary layer on the pressure distribution, the hydrodynamic forces and the vortex shedding behavior were examined. The experimental results show that both the drag and lift coefficients strongly depend on the gap ratio, and are affected by the boundary layer. A downward lift is observed at certain gap ratios in rod-generated boundary layers, and an explanation of this downward lift is given. Two different criteria for calculating the Strouhal number in the literature are discussed in this paper. It is found that the variation of the root-mean-square (RMS) lift coefficient reveals the onset or suppression of the vortex shedding. A quantitative method for identifying the vortex shedding suppression point is proposed. The observations show that the vortex shedding is suppressed at a gap ratio of about 0.2–0.3, depending on the thickness of the boundary layer. This critical gap ratio decreases as the thickness of the boundary layer increases.

A scaling analysis is performed for the transient boundary layer established adjacent to an inclined flat plate following a ramp cooling boundary condition. The imposed wall temperature decreases linearly up to a specific value over a specific time. It is revealed that if the ramp time is sufficiently large then the boundary layer reaches quasi-steady mode before the growth of the temperature is finished. However, if the ramp time is shorter then the steady state of the boundary layer may be reached after the growth of the temperature is completed. In this case, the ultimate steady state is the same as if the start up had been instantaneous. Note that the cold boundary layer adjacent to the plate is potentially unstable to Rayleigh–Benard instability if the Rayleigh number exceeds a certain critical value for this cooling case. The onset of instability may set in at different stages of the boundary layer development. A proper identification of the time when the instability may set in is discussed. A numerical verification of the time for the onset of instability is presented in this study. Different flow regimes based on the stability of the boundary layer have also been discussed with numerical results.

The transient natural convection of variable and constant viscosity fluids in a side cooled cubical cavity is studied experimentally. The convective flow in the cavity is visualized by the shadowgraph technique. The fluid was initially preheated and enough time is allowed to assure uniform temperature distribution. Temperature difference is introduced by a sudden cooling of the two side walls. The results indicate that the transient flow development is characterized by the following distinct processes: the initial growth of the vertical boundary layer and horizontal intrusions, the interaction of the horizontal intrusions and the stratification. New scaling relations are introduced to include the effect of the viscosity variation with temperature. The new suggested scalings showed good agreement with the measurements based on the shadowgraph images.Copyright © 2011 by ASME

In this paper, the scalings incorporating the Prandtl number (Pr) dependence have been obtained by a scaling analysis for the unsteady natural convection boundary layer of an initially quiescent isothermal Newtonian fluid of Pr>1 produced by the sudden imposition of a higher temperature on a vertical plate. It is shown that the transient flow behavior of the resulting boundary layer can be described by a three-region structure and at the start-up stage the boundary layer development is one dimensional and independent of height due to the dominance of pure conduction; however, at steady state it becomes two dimensional and height dependent as the flow becomes dominated by convection. Numerical results demonstrate that the scalings representing the thermal boundary layer development accurately represent their Pr dependence over the whole stage of flow development. The scalings representing the viscous boundary layer development are generally in good agreement with the numerical results with the Pr variation over the whole stage of flow development, although there are small deviations from the numerical results with the Pr variation that are within acceptable limits for scaling.

The transient flow around a thin fin on the sidewall in a differentially heated cavity is visualized using a shadowgraph technique. The transition of the flow from sudden heating to a quasi-steady state may be classified into three stages: an early stage, a transitional stage and a quasi-steady stage. Such classifications are similar to those in the case with a smaller square fin on the sidewall (Xu et al., 2006). However, there are distinct differences of the flow features between the cases with a small square fin and a larger thin fin. In the early stage, a lower intrusion front forms below the fin which induces strong turbulent mixing downstream of the fin and is convected away. In the transitional stage, as the fluid in the cavity is stratified, the flow around the thin fin separates and oscillates. The oscillations break the double-layer structure of the downstream thermal boundary layer adjacent to the sidewall in the quasi-steady stage. It is found that the separation and oscillations of the flow around the thin fin are dependent on the geometry of the fin. The frequency of oscillations has a good linear correlation with the Rayleigh number, but is lower than that of unstable travelling waves in the thermal boundary layer for the case without a fin (approximately 1/2).

Natural convection in a suddenly side-heated cavity with a square obstruction placed at the middle of the hot wall is visualized using a shadowgraph technique. The results show that the thermal boundary layer flow accumulates below the obstruction and forms a horizontal intrusion. Subsequently, the intrusion bypasses the obstruction, and reattaches to the downstream boundary. At the quasi-steady state, the thermal boundary layer forms a double-layer structure, which is split into two sections by the obstruction.

The natural convection in a side-heated cavity with a square obstruction placed in the middle of the hot wall is investigated numerically. The results demonstrate that, firstly. the thenmll boundaIy layer flow, blocked by the obstruction. forms a head, and then the head detaches from the hot wall, bypasses the obstruction, and reattaches to the thermal boundary layer. While the reattachment occurs, a complicated flow with circulations is induced, and the heat transfer through the hot wall is significantly enhanced.

A model for radiation-induced natural convection in a water-filled wedge is described in [3]. With this model there is the potential for a thermal instability [2]. Flow visualisation revealed the primary form of the instability [5], which was confirmed by numerical simulations [4]. A corresponding scaling analysis has identified the critical condition and the controlling parameters as the Prandtl number Pr, the Grashof number Gr, and the cavity aspect ratio A [6].

We perform a two dimensional numerical simulation of transient natural convection in a suddenly differentially heated cavity in order to observe the initial transient flows, particularly the leading edge effect. The numerical results show that the pressure plays a key role in the origination and propagation of the leading edge effect and the deviation of the numerical solution from the theoretical solution is due to the neglect of the convection terms in the theoretical solution of the energy equation. Accordingly, the one dimensional conduction solution does not estimate the transport coefficients. References Mahajan, R. L. and Gebhart, B., Leading edge effects in transient natural convection flow adjacent to a vertical surface, J. Heat Transfer , 100 , 731--733, 1978. Patterson, J. C., Graham, T., Schˆpf, W. and Armfield, S. W., Boundary layer development on a semi-infinite suddenly heated vertical plate, J. Fluid Mech. , 453 , 39--55, 2002. doi:10.1017/S0022112001006553 Patterson, J. C. and Imberger, J., Unsteady natural convection in a rectangular cavity, J. Fluid Mech. , 100 , 65--86, 1980. doi:10.1017/S0022112080001012 Xu, F., Patterson, J. C. and Lei, C., Oscillations of the Horizontal Intrusion in a Side-heated Cavity, 15th Australasian Fluid Mechanics Conference , Sydney, 779--782, 2004. Xu, F., Patterson, J. C. and Lei, C., Shadowgraph observations of the transition of the thermal boundary layer in a side-heated cavity, Exp. Fluids , 38 , 770--779, 2005. doi:10.1007/s00348-005-0960-1 Armfield, S. W. and Patterson, J. C., Wave properties of natural-convection boundary layers, J. Fluid Mech. , 239 , 195--211, 1992. doi:10.1017/S0022112092004373 Armfield, S. W. and Patterson, J. C., Start-up flow on a vertical semi-infinite heated plate, Proc. 7th Australasian Heat and Mass Transfer , Townsville, 37--43, 2000. Gebhart, B., Transient response and disturbance growth in vertical buoyancy-driven flows, J. Heat Transfer , 110 , 1166--1174, 1988. Goldstein, R. J. and Briggs, D. G., Transient free convection about vertical plates and cylinders, J. Heat Transfer , 86 , 490--500, 1964.