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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.

Turbulent natural convection with and without radiation transfer in two-dimensional (2D) and three-dimensional (3D) air-filled differentially heated cavities is numerically investigated using various RANS (Reynolds Averaged Navier–Stokes) turbulence models and the Discrete Ordinates radiation model. Five different two-equation eddy-viscosity models including the standard k–e model, the renormalization group (RNG) k–e model, the realisable k–e model, the standard k–ω model and the shear-stress transport (SST) k–ω model are selected for comparison. Qualitative and quantitative data are presented to demonstrate the effects of three-dimensionality, radiation transfer and the thermal boundary conditions on the horizontal surfaces on the numerical solution of the convective flow in the cavity. The present numerical results are compared against published experimental and direct numerical simulation data. It is found that the predicted thermal stratification in the interior of the cavity is improved when the simulation is extended from 2D to 3D and when the effect of radiation transfer is accounted for. The discrepancy with regard to the interior stratification between the experiment and numerical simulation is mainly caused by the negligence of radiation transfer. The thermal boundary conditions on the horizontal surfaces also have a significant impact on the numerical solution, especially when the radiation transfer is not accounted for. Further, the present results show that all the RANS models are capable of capturing the main features of the flow and the overall performance of these turbulence models in terms of predicting time-averaged quantities is acceptable. It is found that the variation of the numerical results obtained with the three k–e models is very small, whereas the discrepancy between the two k–ω models is significant. The SST k–ω model has the best overall performance and the standard k–ω model has the worst overall performance.

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.

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.

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 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 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%).

This study is concerned with transient natural convection in a water-filled isosceles triangular enclosure subject to cooling at the inclined surfaces and simultaneous heating at the base. The unsteady flows over a range of Grashof numbers are visualized using a shadowgraph technique, and corresponding numerical simulations are carried out using a Finite Volume Method. Both the experiments and numerical simulations have revealed that the transient flow development in the enclosure due to abrupt heating and cooling through the boundaries can be classified into three distinct stages, that is, an early stage, a transitional stage, and a steady/quasi-steady stage. The major flow features at each of the three stages are described and the Grashof number effects on the flow development and heat transfer are discussed. It is found that, for a fixed aspect ratio of 0.5, a transition of the unsteady flow from symmetric to asymmetric structures occurs for Grashof numbers above 2.95 × 104. Moreover, the present heat transfer calculations indicate that the average Nusselt number over the inclined and horizontal surfaces approximately scales with Gr0.2.

A three-dimensional numerical simulation is carried out to investigate the natural convection in a shallow wedge subject to solar radiation. The study reveals three distinct stages of the flow development from an isothermal and stationary state: an initial stage, a transitional stage and a quasi-steady stage. The heat transfer at the initial stage is dominated by conduction from the sloping bottom. The transitional stage starts with the onset of instabilities, and the quasi-steady state is characterised by steady growth of a spatially averaged temperature. The present results have confirmed the earlier observations in a flow visualisation experiment and a two-dimensional simulation.