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Results are presented from the large-eddy simulations (LES) of a wind-driven flow representative of the shallow coastal ocean under the influences of Langmuir forcing and surface heating and cooling fluxes. Langmuir (wind and surface gravity wave) forcing leads to the generation of Langmuir turbulence consisting of a wide range of Langmuir circulations (LCs) or parallel, counterrotating vortices that are aligned roughly in the direction of the wind. In unstratified, shallow coastal regions, the largest of the LCs reach the bottom of the water column. Full-depth LCs are investigated under surface waves with a significant wave height of 1.2 m and a dominant wavelength of 90 m and wave period of 8 s, for a wind speed of 7.8 m s−1 in a 15-m-deep coastal shelf region. Both unstable and stable stratification are imposed by constant surface heat fluxes and an adiabatic bottom wall. Simulations are characterized by Rayleigh and Richardson numbers representative of surface buoyancy forcing relative to wind forcing. For the particular combination of Langmuir forcing parameters studied, although surface cooling is able to augment the strength of LC, a significantly high cooling flux of 560 W m−2 (such that the Rayleigh number is Raτ = 1000) is required in order for turbulence kinetic energy generation by convection to exceed Langmuir production. Such a transition is expected at a lower heat flux for weaker wind and wave conditions and thus weaker LCs than those studied. Furthermore, a surface heating flux of approximately 281 W m−2 (such that the Richardson number is Riτ = 500) is able to inhibit vertical mixing of LC, particularly in the bottom half of the water column, allowing stable stratification to develop.

Interaction between the wind-driven shear current and the Stokes drift velocity induced by surface gravity waves gives rise to Langmuir turbulence in the upper ocean. Langmuir turbulence consists of Langmuir circulation (LC) characterized by a wide range of scales. In unstratified shallow water, the largest scales of Langmuir turbulence engulf the entire water column and thus are referred to as full-depth LC. Large-eddy simulations (LESs) of Langmuir turbulence with full-depth LC in a wind-driven shear current have revealed that vertical mixing due to LC erodes the bottom log-law velocity profile, inducing a profile resembling a wake law. Furthermore, in the interior of the water column, two sources of Reynolds shear stress, turbulent (nonlocal) transport and local Stokes drift shear production, can combine to lead to negative mean velocity shear. Meanwhile, near the surface, Stokes drift shear serves to intensify small-scale eddies leading to enhanced vertical mixing and disruption of the surface log law. A K-profile parameterization (KPP) of the Reynolds shear stress comprising local and nonlocal components is introduced, capturing these basic mechanisms by which Langmuir turbulence in unstratified shallow water impacts the vertical mixing of momentum. Single-water-column, Reynolds-averaged Navier–Stokes simulations with the new parameterization are presented, showing good agreement with LES in terms of mean velocity. Results show that coefficients in the KPP may be parameterized based on attributes of the full-depth LC.

Existing large-eddy simulations (LES) of Langmuir supercells (LS) do not include rotational terms. Despite the fact that the actual coastal ocean is certainly affected by rotation, such simulations are found to provide excellent agreement with a wide range of features of LS observed in the shallow coastal ocean. This note explains why it is indeed acceptable to compare results of a nonrotational LES of LS in a laterally unbounded domain with observations of LS made in a rotating fluid with a lateral boundary.

Results are presented from large-eddy simulations of an unstably stratified open channel flow, driven by a uniform pressure gradient and with zero surface shear stress and a no-slip lower boundary. The unstable stratification is applied by a constant cooling flux at the surface and an adiabatic bottom wall, with a constant source term present to ensure the temperature reaches a statistically steady state. The structure of the turbulence and the turbulence statistics are analyzed with respect to the Rayleigh number ( Ra τ ) representative of the surface buoyancy relative to shear. The impact of the surface cooling-induced buoyancy on mean and root mean square of velocity and temperature, budgets of turbulent kinetic energy (and components), Reynolds shear stress and vertical turbulent heat flux will be investigated. Additionally, colormaps of velocity fluctuations will aid the visualization of turbulent structures on both vertical and horizontal planes in the flow. Under neutrally stratified conditions the flow is characterized by weak, full-depth, streamwise cells similar to but less coherent than Couette cells in plane Couette flow. Increased Ra τ and thus increased buoyancy effects due to surface cooling lead to full-depth convection cells of significantly greater spanwise size and coherence, thus termed convective supercells. Full-depth convective cell structures of this magnitude are seen for the first time in this open channel domain, and may have important implications for turbulence analysis in a comparable tidally-driven ocean boundary layer. As such, these results motivate further study of the effect of surface cooling on tidal boundary layers simulated via an oscillating pressure gradient. Such large-scale structures may also have an important impact on RANS-based (Reynolds-averaged Navier–Stokes equations-based) modeling of turbulence within tidal, convective flows.

Turbulence in the ocean surface layer is generated by time-varying combinations of destabilizing surface buoyancy flux, wind stress forcing, and wave forcing through a vortex force associated with the surface wave field. Observations of time- and depth-averaged vertical velocity variance of full-depth turbulence in shallow unstratified water columns under destabilizing buoyancy forcing are used to determine when process domination can be assigned over a wide range of mixed forcings. The properties of two turbulence archetypes, one representing full-depth Langmuir circulations and the other representing full-depth convection, are described in detail. It is demonstrated that these archetypes lie in distinct regions of the plane of , where and are Langmuir and Rayleigh numbers, respectively, derived from scaling with surface stress velocity and a time scale characteristic of the growth of Langmuir circulation , where and are mean and Stokes velocities, respectively. Situations in which neither process dominates lie between the two end members, with relative dominance given by proximity to one or the other. Cases dominated by direct stress forcing are conspicuous by their absence. In cases of Langmuir domination, surface Stokes velocity is linearly related to , making it impossible to differentiate between scaling depth-averaged vertical velocity variance with , and any other scaling involving both and . A third nondimensional parameter is introduced and used to assess the importance of bottom boundary layer turbulence in a depth-limited system. Questions of time dependence and applicability of results to the open ocean surface boundary layer are considered.

Turbulent shear flows on shallow continental shelves (here shallow means that the interaction with the solid, no-slip bottom is important) are of great importance because of their role in vertical mixing as well as on the transport of sediment and bioactive material. The presence of a wavefield in these areas can lead to the appearance of Langmuir circulation which is known to strongly affect the dynamics of a turbulent flow. To investigate those dynamical effects within a RANS-type modeling framework, we apply a triple decompostion to the LES results of Langmuir circulation in order to further isolate the coherent structures from fluctuating velocity field. The results are compared to the classical double-decomposition. In contrast to the double-decomposition framework, the triple-decompostion more effectively educes the coherent structure field and quantifies the need to take into account the energy exchange between the coherent and random fluctuations as well as the overall impact of the coherent structures on the turbulence dynamics.

Decadal- to centennial-scale variability has been identified in the Arctic Oscillation, but less is known about variations on the millennial scale. A record of sea-ice drift from off the Alaskan coast shows a 1,500-year cycle in the phase of the Arctic Oscillation.

We report on disruption of the log layer in the resolved bottom boundary layer in large-eddy simulations (LES) of full-depth Langmuir circulation (LC) in a wind-driven shear current in neutrally-stratified shallow water. LC consists of parallel counter-rotating vortices that are aligned roughly in the direction of the wind and are generated by the interaction of the wind-driven shear with the Stokes drift velocity induced by surface gravity waves. The disruption is analysed in terms of mean velocity, budgets of turbulent kinetic energy (TKE) and budgets of TKE components. For example, in terms of mean velocity, the mixing due to LC induces a large wake region eroding the classical log-law profile within the range $90\lt { x}_{3}^{+ } \lt 200$. The dependence of this disruption on wind and wave forcing conditions is investigated. Results indicate that the amount of disruption is primarily determined by the wavelength of the surface waves generating LC. These results have important implications for turbulence parameterizations for Reynolds-averaged Navier–Stokes simulations of the coastal ocean.

Turbulent shear flows on shallow continental shelves (here shallow means that the interaction with the solid, no-slip bottom is important) are of great importance because tide- and wind-driven flows on the shelf are drivers of the transfer of momentum, heat, and mass (gas) across the air–sea interface. These turbulent flows play an important role because vertical mixing and current are vectors for the transport of sediment and bioactive material on continental shelves. Understanding the dynamics of this class of flows presents complications because of the presence of a free surface and also because the flow can be driven by a pressure gradient (a tidal current), a stress at the free surface (a wind-driven current), or a combination of both. In addition, the flow can be modified by the presence of a wave field that can induce Langmuir circulation (Langmuir, Science 87:119–123, 1938). Large eddy simulation is used to quantify the effects of pressure gradient and wind shear on the distinctive structures of the turbulent flow. From these computations, an understanding of the physics governing the turbulence of pressure-driven and wind-driven flows, how they can interact in a normal or a tangential direction, and the effect of wave forcing on these flows is obtained.

A three-dimensional numerical model for large-eddy simulation (LES) of oceanic turbulent processes is described. The numerical formulation comprises a spectral discretization in the horizontal directions and a high-order compact finite-difference discretization in the vertical direction. Time-stepping is accomplished via a second-order accurate fractional-step scheme. LES subgrid-scale (SGS) closure is given by a traditional Smagorinsky eddy-viscosity parametrization for which the model coefficient is derived following similarity theory in the near-surface region. Alternatively, LES closure is given by the dynamic Smagorinsky parametrization for which the model coefficient is computed dynamically as a function of the flow. Validation studies are presented demonstrating the temporal and spatial accuracy of the formulation for laminar flows with analytical solutions. Further validation studies are described involving direct numerical simulation (DNS) and LES of turbulent channel flow and LES of decaying isotropic turbulence. Sample flow problems include surface Ekman layers and wind-driven shallow water flows both with and without Langmuir circulation (LC), generated by wave effects parameterized via the well-known Craik–Leibovich (C–L) vortex force. In the case of the surface Ekman layers, the inner layer (where viscous effects are important) is not resolved and instead is parameterized with the Smagorinsky models previously described. The validity of the dynamic Smagorinsky model (DSM) for parameterizing the surface inner layer is assessed and a modification to the surface stress boundary condition based on log-layer behavior is introduced improving the performance of the DSM. Furthermore, in Ekman layers with wave effects, the implicit LES grid filter leads to LC subgrid-scales requiring ad hoc modeling via an explicit spatial filtering of the C–L force in place of a suitable SGS parameterization.

Two different turbulent flows, Langmuir supercells and unstable convection, have been sampled with a VADCP, an acoustic Doppler current profiler (ADCP) with an additional vertical (V) beam. Direct measurements of the profile of vertical velocity variance provided by the vertical beam are used to calculate observational response functions for algorithms used to derive vertical velocity from the 4 beams of a standard ADCP. A theoretical response function derived for the vertical velocity estimate from a single pair of opposed slant beams illustrates the importance of large-scale quasi-coherent flow structures, as well as effects of different angles of slant beams from vertical. Different large-eddy characteristics for Langmuir supercells and unstable convection yield different theoretical response: however in both cases, the theoretical response agrees qualitatively with that derived from observations. For Langmuir supercells, there is additional agreement with numerical response functions generated by using the geometry of a VADCP to sample three-dimensional flow fields available from large eddy simulations (LES). The results from all three approaches show that there can be significant error in vertical velocity inferred from slant beam velocities. The error may be either overor under-estimation, depending upon (usually unknown) features of the large eddies of the turbulent field, such as vertical/horizontal anisotropy, phase coherence, and orientation of horizontally anisotropic turbulent structures relative to the instrument. Given only a standard ADCP, the “best” estimate of vertical velocity variance is not the usual 4-beam estimate, but the larger of the two pair estimates.

Recently, Pruett et al. [Pruett, C.D., Gatski, T.B., Grosch, C.E., Thacker, W.D., 2003. The temporally filtered Navier–Stokes equations: properties of the residual stress. Phys. Fluids 15, 2127–2140] proposed an approach to large-eddy simulation (LES) based on time-domain filtering; their approach was termed temporal large-eddy simulation or TLES. In a continuation of their work, Pruett and collaborators tested their methodology by successfully performing TLES of unstratified turbulent channel flow up to Reynolds number of 590 (based on channel half-height and friction velocity) [Pruett, C.D., Thomas, B.C., Grosch, C.E., Gatski, T.B., 2006. A temporal approximate deconvolution model for LES. Phys. Fluids 18, 028104, 4p]. Here, we carefully analyze the TLES methodology in order to understand the role of its key components and in the process compare TLES to more traditional approaches of spatial LES. Furthermore, we extend the methodology to stably stratified turbulent channel flow.

Results of large-eddy simulation (LES) of Langmuir circulations (LC) in a wind-driven shear current in shallow water are reported. The LC are generated via the well-known Craik–Leibovich vortex force modelling the interaction between the Stokes drift, induced by surface gravity waves, and the shear current. LC in shallow water is defined as a flow in sufficiently shallow water that the interaction between the LC and the bottom boundary layer cannot be ignored, thus requiring resolution of the bottom boundary layer. After the introduction and a description of the governing equations, major differences in the statistical equilibrium dynamics of wind-driven shear flow and the same flow with LC (both with a bottom boundary layer) are highlighted. Three flows with LC will be discussed. In the first flow, the LC were generated by intermediate-depth waves (relative to the wavelength of the waves and the water depth). The amplitude and wavelength of these waves are representative of the conditions reported in the observations of A. E. Gargett & J. R. Wells in Part 1 (J. Fluid Mech. vol .000, 2007, p. 00). In the second flow, the LC were generated by shorter waves. In the third flow, the LC were generated by intermediate waves of greater amplitude than those in the first flow. The comparison between the different flows relies on visualizations and diagnostics including (i) profiles of mean velocity, (ii) profiles of resolved Reynolds stress components, (iii) autocorrelations, (iv) invariants of the resolved Reynolds stress anisotropy tensor and (v) balances of the transport equations for mean resolved turbulent kinetic energy and resolved Reynolds stresses. Additionally, dependencies of LES results on Reynolds number, subgrid-scale closure, size of the domain and grid resolution are addressed.In the shear flow without LC, downwind (streamwise) velocity fluctuations are characterized by streaks highly elongated in the downwind direction and alternating in sign in the crosswind (spanwise) direction. Forcing this flow with the Craik–Leibovich force generating LC leads to streaks with larger characteristic crosswind length scales consistent with those recorded by observations. In the flows with LC, in the mean, positive streaks exhibit strong intensification near the bottom and near the surface leading to intensified downwind velocity ‘jets’ in these regions. In the flow without LC, such intensification is noticeably absent. A revealing diagnostic of the structure of the turbulence is the depth trajectory of the invariants of the resolved Reynolds stress anisotropy tensor, which for a realizable flow must lie within the Lumley triangle. The trajectory for the flow without LC reveals the typical structure of shear-dominated turbulence in which the downwind component of the resolved normal Reynolds stresses is greater than the crosswind and vertical components. In the near bottom and surface regions, the trajectory for the flow with LC driven by wave and wind forcing conditions representative of the field observations reveals a two-component structure in which the downwind and crosswind components are of the same order and both are much greater than the vertical component. The two-component structure of the Langmuir turbulence predicted by LES is consistent with the observations in the bottom third of the water column above the bottom boundary layer.

A time series of hydrographic measurements, temperature and salinity versus depth, on the shelf in the northern Gulf of Alaska (GAK 1) is used to determine the seasonal and interannual variability of the hydrography and mixed layer depth from 1974 through mid-1998. This is one of the first opportunities to incorporate salinity into the mixed layer depth (MLD) determination in this region where the density is highly dependent on salinity. The MLD changes seasonally from about 40 m in summer to more than 160 m in winter. This has potential implications for vertical fluxes of nutrients via winter MLD, leading to their annual replenishment. Spectral analysis of MLDs show that the time series have similar periodicities to the hydrography (decadal and El Nino-Southern Oscillation (ENSO)). The MLD trend during 1974–1998 has a slight increase in the deepest winter MLD that is, however, not statistically significant at the 90% level. This is in contrast to previous studies which found a significant shoaling of the winter MLD in the offshelf region of the Gulf of Alaska at Ocean Station P (OSP) [Freeland, H., Denman, K., Wong, C.S., Whitney, F., Jacques, R., 1997. Evidence of change in the winter mixed layer in the northeast Pacific Ocean. Deep Sea Research 44, 2117–2129]. This difference in the response of the marine system is consistent with an increase in the circulation of the Alaskan Gyre with enhanced upwelling in the central gulf (OSP) and enhanced downwelling along the coast (GAK 1).

Recent measurements at a cabled sea-floor node in 15 meters of water off the coast of New Jersey suggest that Langmuir supercells, Langmuir circulations that achieve vertical scales equal to the water depth under extended storms, are an important mechanism for major sediment resuspension events on the extensive shallow shelves off the eastern U.S. coast. Because sediment resuspension is a prelude to transport, supercell events are a necessary condition for major sediment transport. Such events may also contribute to shelf-sea exchange and to offshore gradation of benthic community structure in shallow seas.

Recent interest in the development of a unifying framework among direct numerical simulations, large-eddy simulations, and statistically averaged formulations of the Navier–Stokes equations, provides the motivation for the present paper. Toward that goal, the properties of the residual (subgrid-scale) stress of the temporally filtered Navier–Stokes equations are carefully examined. This includes the frame-invariance properties of the filtered equations and the resulting residual stress. Causal time-domain filters, parametrized by a temporal filter width 0

A single-layer, reduced-gravity, double-gyre primitive equation model in a 2000 km × 2000 km square domain is used to test the accuracy and sensitivity of time-dependent Eulerian velocity fields reconstructed from numerically generated drifter trajectories and climatology. The goal is to determine how much Lagrangian data is needed to capture the Eulerian velocity field within a specified accuracy. The Eulerian fields are found by projecting, on an analytic set of divergence-free basis functions, drifter data launched in the active western half of the basin supplemented by climatology in the eastern domain. The time-dependent coefficients are evaluated by least squares minimization and the reconstructed fields are compared to the original model output. The authors find that the accuracy of the reconstructed fields depends critically on the spatial coverage of the drifter observations. With good spatial coverage, the technique allows accurate Eulerian reconstructions with under 200 drifters deploy...

Nowcasts of the surface velocity field in Monterey Bay are made for the period August 1–9, 1994, using HF radar observations blended with results from a primitive equation model. A spectral method called normal mode analysis was used. Objective spatial and temporal filtering were performed, and stream function, velocity potential, relative vorticity, and horizontal divergence were calculated over the domain. This type of nowcasting permits global spectral analysis of mode amplitudes, calculation of enstrophy, and additional analyses using tools like empirical orthogonal functions. The nowcasts reported here include open boundary flow information from the numerical model. Nowcasts using no open boundary flow information, however, still provide excellent results for locations within the observation footprint. This method, then, is useful for filtering high-resolution data like HF radar observations, even when open boundary flow information is unavailable. Also, since the nowcast velocity gradient fields were much less noisy than the observations, this may be an effective method for preconditioning high-resolution observation sets for assimilation into a numerical model.

In order to expand the predictive capability of single-point turbulence closure models to account for the early-stage transition regime, a methodology for the formulation and calibration of model equations for the ensemble-averaged disturbance kinetic energy and energy dissipation rate is presented. The calibration is based on homogeneous shear flow where disturbances can be described by rapid distortion theory (RDT). The relationship between RDT and linear stability theory is exploited in order to obtain a closed set of modeled equations. The linear disturbance equations are solved directly so that the numerical simulation yields a database from which the closure coefficients in the ensemble-averaged disturbance equations can be determined.

Interannual salinity variations in North Atlantic Subtropical Mode Water (STMW) are well known although the cause is less well understood. Attempts to model local salinity variation with local evaporation and precipitation have not been successful and some authors invoke advection of low salinity water as the cause. Examination of the STMW and North American river runoff data suggests that runoff may partly explain the salinity variations. It is known that low salinity water resulting from Mississippi River outflow is transported well past Cape Hatteras. Spearman Rank Correlation analysis and spectra and cross-spectra Fourier correlation analysis both show that river flow is significantly inversely correlated with STMW salinity. This result suggests that North American river flow may have an influence on the salinity of STMW.

The decay of laminar disturbances and turbulence in mean shear-free flows is studied. In laminar flows, such disturbances are linear superpositions of modes governed by the Orr–Sommerfeld equation. In turbulent flows, disturbances are described through transport equations for representative mean quantities. The link between a description based on a deterministic evolution equation and a probability-based mean transport equation is established. Because an uncertainty in initial conditions exists in the laminar as well as the turbulent regime, a probability distribution must be defined even in the laminar case. Using this probability distribution, it is shown that the exponential decay of the linear modes in the laminar regime can be related to a power law decay of both the (ensemble) mean disturbance kinetic energy and the dissipation rate. The evolution of these mean disturbance quantities is then described by transport equations similar to those for the corresponding turbulent decaying flow.

We discuss volume line integral convolution (LIC) techniques for effectively visualizing 3D flow, including using visibility-impeding halos and efficient asymmetric filter kernels. Specifically, we suggest techniques for selectively emphasizing critical regions of interest in a flow; facilitating the accurate perception of the 3D depth and orientation of overlapping streamlines; efficiently incorporating an indication of orientation into a flow representation; and conveying additional information about related scalar quantities such as temperature or vorticity over a flow via subtle, continuous line width and color variations.

Experimental observations show that the presence of small tabs on the edge of a hot, compressible jet exiting into a slower moving, colder ambient flow can increase the rate of spreading of the jet. This suggests that the rate of mixing of the jet and the ambient fluid is also increased. In order to elucidate the physical mechanism responsible for the increased spreading rate a set of calculations was carried out within the framework of the compressible three dimensional Navier–Stokes equations. A series of grid refinements were made to assess the accuracy of the results. We first simulated the flow without the tabs, obtaining reasonable agreement with experimental measurements of the velocity. We then simulated the flow, without tabs, over a range of values of the convective Mach number in order to determine the dependence of the mixing on this parameter. Simulations with modeled tabs were also carried out. In these calculations the effect of the tabs on the flow was modeled by pairs of counter-rotating vortices. The results of these calculations indeed show that the presence of the tabs increase the spreading rate of the jet. The basic physical mechanism responsible for the enhanced spreading rate is discussed and qualitative comparisons with flow visualizations are made.

We present the results of a study of the inviscid two-dimensional spatial stability of a parallel compressible mixing layer in a binary gas. The parameters of this study are the Mach number of the fast stream, the ratio of the velocity of the slow stream to that of the fast stream, the ratio of the temperatures, the composition of the gas in the slow stream and in the fast stream, and the frequency of the disturbance wave. The ratio of the molecular weight of the slow stream to that of the fast stream is found to be an important quantity and is used as an independent variable in presenting the stability characteristics of the flow. It is shown that differing molecular weights have a significant effect on the neutral-mode phase speeds, the phase speeds of the unstable modes, the maximum growth rates and the unstable frequency range of the disturbances. The molecular weight ratio is a reasonable predictor of the stability trends. We have further demonstrated that the normalized growth rate as a function of the convective Mach number is relatively insensitive (Approx. 25%) to changes in the composition of the mixing layer. Thus, the normalized growth rate is a key element when considering the stability of compressible mixing layers, since once the basic stability characteristics for a particular combination of gases is known at zero Mach number, the decrease in growth rates due to compressibility effects at the larger convective Mach numbers is somewhat predictable.

We present the results of a study of the structure of a parallel compressible mixing layer in a binary mixture of gases. The gases included in this study are hydrogen (H2), helium (He), nitrogen (N2), oxygen (O2), neon (Ne) and argon (Ar). Profiles of the variation of the Lewis and Prandtl numbers across the mixing layer for all 30 combinations of gases are given. It is shown that the Lewis number can vary by as much as a factor of 8 and the Prandtl number by a factor of 2 across the mixing layer. Thus assuming constant values for the Lewis and Prandtl numbers of a binary gas mixture in the shear layer, as is done in many theoretical studies, is a poor approximation. We also present profiles of the velocity, mass fraction, temperature and density for representative binary gas mixtures at zero and supersonic Mach numbers. We show that the shape of these profiles is strongly dependent on which gases are in the mixture as well as on whether the denser gas is in the fast stream or the slow stream.

Measurements of the velocity field created by a shallow bump on a wall revealed that an energy peak in the spanwise spectrum associated with the driver decays and an initially small‐amplitude secondary mode rapidly grows with distance downstream of the bump. Linear theories could not provide an explanation for this growing mode. The present Navier–Stokes simulation replicates and confirms the experimental results. Insight into the structure of the flow was obtained from a study of the results of the calculations and is presented.

The results of measurements of the disturbance velocity field generated in a boundary layer by a shallow three‐dimensional bump oscillating at a very low frequency on the surface of a flat plate are reported. The disturbance was entirely confined to the boundary layer. Profiles of the mean velocity, the disturbance velocity at the fundamental frequency, and at the first harmonic are presented. These profiles were measured both upstream and downstream of the oscillating bump. About 100 boundary layer thicknesses downstream of the bump the intensity had a maximum near η=2, with a magnitude of about 0.2%. Measurements of the disturbance velocity were also made at various spanwise and downstream locations at a fixed distance from the boundary of one displacement thickness. The spanwise profiles of the disturbance field changed dramatically from the near‐field region of the bump to the far downstream region. Finally, the spanwise spectrum of the disturbances at three locations downstream of the bump are presented. The spanwise spectrum of the disturbance showed a primary peak consistent with the motion and geometry of the driver. This peak decreased slowly with downstream distance. In addition, a small secondary peak in the spanwise spectrum was apparent near the bump. This peak increased rapidly with downstream distance.

In this paper the transition from convective to absolute instability in a reacting compressible mixing layer with finite rate chemistry is examined. The reaction is assumed to be one step, irreversible, and of Arrhenius type. It is shown that absolute instability can exist for moderate heat release without backflow. The effects of the temperature ratio, heat release parameter, Zeldovich number, equivalence ratio, direction of propagation of the disturbances, and the Mach number on the transition value of the velocity ratio are given. The present results are compared to those obtained from the flame sheet model for the temperature using the Lock similarity solution for the velocity profile. Finally, the structure of the wave packets produced by an impulse in the absolutely unstable flow is examined.

A model problem is proposed to investigate the steady response of a reacting, compressible laminar jet to Mach waves generated by wavy walls in a channel of finite width. The model consists of a two‐dimensional jet of fuel emerging into a stream of oxidizer which are allowed to mix and react in the presence of the Mach waves. The governing equations are taken to be the steady parabolized Navier–Stokes equations which are solved numerically. The kinetics is assumed to be a one‐step, irreversible reaction of the Arrhenius type. Two important questions on the Mach wave–flame interactions are discussed: (i) how is the flame structure altered by the presence of the Mach waves, and (ii) can the presence of the Mach waves change the efficiency of the combustion processes?

In this article, we present a multigrid algorithm for parallel computers, the chopped parallel multigrid (CPMG) algorithm. The CPMG algorithm improves the processor utilization by reducing the work load on coarse grids without affecting the convergence rate of the algorithm. This is in contrast to earlier approaches (Gannon and van Rosendale, 1986; Frederickson and McBryan, 1989), where unutilized processors are used to improve the convergence rate. The CPMG algorithm reduces the coarse grid work bychopping the alternate cycles of multigrid. Using analytical results and simulations on sequential machines we show that the CPMG can achieve almost the same convergence rate as standard MG for many cases. Analytically we show that the advantage gained by CPMG over standard MG on a mesh connected massively parallel machine is 33% in hardware utilization, 50% in communication overheads and 38% in overall execution time. We have also evaluated the performance of CPMG on an actual massively parallel machine, the DAP-510. The advantage gained by CPMG over standard MG is 35% in overall execution time. Moreover, the CPMG can be integrated with other parallel multigrid algorithms, such as the PSMG algorithm (Frederickson and McBryan, 1989) and Decker's algorithm (Decker, 1990).

The ignition and structure of a reacting compressible mixing layer is considered using finite rate chemistry lying between two streams of reactants with different freestream speeds and temperatures. Numerical integration of the governing equations show that the structure of the reacting flow can be quite complicated depending on the magnitude of the Zeldovich number. An analysis of both the ignition a diffusion flame regimes is presented using a combination of large Zeldovich number asymptotics and numerics. This allows to analyze the behavior of these regimes as a function of the parameters of the problem.

We present the results of a study of the inviscid spatial stability of a parallel three-dimensional compressible mixing layer. The parameters of this study are the Mach number of the fast stream, the ratio of the speed of the slow stream to that of the fast stream, the ratio of the temperature of the slow stream to that of the fast stream, the direction of the crossflow in the fast stream, the frequency, and the direction of propagation of the disturbance wave. Stability characteristics of the flow as a function of these parameters are given. Certain theoretical results are presented which show the interrelations between these parameters and their effects on the stability characteristics. In particular, the three-dimensional stability problem for a three-dimensional mixing layer at Mach zero can be transformed to a two-dimensional stability problem for an equivalent two-dimensional mean flow. There exists a one-parameter family of curves such that for any given direction of mean flow and of wave propagation one can apply this transformation and obtain the growth rate from the universal curves. For supersonic couvective Mach numbers, certain combinations of crossflow angle and propagation angle of the disturbance can increase the growth rates by a factor of about two. and thus enhance mixing.

We report the results of a comprehensive comparative study of the inviscid spatial stability of a parallel compressible mixing layer using various models for the mean flow. The models are (i) the hyperbolic tangent profile for the mean speed and the Crocco relation for the mean temperature, with the Chapman viscosity–temperature relation and a Prandtl number of one; (ii) the Lock profile for the mean speed and the Crocco relation for the mean temperature, with the Chapman viscosity-temperature relation and a Prandtl number of one; and (iii) the similarity solution for the coupled velocity and temperature equations using the Sutherland viscosity–temperature relation and arbitrary but constant Prandtl number. The purpose of this study was to determine the sensitivity of the stability characteristics of the compressible mixing layer to the assumed thermodynamic properties of the fluid. It is shown that the qualitative features of the stability characteristics are quite similar for all models but that there are quantitative differences resulting from the difference in the thermodynamic models. In particular, we show that the stability characteristics are sensitive to the value of the Prandtl number and to a particular value of the temperature ratio across the mixing layer.

There are two ways, other than the standard fast Fourier transform (FFT) algorithm, of computing Fourier transforms of real data, namely, (1)the real fast Fourier transform (RFFT) algorithm, and (2) the fast Hartley transform (FHT) algorithm. On a sequential computer, it has been shown that both the RFFT and the FHT algorithms are faster than the FFT algorithm. However, it is not obvious that the same is true on a parallel machine. The communication requirements of the RFFT and the FHT algorithms, which are critical to the cost of any parallel implementation, are different from those of the FFT algorithm. In this paper we present efficient implementations of the RFFT and the FHT algorithms on a hypercube machine. Experimental results are given for the implementation of the RFFT and the FHT algorithms on the NCUBE machine.

We report the results of an inviscid spatial stability calculation for a compressible reacting mixing layer. The limit of infinite Damkohler number is taken and the diffusion flame is approximated by a flame sheet. Results are reported for the phase speeds of the neutral waves and maximum growth rates of the unstable waves as a function of the parameters of the problem: the ratio of the temperature of the stationary stream to that of the fast stream, the Mach number of the fast stream, the heat release per unit mass fraction of the reactant, the equivalence ratio of the reaction, and the frequency of the disturbance. These results are compared to the phase speeds and growth rates of the corresponding non-reacting mixing layer. We show that the addition of combustion has important, and complex, effects on the flow stability. In particular, we show that the flow can become absolutely unstable with a sufficient amount of heat release.

The article of record as published may be found at http://dx.doi.org/10.1111/j.1365-2419.2006.00408.x Declines of Steller sea lion (Eumetopias jubatus) populations in the Aleutian Islands and Gulf of Alaska could be a consequence of physical oceanographic changes associated with the 1976-77 climate regime shift. Changes in ocean climate are hypothesized to have affected the quantity, quality, and accessibility of prey, which in turn may have affected the rates of birth and death of sea lions. Recent studies of the spatial and temporal variations in the ocean climate system of the North Pacific support this hypothesis. Ocean climate changes appear to have created adaptive opportunities for various species that are preyed upon by Steller sea lions at mid-trophic levels. The east–west asymmetry of the oceanic response to climate forcing after 1976-77 is consistent with both the temporal aspect (populations decreased after the late 1970s) and the spatial aspect of the decline (western, but not eastern, sea lion populations decreased). These broad-scale climate variations appear to be modulated by regionally sensitive biogeographic structures along the Aleutian Islands and Gulf of Alaska, which include a transition point from coastal to open-ocean conditions at Samalga Pass westward along the Aleutian Islands. These transition points delineate distinct clusterings of different combinations of prey species, which are in turn correlated with differential population sizes and trajectories of Steller sea lions. Archaeological records spanning 4000 yr further indicate that sea lion populations have experienced major shifts in abundance in the past. Shifts in ocean climate are the most parsimonious underlying explanation for the broad suite of ecosystem changes that have been observed in the North Pacific Ocean in recent decades.

[1] Water column temperatures on the shelf in the northern Gulf of Alaska have increased more than 0.8°C and vertical density stratification has increased since 1970 near Seward, Alaska throughout the 250 m depth. This high latitude marine system has low water temperatures, high rates of precipitation, glacial melting, high wind speeds and high rates of biological productivity. A more than 300 km alongshore shift (locally westward) of isotherms is suggested. The observations are consistent with a conceptual ocean-atmosphere circulation model that employs coastal freshwater discharge, glacial ablation and wind forcing. Positive regional feedback mechanisms accelerate the discharge and poleward heat flux, leading to even higher temperatures, increased ocean stratification and increased storminess. This warming and ocean freshening will have significant impacts on the atmosphere and marine ecosystems of the Northeast Pacific, Bering Sea, Arctic Ocean and quite possibly global ocean circulation.

Recently, Pruett et al. [Pruett, C.D., Gatski, T.B., Grosch, C.E., Thacker, W.D., 2003. The temporally filtered Navier–Stokes equations: properties of the residual stress. Phys. Fluids 15, 2127–2140] proposed an approach to large-eddy simulation (LES) based on time-domain filtering; their approach was termed temporal large-eddy simulation or TLES. In a continuation of their work, Pruett and collaborators tested their methodology by successfully performing TLES of unstratified turbulent channel flow up to Reynolds number of 590 (based on channel half-height and friction velocity) [Pruett, C.D., Thomas, B.C., Grosch, C.E., Gatski, T.B., 2006. A temporal approximate deconvolution model for LES. Phys. Fluids 18, 028104, 4p]. Here, we carefully analyze the TLES methodology in order to understand the role of its key components and in the process compare TLES to more traditional approaches of spatial LES. Furthermore, we extend the methodology to stably stratified turbulent channel flow.