Turbulent Kinetic Energy Budget Research Articles

Numerical investigations of vortex dynamics and loss generation in the corner separation region of a high subsonic compressor blade

Three-dimensional corner separation seriously deteriorates the aerodynamic performance of a compressor blade. In this study, the complicated vortex dynamics and loss mechanism in the corner region of a high subsonic compressor blade (the inlet Mach number is 0.67) are investigated using large eddy simulations (LESs) at a Reynolds number (Re) of 5.6 × 105. The results show that the predicted total pressure loss and outlet flow angle match well with the experimental data, indicating that the LES method can accurately predict the size and strength of corner separation in the compressor blade. With the passage vortex rolling up and further interacting with the low-momentum fluids originating from the end wall boundary layers and the local blade boundary layers, strong shear strain induces a large-scale concentrated shedding vortex (CSV) near the spanwise location of x/H = 0.3. The formation and rolling-up of the CSV not only cause the strongest flow blockage but also strengthen the turbulence anisotropy. As the CSV moves toward the trailing edge, the strong interaction with a pair of counter-rotating vortices shed in the wake region (wake shedding vortex) further accelerates the local generation of turbulent kinetic energy (TKE). Detailed TKE budget analysis shows that the streamwise Reynolds normal stress (w′w′¯) plays the most decisive role in the TKE production term. Furthermore, we demonstrate that the strength of turbulence anisotropy is positively correlated with the TKE budget. Therefore, turbulence anisotropy should be considered carefully in predicting the loss level in the corner region of a compressor blade.

Understanding tidal mixing at the Strait of Gibraltar: A high-resolution model approach

The Strait of Gibraltar is a narrow and shallow channel that controls the Mediterranean Sea thermohaline and biogeochemical balances. Strong tidal currents significantly modulate exchanges across this strait and induce an intense vertical mixing, impacting both the Mediterranean Sea and the Atlantic Ocean on a climatic scale. However, the turbulent processes controlling the tidal mixing location, timing, and magnitude remain unclear. To fill this gap, we investigate tidal mixing at the Strait of Gibraltar in yearly twin tidal and non-tidal simulations from a regional configuration of the three-dimensional numerical model MITgcm, using a high spatial resolution around the Strait of Gibraltar (1/200°, 100 vertical levels). More specifically, we investigate the model turbulence closure scheme, based on a turbulent kinetic energy budget, and illustrate that vertical buoyancy fluxes should be preferred to diapycnal diffusivities as mixing indicators. In agreement with previous literature, we find that tides strongly intensify vertical mixing and motions within the Strait of Gibraltar. We then demonstrate that tidal mixing relies on two main ingredients: a sustained vertical shear of horizontal velocities and a local weakening of stratification. In the Mediterranean layer, the former drives diapycnal mixing near the seafloor and the latter in shallower areas above the prominent sills of the strait. We also evidence the frequent but irregular occurrences of static instabilities in the vicinity of these sills. In the Atlantic layer, both vertical shear and stratification are involved in diapycnal mixing that develops along the trail of the eastward internal bore released at the Camarinal sill. At high frequency, the local weakening of stratification results from convergence and divergence patterns in the vicinity of the Camarinal and Espartel sills, feeding recirculation cells between the Atlantic and Mediterranean layers. In addition, we highlight that diapycnal mixing mainly develops during the westward tidal phase in the Mediterranean layer and the eastward tidal phase in the Atlantic layer. We conclude by proposing a revised conceptual view of tidal mixing at the Strait of Gibraltar, where tidally-induced recirculation cells play an instrumental role in transforming the exchanged water masses. Overall, this study emphasizes the relevance of a realistic representation of both tides and abrupt topography to simulate the exchanges through the Strait of Gibraltar and argues for the use of a specific tidal mixing parameterization otherwise.

Hydrodynamics affected by submerged vegetation with different flexibility under unidirectional flow

Submerged vegetation changes the hydrodynamic characteristics of rivers, lakes, wetlands, and coastal zones. However, only a few studies have focused on the effect of flexible submerged vegetation on hydrodynamic characteristics under unidirectional flow. Therefore, laboratory experiments were conducted to study the effects of submerged vegetation with different flexibility on the flow structure and turbulence characteristics under unidirectional flow. The results showed that the reconfiguration and coordination of wave motion of flexible submerged vegetation redistribute flow velocity, Reynolds stress, and turbulent kinetic energy inside and outside of the vegetation canopy. With a gradual decrease in the deflection height of vegetation, the differences in dimensionless velocity, dimensionless mixed layer thickness, bulk drag coefficient, averaged turbulent kinetic energy, and the averaged contribution rate of its shear production term for the vegetation canopy also decrease; the trend of the penetration depth of Reynolds stress is opposite. Based on the turbulent kinetic energy budget equation, a turbulent kinetic energy model (TKE model) was established, which can be used to predict the turbulent kinetic energy and its shear production term within the vegetation canopy. Here, the scaling factor was determined by the vegetation canopy Cauchy number. The TKE model can be applied under unidirectional flow conditions for submerged vegetation with different flexibilities with high accuracy. It is a simple method to predict vegetation-induced turbulence and the characteristics of sediment and material transport under the influence of submerged vegetation with different flexibility.

Energetics of buoyancy-generated turbulent flows with active scalar: pure buoyant plume

A framework for the budget of Reynolds stress, temperature and density variations, turbulent mass flux and turbulent heat flux is presented for buoyancy-generated turbulent flows with a focus on turbulent plumes. The dynamical interactions between the turbulence generated from the velocity and thermodynamic fluctuations in thermal and heated gas plumes is studied. A large-eddy simulation tool has been used to simulate heavier and lighter than air plumes released from a circular heated source for high Reynolds number (Re). The budget equations are developed using a Favre-averaging approach. Both heated air plumes and heated gas plumes, namely, heated ${\rm SO}_2$ and heated ${\rm CH}_4$ plumes, are included in the study. The study focuses on addressing key questions – does the turbulence kinetic energy (TKE) spectrum follow the classical inertial $-5/3$ spectrum or is there a $-3$ buoyancy regime with a different scaling law? Fundamental pathways for generation of turbulence through velocity fluctuations, and temperature and density fluctuations are discussed. Analysis of the TKE and scalar variance budget equations has demonstrated that multiple mechanisms dominate the transport of Reynolds stresses, and in particular that correlations between the density and the velocity dominates the turbulence production mechanisms. Entrainment is connected to the turbulent transport and pressure-dilation processes.

Turbulent Kinetic Energy Budgets over Gentle Topography Covered by Forests

Abstract Large-eddy simulations of flow over a “horizontally” uniform model forest are used to investigate the effects of gentle topography on the turbulent kinetic energy (TKE) budget within the canopy roughness sublayer. Despite significant differences between simulations using idealized sinusoidal topography and real topography of the Amazon forest, results indicate that the effects of topography are located predominantly in the upper canopy and above, and are mostly caused by mean advection of TKE. The “horizontally” averaged TKE budget from idealized and real gentle topographies are almost identical to that for flat terrain, including a clear inertial layer above the roughness sublayer in which shear production is balanced by local dissipation. At topography crests, where observational towers are usually located, mean vertical advection of TKE can be as important as horizontal advection. We propose the use on an approximate TKE balance equation to estimate mean advection from single tower measurements, and introduce a new advection index that can be used as a proxy to quantify the importance of the topography on the TKE budget.

On the dynamics of buoyant jets in a linearly stratified ambient

We report mean flow and turbulence characteristics of a buoyant jet evolving in a linearly stratified ambient with stratification strength N=0.4 s−1. The velocity and density fields are captured experimentally using simultaneous particle image velocimetry and planar laser-induced fluorescence technique. We report our findings by strategically choosing four axial locations such that it covers different flow regimes; namely, momentum-dominated region, buoyancy-dominated region, neutral buoyant layer, and plume cap region. The results at these axial locations are presented as a function of the radial co-ordinate to provide a whole field picture of the flow dynamics. From the mean axial velocity and density fields, it is seen that the velocity and the scalar (density) widths are of the same magnitude in the momentum-dominated region but show significant difference in the buoyancy-dominated region and beyond. It is also seen that the axial velocity for the buoyant jet is consistently higher than pure jet at different axial locations due to buoyancy-aided momentum. With the help of turbulent kinetic energy (TKE) budget analysis, it is seen that the shear production (P) and TKE dissipation (ϵ) for a buoyant jet are higher compared to the case of pure jet at different axial locations, cementing the role of buoyancy and stratification on the flow dynamics. Further, it is observed that the buoyancy flux (B) aids and destroys TKE intermittently in the radial direction, and it is at least O(102) smaller than P, ϵ, and the mean flow buoyancy flux (F). Finally, the relative strength of the turbulent transport of momentum to that of scalar in the radial direction is quantified using the turbulent Prandtl number, Prt. It is seen that Prt ≈1 upto the neutral buoyant layer and ≈ 0.6 in the plume cap region. The current set of results obtained from experiments are first of its kind and elucidates various aspects of the flow which hitherto remained unknown and will also prove to be useful in testing numerical simulations for buoyancy-driven flows.

Turbulence and Diffusion on Weakly Stable and Stable Nights near a 300 m Tower in a Complex Landscape

Abstract Turbulence and winds below 328 m were measured on 5 successive nights in a program to study tracer transport in the nocturnal boundary layer at a site with moderately complex terrain and mixed land use. The instruments included sonic anemometers and CO2/H2O analyzers at four levels on a 328 m tall tower, a minisodar/RASS system, a midrange sodar, a ceilometer, and an array of 61 m towers. Preliminary simulations indicated satisfactory perfluorocarbon mixing to 68 m but insufficient transport to the 328 m level on both weakly stable and stable nights, possibly due to insufficient turbulence kinetic energy and/or small vertical mixing lengths, or the presence of meso-β fronts, e.g., sea-breeze fronts, that could transport trace chemicals efficiently to 328 m. To examine the problem further, time–height distributions of turbulence kinetic energy (TKE), mixing length, Richardson number, potential temperature, and winds were derived from the observations of mean winds and temperature and the TKE budget equation, interpolated to fit the observations, under the flux/gradient and z-less scaling assumptions, and displayed with aerosol profiles. The results indicated higher and more variable levels of TKE and mixing lengths above a typical turbulence maximum at 30–50 m. Oscillations with periods of ∼2 h were common and occasional meso-β fronts and shear zones between 75 and 150 m were seen, which increased TKE aloft and in some cases led to a poorly defined boundary layer top. Significance Statement The atmosphere’s boundary layer is the interface between the free atmosphere and natural and human activity near Earth’s surface. The daytime boundary layer has been studied extensively and, because of vigorous sun-driven mixing, is well understood and readily parameterized in forecast and global climate models. In contrast, the nocturnal boundary layer is less well understood or predictable because turbulence is weak and tends to decouple it from the surface and the free atmosphere above. This paper focuses on the least-studied upper part of the nocturnal boundary layer over the southeastern United States where topography and land–sea contrast affect winds, turbulence, and chemical transport.

Comparison of the mean flow and turbulence characteristics of a single offset jet and a dual offset jet

This study compares the mean flow characteristics of a dual offset jet, comprising two 2-dimensional or plane turbulent offset jets, to a single offset jet. An in-house computational model is used to solve the incompressible form of the governing equations which are based on the standard k−ϵ Reynolds Averaged Navier–Stokes turbulence model. The offset ratio, defined as the vertical distance from the solid wall to the jet centreline divided by the nozzle width, of the upper jet is varied from 7 to 13, while the same for the lower jet is equal to 3. The jets’ inlet Reynolds number is 10,000 with a turbulence intensity of 5%. The mean flow results reveal that the presence of the second offset jet greatly influences the flow patterns compared to those of the single offset jet, although at some distance downstream of the inlet, the flow fields of both jet configurations resemble that of a classical wall jet. A single recirculation zone is formed underneath the single offset jet, whereas the flow field of the dual offset jet comprises two recirculation zones, one below the lower jet and the other between the two jets. In the pre-impingement region, the dual offset jet experiences a more rapid decay of the jet half width as compared to the single offset jet; however, the rate of growth of the jet half width for the single offset jet is faster than the dual offset jet. The self-similar solutions confirm that the dual offset jet begins to preserve self-similar characteristics for the mean flow field at a downstream distance greater than that for the single offset jet. For a given offset ratio, the total momentum flux for the single offset jet is found to be greater than that for the dual offset jet. Furthermore, the turbulent Reynolds stresses in the neighbourhood of the merging point are greater for the dual offset jet, but near the reattachment point, they are greater for the single offset jet. No self-similar characteristic of turbulence Reynolds stresses is obtained for both the jets. The turbulent kinetic energy budget reveals the highest value of the production term in the outer shear layer of the lower offset jet for the dual offset jet, which is greater than that for the single offset jet.

Effect of interaction strength on recovery downstream of incident shock interactions

Direct numerical simulations of a supersonic turbulent boundary layer on a flat plate interacting with an impinging shock wave are carried out with two different incident shock angles at Mach 2.25. The effect of the interaction strength on the recovery process in the downstream region is systematically studied, including the turbulence evolution, the statistical and structural properties of wall pressure fluctuations, and the generation of mean skin friction and wall heat flux. The variations of the Reynolds stress components, the anisotropy tensor, and the turbulent kinetic energy budget in the two flow cases highlight a slow reversal tendency and an increasingly pronounced importance of the outer-layer large-scale structures in the relaxation region of the strong interaction. We find that the effect of increasing the interaction strength on the fluctuating wall pressure is reflected by a decrease in the characteristic frequencies, an increase in the spatial extent, and a decrease in the convection velocity. We decompose the mean skin friction and wall heat flux into different physically informed contributions and reveal that the mean wall heat flux generation is the same regardless of the interaction strength; in contrast, the generation mechanism of mean skin friction is found to be fundamentally changed. A novel scale-decomposition method is used to quantify the effect of the increased interaction strength on the leading components, and it is demonstrated that the energetic outer-layer large-scale structures are the dominant contributor in the recovery process as the interaction strength is increased.

Control of separated flow transition over a highly loaded compressor blade via dynamic surface deformation

The laminar separation and transition process seriously deteriorate the aerodynamic performance of a compressor blade at a low Reynolds number (Re). To suppress the laminar separation without reattachment over a highly loaded compressor blade at Re=3.5 × 105, an active flow control strategy based on dynamic surface deformation (DSD) is numerically investigated by large eddy simulations (LESs). The control mechanism of DSD is analyzed, and the vortex dynamics in the transition process are resolved. Furthermore, the loss mechanism is clarified based on the turbulent kinetic energy (TKE) budget analysis. For the uncontrolled case, the rolling-up and breakdown of large-scale hairpin vortices accelerate the generation of turbulent fluctuations, which distinctly extend the region of high-level TKE production term and thus cause large total pressure loss. As the DSD is activated at the oscillation frequency f0 (f0 is the vortex shedding frequency in separated shear layers), periodic pressure fluctuation waves are induced with the appearance of small-scale vortices. The convection of these vortices enlarges the local vorticity and makes the boundary layer velocity profile fuller, which successfully eliminates the large-scale laminar separation on the compressor blade. As such, the region of high-level TKE production term shrinks distinctly due to the weakened vortex dynamics, and the total pressure loss is reduced by 78.9%. With increasing the oscillation frequency from f0 to 2f0 or 4f0, the loss is slightly enlarged due to the rapid growth of turbulent boundary layers, but it is still lower than that of the uncontrolled case. The results demonstrate that DSD is feasible in controlling large-scale laminar separation, and there exists an optimal oscillation frequency.

DNS analysis of turbulence modulation by lean premixed prevaporized spray flames in a model combustor

Turbulence modulation by lean premixed prevaporized (LPP) spray flames, which involve droplet motion, evaporation and gaseous reaction, is complicated and essential to organizing clean and efficient combustion. Direct numerical simulations of LPP combustion in a model swirling combustor under high pressure of 20 bar are performed. The gaseous flow is solved in the low-Mach-number limit, and the droplets are tracked as two-way coupled Lagrangian particles. The corrected infinite thermal conductivity model is adopted to describe droplet evaporation, and a reduced two-step kerosene/air chemistry mechanism is used to present combustion. Four cases, i.e., a non-reacting gaseous flow, a non-reacting spray flow and two reacting spray flows with different droplet sizes, are conducted to cover key features of LPP flame on turbulence modulation. The results show that the spray combustion significantly depresses the mean axial velocity on the centerline in the upstream, indicating an enhancement of the inner recirculation zone. The influence of droplets on the mean and fluctuating velocities is generally negligible except on the azimuthal modulation, while combustion can increase the velocities, which is more evident in downstream due to the pressure effect. In reacting cases, the turbulent kinetic energy (TKE) spectra in the shear layers reduce at high wavenumbers, reflecting the combustion-induced dissipation at small scales (below the laminar flame thickness scale). Besides, droplet evaporation can introduce energy at small scales while this modulation is balanced by combustion. Moreover, TKE budget analysis indicates that spray combustion mainly depresses the TKE and redistributes mean shear along the radial direction. Heat release increases the local fluid viscosity, depresses local turbulent transport, and increases viscous dissipation. Finally, the vortex stretching analysis shows that LPP combustion enhances the alignment with the intermediate strain rate component.

Direct numerical simulation of supersonic bump flow with shock impingement

Direct numerical simulations are carried out to identify the effects of shock impingement on the behavior of bump flow at freestream Mach number of 2.25. Two cosine-shaped bump cases, with and without an impinging oblique shock at an angle of 33.2°, are compared. The shock impingement exhibits a remarkable influence on the pattern of the shock system and on the size of the separation region. A spectral analysis finds that low-frequency unsteadiness is significantly enhanced by the impingement interaction, and the proper orthogonal decomposition highlights the low-frequency breathing motion of the separation bubble, which is accurately reconstructed using only the first ten low-order modes. Downstream of the bump, both the Reynolds stress components and the turbulence kinetic energy exhibit a general amplification, with the peaks reoccurring at outer wall-normal locations. A turbulent kinetic energy budget analysis shows the greatly increased production in the outer layer which is balanced by turbulent transport and dissipation. An anisotropy-invariant map analysis identifies enhanced isotropic turbulence in the vicinity of the bump, which is qualitatively modified into a two-component axisymmetric state around the reattachment point. In addition, the mean skin friction decomposition suggests that the shock impingement has little influence on the predominant contribution of turbulence kinetic energy production, apart from the spatial growth dominance at the bump summit in the absence of the impinging shock. Interestingly, a scale-decomposed analysis quantitatively demonstrates that the contributions of small-scale structures are attenuated, but those of large-scale ones are relatively increased, with a contribution of more than 80% with shock impingement.

Numerical Prediction of Turbulent Drag Reduction with Different Solid Fractions and Distribution Shapes over Superhydrophobic Surfaces

The exploration of superhydrophobic drag reduction has been and continues to be of significant interest to various industries. In the present work, direct numerical simulation (DNS) is utilized to investigate the effect of the parameters on the drag-reducing performance of superhydrophobic surfaces (SHS). Simulations with a friction Reynolds number of 180 were carried out at solid fraction values of ϕs=116,111, and 14, and three distribution shapes: aligned, staggered, and random. The top wall is the smooth one, and the bottom wall is a superhydrophobic surface (SHS). Drag reduction and Reynolds stress profiles are compared for all cases. The turbulent kinetic energy budget, including production, dissipation, and diffusion, is presented with respect to the solid fraction and type of distribution to investigate the drag reduction mechanism. The sizes of the longitudinal vortices and formation of hairpin vortices are investigated through the observation of coherent structures. The simulation of a post model is a useful method to study the drag reduction for different solid fraction values and distribution geometries. Our study demonstrates that the drag reduction could acquire 42% with the solid fraction value ϕs=116 and an aligned distribution shape for post superhydrophobic surface geometry. Our study also showed the relationship of the Reynolds stress component (R11, R22, and R33) to the drag reduction with the differences in the solid fraction values and distribution geometry. In which, the R11 component has the most change between an aligned distribution and a random one. The peak value of R11 tends to shift away from the SHS wall. In addition, the analysis of the TKE budget over the superhydrophobic surface was performed, which can be adopted as a useful resource in turbulence modeling based on RANS methodology.

Turbulent kinetic energy budgets over gentle topography covered by forests

Turbulent kinetic energy budgets over gentle topography covered by forests

Anisotropic Turbulent Kinetic Energy Budgets in Compressible Rectangular Jets

Turbulence is governed by various mechanisms, such as production, dissipation, diffusion, dilatation and convection, which lead to its evolution and decay. In high-speed flows, turbulence becomes complicated due to compressibility effects. Therefore, the goal of the current work is to characterize these mechanisms in rectangular supersonic jets by directly evaluating their contributions in turbulent kinetic energy (TKE) budget equation. The budgets are obtained using high-fidelity Large Eddy Simulations that employ WALE subgrid-scale model. Jet nearfield data are validated with PIV experimental measurements, available from the literature, which include mean flow and second-order statistics. To ensure spatial resolution and temporal convergence of higher-order statistics, qualitative performance metrics are presented. The results indicate that TKE production is the major source term, while pressure-dilatation term acts as a sink throughout the development of the jet. The diffusion term has the highest contribution from triple-velocity correlations, followed by pressure diffusion and molecular diffusion. Subgrid-scale diffusion and dissipation are also evaluated and their contributions are minimal. Each term is presented on both minor and major axis plane and reveals asymmetry in the statistics. A detailed explanation of budget contributions is provided, leading to the mechanisms responsible for the anisotropy of TKE.

Simulation-based study of turbulent aquatic canopy flows with flexible stems

Large-eddy simulation (LES) is performed to investigate the dynamics of flow and canopy motions and the energy transfer in turbulent canopy flows. Different from the traditional approach that models the canopy as a continuous medium with a drag coefficient prescribed a priori, an immersed boundary method together with a beam model is employed to explicitly capture the dynamics of individual stems and resolve monami. The simulation cases cover a broad range of stem flexibilities from rigid stems to oscillatory stems to stems yielding to the flow. For highly flexible canopies, the stem fluctuation is small such that the canopy behaves like a rigid canopy, which is used to explain the similarities of the flow features between rigid and highly flexible canopies. Analyses of the turbulent kinetic energy (TKE) budget show that, in the flexible canopy cases, the waving term associated with the canopy drag–flow velocity correlation can be as large as one-half of the shear production term near the canopy top. Spectral TKE budget analyses further reveal dominant effects at two characteristic scales: the monami scale associated with the coherent structures in the mixing layer and the wake scale associated with the interval between adjacent stems. For the TKE in flexible canopies, the waving term is found to play an important role in the interscale and wall-normal transport terms. Our LES data show that the spectral shortcut mechanism proposed by previous studies is caused by the waving term.

Flow Over a Square Cylinder at Intermediate Reynolds Numbers

Abstract This study experimentally investigates the flow over a stationary square cylinder in the test section of a subsonic wind tunnel. Hotwire anemometry (CTA type), particle image velocimetry (2C-PIV), and flow visualization techniques are used in the study to characterize the flow properties. The study is carried out at four intermediate Reynolds numbers (blocking width 'B' as the characteristic length) 600, 800, 1000, and 2000. The flow over the circular cylinder and square cylinder differs, particularly at intermediate Reynolds numbers, but the literature lacks detailed flow behavior over a square cylinder beyond the wake transition regime. Re = 600 is the critical Reynolds number as the flow changes from a disordered fine-scale three-dimensional regime to a shear layer transition regime. The effects of the regime alterations on the flow properties, vortex shedding frequency, and mean drag coefficient are reported in the study for all Reynolds numbers. The flow visualization supplements the CTA and PIV measurements. The turbulent kinetic energy budget has also been compared for all Reynolds numbers.

Drag enhancement by the addition of weak waves to a wave-current boundary layer over bumpy walls

We present direct numerical simulation results of a wave-current boundary layer in a current-dominated flow regime (wave driven to steady current ratio of 0.34) over bumpy walls for hydraulically smooth flow conditions (wave orbital excursion to roughness ratio of 10). The turbulent, wave-current channel flow has a friction Reynolds number of $350$ and a wave Reynolds number of $351$ . At the lower boundary, a bumpy wall is introduced with a direct forcing immersed boundary method, while the top wall has a free-slip boundary condition. Despite the hydraulically smooth nature of the wave-driven flow, the phase variations of the turbulent statistics for the bumpy wall case were found to vary substantially when compared with the flat wall case. Results show that the addition of weak waves to a steady current over flat walls has a negligible effect on the turbulence or bottom drag. However, the addition of weak waves to a steady current over bumpy walls has a significant effect through enhancement of the Reynolds stress (RS) accompanied by a drag coefficient increase of $11\,\%$ relative to the steady current case. This enhancement occurs just below the top of the roughness elements during the acceleration portion of the wave cycle: Turbulent kinetic energy (TKE) is subsequently transported above the roughness elements to a maximum height of roughly twice the turbulent Stokes length. We analyse the TKE and RS budgets to understand the mechanisms behind the alterations in the turbulence properties due to the bumpy wall. The results provide a mechanistic picture of the differences between bumpy and flat walls in wave-current turbulent boundary layers and illustrate the importance of bumpy features even in weakly energetic wave conditions.

Large-eddy simulation of gusty wind turbulence over a travelling wave

Wind gustiness in the marine atmospheric boundary layer affects significantly the dynamics of air–sea interaction. To understand the impacts of wind gust events, we perform large-eddy simulation of wind turbulence over a travelling wave to investigate the response of the wind field to an impulsive wind speed increase or decrease. It is found that the turbulence fluctuations and the terms in the turbulent kinetic energy budget equation have a delayed response to the change in the mean flow, while the response of the wave-coherent motions is quasi-stationary. The wave-coherent motions are investigated quantitatively through comparison with a viscous curvilinear model developed by Cao et al. (J. Fluid Mech., vol. 901, 2020, A27) and Cao & Shen (J. Fluid Mech., vol. 919, 2021, A38). We observe an asymmetric hysteresis between the growing wind and the decaying wind in the evolution of the form drag and the viscous drag. We find further that the variation of the wave growth rate during the wind gust is related closely to the contribution from the out-of-phase component of the vertical velocity. Our discoveries provide evidence for the necessity of improving non-equilibrium turbulence and wind input modelling to account for the wind gustiness effect in future studies.

Analysis of scale-dependent kinetic and potential energy in sheared, stably stratified turbulence

Budgets of turbulent kinetic energy (TKE) and turbulent potential energy (TPE) at different scales $\ell$ in sheared, stably stratified turbulence are analysed using a filtering approach. Competing effects in the flow are considered, along with the physical mechanisms governing the energy fluxes between scales, and the budgets are used to analyse data from direct numerical simulation at buoyancy Reynolds number $Re_b=O(100)$ . The mean TKE exceeds the TPE by an order of magnitude at the large scales, with the difference reducing as $\ell$ is decreased. At larger scales, buoyancy is never observed to be positive, with buoyancy always converting TKE to TPE. As $\ell$ is decreased, the probability of locally convecting regions increases, though it remains small at scales down to the Ozmidov scale. The TKE and TPE fluxes between scales are both downscale on average, and their instantaneous values are correlated positively, but not strongly so, and this occurs due to the different physical mechanisms that govern these fluxes. Moreover, the contributions to these fluxes arising from the sub-grid fields are shown to be significant, in addition to the filtered scale contributions associated with the processes of strain self-amplification, vortex stretching and density gradient amplification. Probability density functions (PDFs) of the $Q,R$ invariants of the filtered velocity gradient are considered and show that as $\ell$ increases, the sheared-drop shape of the PDF becomes less pronounced and the PDF becomes more symmetric about $R=0$ .