Turbulence Production Research Articles

Unsteady numerical investigations of the effect of guide vane openings on the hydrodynamic characteristics under stall conditions in a pump-turbine pump mode

The stall is extremely prone to surge of hydraulic loss, excessive pressure fluctuation and radial force of the pump-turbine in pump mode. These can pose a great threat to the safety operation of the unit. Current research focuses more on the manifestations and propagation mechanisms of the stall, which has limitations and effective methods for passive stall suppression cannot be directly identified. In this paper, unsteady simulations based on the SST-SAS turbulence model are conducted to discuss the effects of guide vane openings on the hydrodynamic characteristics under stall conditions of the pump-turbine from the perspectives of flow pattern, energy loss, pressure fluctuation and radial force. Firstly, the performance test results show that the positive slope of the flow-head curves is the largest at small guide vane openings and smallest at optimal guide vane openings. Then, energy loss analysis based on the energy balance equation indicates that the energy loss in the stay vane is most influenced by guide vane openings, with maximum turbulent kinetic energy production at large guide vane openings. Furthermore, the analysis of the stall characteristics in the impeller illustrates that at large guide vane openings, the axial meridional velocity in the impeller is negative under deep stall conditions, and the flow separation and vortex induce a great local pressure drop in the suction surface of impeller blades near the shroud. Subsequently, the stall characteristics analysis in the diffuser reveals that large-scale vortices in the vaneless regions and stay vane channels result in more severe flow blockage and higher energy loss at large guide vane openings. As the increased guide vane openings, the Rotor-stator interaction effect is weakened by the unstable flow pattern in the diffuser, and the low frequency and near blade frequency signals gradually become the dominant frequencies in the diffuser. Finally, the simulation results in the volute show that the unstable flow pattern in the diffuser provides poor inlet conditions for the volute, which significantly increases the energy loss and pressure fluctuations in the volute. The increase of guide vane openings can also make the flow inhomogeneity in the volute worse. The radial forces on the impeller and diffuser under deep stall conditions both increase with increasing guide vane openings due to the unstable flow patterns.

Turbulent transfer and entrainment in a low-density jet

We investigate the dynamics of a low-density round jet, with a focus on the mechanisms governing the turbulent momentum and mass transfers as well as on the entrainment of ambient fluid. To that purpose, we combine a theoretical analysis, laboratory experiments and numerical simulations. The theoretical analysis relies on a general formulation of the entrainment decomposition for the case of large density differences, revealing the role of the processes contributing to the entrainment: turbulent kinetic energy production and variation in the shape of the mean velocity radial profiles. The spatial evolution of these terms has been evaluated by means of challenging experiments, providing a unique data set of combined velocity and density statistics of a low-density jet and an air jet. The same flows are investigated by means of large-eddy simulation (LES). Other than for providing complementary information on flow statistics, LES is here used to investigate the role of varying conditions imposed at the source, notably concerning the shape of the inlet velocity profile and the presence of a bottom wall surrounding the source. Experimental and numerical results provide clear insight on how a reduced density within the jet enhances the turbulent kinetic energy production (compared to an iso-density jet) and modifies the shape of the mean velocity profiles. Despite its clear influence on the flow statistics, the reduced density has overall little influence on the entrainment rate, which also shows little sensitivity to varying source conditions.

Outer-layer similarity and energy transfer in a rough-wall turbulent channel flow

Direct numerical simulations (DNSs) are performed to investigate the roughness effects on the statistical properties and the large-scale coherent structures in the turbulent channel flow over three-dimensional sinusoidal rough walls. The outer-layer similarities of mean streamwise velocity and Reynolds stresses are examined by systematically varying the roughness Reynolds number $k^{+}$ and the ratio of the roughness height to the half-channel height $k / \delta$ . The energy transfer mechanism of turbulent motions in the presence of roughness elements with different sizes is explored through spectral analysis of the transport equation of the two-point velocity correlation and the scale-energy path display of the generalized Kolmogorov equation. The results show that, with increasing $k^+$ , the downward shift of the mean streamwise velocity profile in the logarithmic region increases and the peak intensities of turbulent Reynolds stresses decrease. At an intermediate Reynolds number ( $Re_{\tau }= 1080$ ), the length scale and intensity of the large-scale coherent structures increase for a small roughness ( $k^{+}=10$ ), which leads to failure of the outer-layer similarity in rough-wall turbulence, and decrease for a large roughness ( $k^{+}=60$ ), as compared with the smooth-wall case. The existence of the small roughness ( $k^{+}=10$ ) enhances the mechanism of inverse energy cascade from the inner-layer small-scale structures to the outer-layer large-scale structures. Correspondingly, the self-sustaining processes of the outer-layer large-scale coherent structures, including turbulent production, interscale transport, pressure transport and spatial turbulent transport, are all enhanced, whereas the large roughness ( $k^{+}=60$ ) weakens the energy transfer between the inner and outer regions.

Explainability analysis of neural network-based turbulence modeling for transonic axial compressor rotor flows

Model–consistent training has become trending for data-driven turbulence modeling since it can improve model generalizability and reduce data requirements by involving the Reynolds–averaged Navier–Stokes (RANS) equation during model learning. Neural networks are often used for the Reynolds stress representation due to their great expressive power, while they lack interpretability for the causal relationship between model inputs and outputs. Some post–hoc methods have been used to explain the neural network by indicating input feature importance. However, for the model–consistent training, the model explainability involves the analysis of both the neural network inputs and outputs. That is, the effects of model output on the RANS predictions should also be explained in addition to the input feature analysis. In this work, we investigate the explainability of the model–consistent learned model for the internal flow prediction of NASA Rotor 37 at its peak efficiency operating condition. The neural–network–based corrections for the Spalart–Allmaras turbulence model are learned from various experimental data based on the ensemble Kalman method. The learned model can noticeably improve the velocity prediction near the shroud. The explainability of the trained neural network is analyzed in terms of the model correction and the input feature importance. Specifically, the learned model correction increases the local turbulence production in the vortex breakdown region due to non–equilibrium effects, which capture the blockage effects near the shroud. Besides, the ratio of production to destruction and the helicity are shown to have relatively high importance for accurately predicting the compressor rotor flows based on the Shapley additive explanations method.

Assessment of turbulence correction for actuator-line model of a horizontal-axis tidal stream turbine in near-wake region

Near-wake characteristics of a turbine play an important role in turbine–wake interactions and performance assessment in turbine arrays. In this study, the near-wake flow behind a laboratory-scale tidal stream turbine is simulated and compared with experimental data. An actuator-line model is used to represent the rotating blades. Further, two physics-based turbulence corrections are proposed for unsteady Reynolds-averaged Navier–Stokes (URANS) modeling of the tidal stream turbine. These corrections seek to model additional turbulent production near the blade boundary layer and in the tip shear region. The data analysis for the fluctuating velocity spectrum in the experiment highlights that the turbulence kinetic energy (TKE) can be decomposed into three parts: the background turbulence from the onset flow, rotor-scale turbulence, and blade-induced turbulence. The blade-induced turbulence dominates near the rotor plane and decreases sharply beyond one diameter downstream. Near-wake profiles of velocity and TKE are compared with experimental data. The results show that turbulence corrections in the URANS model enhance the production of turbulence induced by the blade rotation. It can improve turbulence prediction in the near-wake region with a minor impact on the loads and wake velocity.

Study on the Energy Loss Characteristics of Shaft Tubular Pump Device under Stall Conditions Based on the Entropy Production Method

This study aimed to reveal the energy loss characteristics of each part of the shaft tubular pump device (STPD) under stall conditions. Numerical simulations were conducted by using the SST k-ω turbulence model with curvature correction, and the reliability of the simulation results was verified by a model test. The entropy production method was used to evaluate and visualize the energy loss. The results show that turbulent entropy production (TEP) is the main source of energy loss in each component of the STPD, and the TEP increases significantly with the deterioration of stall. The energy loss in the impeller is mainly concentrated near the shroud and hub, while in the guide vanes it is mainly concentrated near the shroud and suction surface of the blades. In addition, with the deterioration of stall, the energy loss in the inlet of the impeller and guide vanes increases significantly. Influenced by the backflow from the impeller, there is a significant amount of energy loss at the outlet segment of the inlet passage, and the location of the high-energy-loss region is consistent with the backflow region. Affected by the flow separation vortex at the tail of the guide vanes, the energy loss in the outlet passage is mainly concentrated at the inlet segment.

Improving performance of H-Type NACA 0021 Darrieus rotor using leading-edge stationary/rotating microcylinders: Numerical studies

In the current paper, a computational study has been performed to simulate a novel concept in which a fixed/rotating microcylinder is installed upstream of the leading edge of the NACA 0021 airfoil, aiming to enhance the performance of the H-type Darrieus rotor. The idea behind implementing a fixed/rotating microcylinder is to enhance the lift to drag ratio due to increasing near-wall momentum through generated vortices transferring the momentum from the outer flow to the near-wall flow region of the airfoil. Parametric analyses for the microcylinder including its location, size, shape (circular, square and rhombus), and rotation were performed. The commercial Computational Fluid Dynamics (CFD) package ANSYS Fluent was used for solving the Unsteady Reynolds Averaged Navier-Stokes (URANS), and turbulence equations. The code has been based on Finite Volume Method (FVM) with the pressure-based solver developed for low-speed incompressible flows. The semi-implicit method for pressure-linked equation (SIMPLE) was used to solve the discretized equations. The URANS was used with adopting the SST k-ω turbulence model to find out the optimum rotor by utilizing the microcylinder model. An optimization methodology using Response Surface Optimization (RSM) based on Kriging method has been first performed to find the optimum size and location of a circular microcylinder. The optimization study indicated an optimum microcylinder diameter (d/C = 0.0085313), at an upstream chordwise distance and normal to it 0.070275 and 0.02303 of the chord length (C), respectively. The results showed also that a small static circular microcylinder of d/C = 0.009 and installed at 0.075C from the leading edge (MC5) is an efficient geometry at high regime of tip-speed ratios (TSR≥2.2) rather than lower regime of TSRs. When these superior set of rotating (5 rad/s) microcylinder (MC5) parameters were adopted, significant enhancement of power coefficient (Cp) could be achieved and a considerable improvement of the maximum power coefficient (Cpmax) up to 120 % at TSR = 3 appeared. A physical analysis of the flow fields using the contours of vorticity, pressure and turbulence energy has been performed to illustrate the effect of rotating microcylinder for improving rotor performance. The vorticity contours showed the ability of rotating microcylinder for generating a strong vortex structure in its wake for enhancing turbulence production around the blades, which delayed the known strong stall of the blades by diminishing the separation bubble size. This generally improved the blades aerodynamic performance and enhancing the lift-to-drag ratio.

Large-scale motions in a turbulent natural convection boundary layer immersed in a stably stratified environment

This study investigates the coherence of turbulent fluctuations in a turbulent vertical natural convection boundary layer immersed in a stably stratified medium (turbulent buoyancy layer). A turbulent buoyancy layer of a fluid having a Prandtl number of $0.71$ at a Reynolds number of $800$ is numerically simulated using direct numerical simulation. The two-point correlations reveal that the streamwise velocity fluctuations are coherent over large streamwise distances, with the length scale of the streamwise coherence being greater than the boundary layer thickness. This is due to large-scale motions (LSMs), similar to the LSMs observed in canonical wall-bounded turbulence despite the stark differences in flow dynamics. Both high-speed (positive) and low-speed (negative) streamwise velocity fluctuations form LSMs, with their streamwise length scales increasing with increasing wall-normal distance. High-speed LSMs are composed of upwash flow with high temperatures, while low-speed LSMs are composed of downwash flow with low temperatures. Both high-speed and low-speed LSMs meander appreciably in the streamwise direction, with the degree of meandering being correlated with the sign of the spanwise velocity fluctuations. The LSMs exhibit coherence across significant wall-normal distances and contribute significantly to the turbulence production in the outer layer. Examining the one-dimensional energy spectra of the turbulent buoyancy layer shows that the LSMs are the dominant energy-containing motions, implying that the length scale of the energy-containing range is of the order of boundary layer thickness. Notably, wall-normal velocity, spanwise velocity and buoyancy fluctuations do not form LSMs with streamwise length scales comparable to streamwise velocity fluctuations.

Turbulent cascade in fully developed turbulent channel flow

We show that Kolmogorov scale-by-scale equilibrium in the intermediate layer of a fully developed turbulent channel flow is only achieved asymptotically around the Taylor length and, therefore, not in an inertial range. Furthermore, we analyse scale-by-scale turbulence production and interscale turbulence energy transfer in terms of alignments/anti-alignments of fluctuating velocities, straining/compressive relative motions, forward/inverse interscale transfer/cascade and homogeneous/non-homogeneous interscale transfer rate contributions. We also propose leading order scalings for second- and third-order two-point statistics, including the extremum interscale turbulence energy transfer rate and a second-order anisotropic structure function, which acts as a scale-by-scale Reynolds shear stress and determines the scale-by-scale (two-point) turbulence production rate.

Direct Numerical Simulation and Large Eddy Simulation of a 67-Pebble-Bed Experiment

An in-depth understanding of the flow physics in packed beds is critical for developing simulation tools for pebble bed reactors. Advances in computing power have now made the full-core pebble-resolved computational fluid dynamics simulation of these systems possible. This work presents validation of the velocity and pressure predictions made by the spectral element code NekRS followed by a study of the turbulent kinetic energy and turbulent heat flux budgets. Two cases with corresponding experiments are considered: a bed of 67 pebbles with Re = 1460 and a bed of 789 pebbles with 324 < Re < 1024. Velocity and pressure drop comparisons are performed with the two cases, respectively. Good agreement is found between the experiments and their respective NekRS simulations. The 67-pebble case was then used to perform a direct numerical simulation to extract the turbulent kinetic energy and turbulent heat flux budget terms. Analysis of the turbulent kinetic energy production revealed large areas of negative production near the bottom surfaces of the pebbles. Further investigation revealed a trend between the average amount of negative turbulent kinetic energy production and the local porosity. These results continue to suggest that inertial effects play a large role in differentiating near-wall flow from bed-interior flow.

Model and method to predict the turbulent kinetic energy induced by tidal currents, application to the wave-induced turbulence

A prediction model for the turbulent kinetic energy (TKE) induced by tidal-currents is proposed as a function of the barotropic velocity only, along with a robust method evaluating the different parameters involved using Acoustic Doppler Current Profiler (ADCP) measurements from Alderney Race. We find that the model is able to reproduce correctly the TKE profiles with coefficients of correlation on average higher than 0.90 and normalised root-mean-square errors (NRMSE) less than 14%. Different profiles are also tested for the mean velocity, no satisfactory prediction model is found but we are able to have decent estimates of the velocity shear and friction velocity. Two applications are then carried out. First the turbulent budget terms are estimated and discussed. We identify the turbulent production and dissipation of TKE as the most important mechanisms, then we discuss the validity of several theoretical results derived for isotropic turbulence for this application. A strong departure for the estimation of the turbulent dissipation is notably found and explained by the turbulent anisotropy. At last the prediction model for the TKE is used to infer the wave-induced TKE. We show the importance of removing the tidal component, waves can have a strong influence down to mid-depth.

A numerical study of aeration characteristics of a plunging solitary wave on a slope

In this paper, the characteristics of aerated flow under a plunging solitary wave on a 1:20 sloping beach are investigated numerically. The numerical model solves the Reynolds-averaged Navier–Stokes equations for mean flow. The turbulence is described by the k−ε model, in which the turbulence production and dissipation modified by entrained air bubbles are considered by an additional term. A transient equation is solved for air bubble transportation. The numerical model is validated by comparing the air bubble concentration, mean flow velocities, and turbulent kinetic energy against experimental data, demonstrating its capability for simulating transient aerated flows under breaking waves. The validated model is further applied to reveal the detailed interaction of the entrained air bubbles and the turbulent free surface flows during the wave breaking process. Plunging breaking wave consists of four stages, namely, the wave front steepening, the initiation of overturning, the transitional stage, and the quasi-steady bore propagation stage. The results reveal that the overturning and breaking wave front is the main source for turbulence generation and air entrainment in the initiation and transitional stage of breaking wave, respectively. The entrained air bubbles are mainly transported backward and downward by turbulence structures and forming distinct bubble vortex rollers near the bottom. The distribution of air bubble concentration shows a linear correlation to the distribution of turbulence quantities in the initial and transitional stage of breaking wave, demonstrating the important role of local turbulent structures on air entrainment and transportation.

Study of Energy Loss Characteristics of a Shaft Tubular Pump Device Based on the Entropy Production Method.

The unstable flow of a shaft tubular pump device (STPD) leads to energy loss, thereby reducing its efficiency. The aim of this study is to investigate the distribution pattern of energy loss in STPDs. This paper reveals that the two components with the highest proportion of energy loss are the impeller and the outlet passage. Furthermore, turbulent entropy production is the primary cause of energy loss. Due to the wall effect, the energy loss in the impeller mainly occurs near the hub and shroud. Additionally, the presence of a tip leakage vortex near the shroud further contributes to the energy loss in the region near the shroud. This results in the energy loss proportion exceeding 40% in the region with a volume fraction of 14% near the shroud. In the outlet passage, the energy loss mainly occurs in the front region, with a volume fraction of 30%, and the energy loss in this part accounts for more than 65%. Finally, this study reveals the locations of the vortex in the STPD under different flow-rate conditions, and when the distribution of energy loss is visualized, it is found that the energy loss occurs high in the vortex regions.

A family of adverse pressure gradient turbulent boundary layers with upstream favourable pressure gradients

A flat-plate turbulent boundary layer (TBL) is experimentally subjected to a family of 22 favourable–adverse pressure gradients (FAPGs) using a ceiling panel of variable convex curvature. We define FAPGs as a sequence of streamwise pressure gradients in the order of favourable followed by adverse, similar in sequence to the pressure gradients over the suction side of an airfoil. For the strongest pressure gradient case, the acceleration parameter, $K$ , varied spatially from $6 \times 10^{-6}$ to $- 4.8 \times 10^{-6}$ . The adverse pressure gradient (APG) region of this configuration is studied using particle image velocimetry in the streamwise–wall-normal plane. The statistics of the APG TBL show that the upstream favourable pressure gradient (FPG) exerts a strong and lasting downstream influence, and that the rapid spatial changes in the pressure gradients imposed cause an internal boundary layer to grow within the TBL for 15 of the cases studied. The internal layer typically occupies 20 $\%$ of the boundary layer thickness and dominates the boundary layer response, containing the peak turbulent production, peak strength and population of vortices, and most of the spectral energy content of the flow. The outer layer, on the other hand, develops in the APG region without considerable changes to the state dictated by the upstream FPG. These trends are in contrast to APG TBLs that originate from a zero pressure gradient region, where the outer/wake region is known to dominate TBL response. The observed changes are quantified across the family of FAPGs imposed.

Manipulation of a turbulent boundary layer using active surface deformations

We experimentally evaluate whether active wall-normal surface deformations are suitable for the targeted control of very-large-scale motions (VLSMs) in a turbulent boundary layer at a friction Reynolds number of $Re_\tau =2600$ . Circular surface deformations with a diameter $D$ roughly equal to the boundary layer thickness $\delta$ are generated periodically at a constant amplitude of $0.03\delta$ and at actuation frequencies of $St=0.05$ to 0.20, where $St$ is the Strouhal number based on $D$ and the free stream velocity $U_\infty$ . The resulting impact on the flow was captured using high-speed particle image velocimetry and analysed using a triple decomposition. We find that the active surface deformations produce high- and low-speed streamwise velocity fluctuations that are concentrated along the centreline of the actuator. These motions have a negligible impact on the mean velocity profile downstream, i.e. they are truly high and low speed with respect to the unactuated base flow. The motions produced at $St\lesssim 0.1$ are comparable to synthetic VLSMs in terms of their lengths and widths but with a reduced wall-normal extent and rapidly decaying strength. These synthetic motions produce a strong modulation of the turbulence similar to that of the naturally occurring VLSMs. Most notably, we observe that synthetic high-speed motions with magnitudes of the order of $0.05U_\infty$ cause up to a 30 % reduction in turbulence production within the logarithmic layer. The strength and turbulence-modulating characteristics of the synthetic motions appear well suited for targeting the naturally occurring VLSMs locally using a control scheme.

High-resolution simulations of a turbulent boundary layer impacting two obstacles in tandem

We created a new publicly available data set of high-fidelity numerical simulations for two obstacles in tandem invested by a fully resolved turbulent boundary layer. In the three configurations of skimming flow, wake interference, and isolated roughness, we identify the regions of intense turbulent fluctuations, production and transport of turbulent kinetic energy, and examine the anisotropy-invariants map.

Direct numerical simulations of oscillatory boundary layers over rough walls

Numerical simulations of turbulent oscillatory flow over a bed made of fixed, identical spherical particles have been performed. Oscillations are imposed through a shear-driven forcing by means of an harmonic velocity boundary condition on the bed. A parametric study on the effect of the particle size and Reynolds number, spanning from the laminar to the fully-turbulent regimes, has been performed. Results show that the temporal evolution of the flow over the rough bed is modified compared to the classical Stokes’ solution for smooth-wall laminar boundary layers. In the turbulent cases, the phase shift in the velocity at various distances from the bed is reduced compared to the laminar case. The phase shift reduction seems predominantly dependent on the Reynolds number rather than the bed morphology, which suggests that a unique curve may exist for large enough values of the Reynolds number. Turbulence is observed during the deceleration phases of the cycle, with the presence of a logarithmic layer in the velocity profile, and “canonical” distribution of Reynolds shear stress and turbulent kinetic energy production. During the acceleration, the logarithmic region is suppressed and the Reynolds shear stress changes sign. Nevertheless, the turbulent kinetic energy production becomes only slightly negative, because the shear is also very small during these phases. A good correlation between Reynolds and shear stresses is also evidenced from the eddy viscosity profiles, which show the presence of plateau in the outer layers approximately constant across the phases of the cycle. Turbulence in the outer layers is related to structures which develop during previous cycles and propagate from the bed to the bulk of the channel. When the flow is fully developed, anisotropy maps show similar distributions to unidirectional wall-bounded flows, while departures from canonical distributions during the transient phases are mild, because the flow responds very rapidly to the time-varying forcing.

Behavioral patterns of turbulent kinetic energy budget and quadrant analysis for flows over bedform under the influence of downward seepage

Seepage is one of the important factors involved in natural flow conditions, contributing to changes in flow turbulence patterns and morphological changes due to the transport of sediments. This transport of sediment particles influences the development of fluvial bedforms in any river channel. However, previous research on fluvial dynamics has not considered the influence of seepage on the flow field over the fluvial bedforms. The present experimental research aims to explore the behavioral patterns of turbulent kinetic energy, the turbulent kinetic energy (TKE) budget, and quadrant analysis for flows over two-dimensional dune shaped bedforms in the absence and presence of downward seepage. Results from the study illustrate that at the measurement locations on the initial and lee side sections of a dune, the TKE increases with the introduction of downward seepage, leading to an increase in turbulence production near the bed-surface region. The flow energy under both no seepage and seepage conditions contributes mainly to the turbulent production. Turbulence diffusion and dissipation rates have been found to decline in the near-bed region of the initial and lee side sections of the dune. However, turbulent production has been found to be significantly higher in the presence of downward seepage than under the no seepage condition. Similarly, turbulent kinetic energy flux increases in the streamwise direction, while it reduces in the vertical direction at initial sections and lee side sections of the dune under seepage conditions. However, at the middle sections and crest portion of the dune, opposite behavioral patterns are observed for all the aforementioned turbulent entities. Quadrant analysis reveals that the sweep and ejection event increases while inward and outward interaction reduces in the near bed zone. Although the contribution of both sweep and ejection events increases in the presence of downward seepage, sweep events have clear dominance in the near bed region, suggesting the possibility of a higher rate and amount of sediment transportation than under the no seepage condition.

Effects of Breaking and Non‐Breaking Surface Wave Mixing on the Changjiang River Plume Dynamics in Summer

AbstractA wave‐current coupled model is implemented to investigate the impact of breaking and non‐breaking surface wave mixing on the structure and dynamics of the Changjiang River plume. Two main non‐breaking wave mixing schemes, modifying the turbulent viscosity directly versus adding wave‐induced turbulence production in the turbulence closure model, are incorporated to the Coupled Ocean‐Atmosphere‐WAVE‐Sediment Transport modeling system. Surface wave mixing typically thickens the plume and traps more freshwater in the near‐ and mid‐field regions. The surface turbulent kinetic energy produced by breaking waves corresponds to small wave energy input in fair weather conditions and has a moderate effect on the Changjiang River plume. In contrast, the addition of non‐breaking wave mixing enhances the turbulent viscosity roughly an order of magnitude in the surface layer. Simulations with non‐breaking wave mixing improve the representation of the plume structure compared to models without wave mixing or with only breaking wave mixing. The Changjiang River plume exhibits a north‐south asymmetry in both salinity and current field in summer. Further adding the non‐breaking wave mixing reduces the surface Ekman velocity and lowers the offshore plume expansion rate through interactions between the upwelling favorable winds and the Ekman layer depth. The resulting adjustment to the internal pressure gradient enhances the buoyancy current and magnifies the asymmetric structure of the Changjiang River plume in summer. While the two non‐breaking wave mixing schemes are conceptually different, our modeling experiments suggest that they have similar effects on the plume structure.

Study of compressible turbulent plane Couette flows via direct numerical simulation

Compressible turbulent plane Couette flows are studied via direct numerical simulation for wall Reynolds numbers up to $Re_w=10\ 000$ and wall Mach numbers up to $M_w=5$ . Various turbulence statistics are compared with their incompressible counterparts at comparable semilocal Reynolds numbers $Re^*_{\tau,c}$ . The skin friction coefficient $C_f$ , which decreases with $Re_w$ , only weakly depends on $M_w$ . On the other hand, the thermodynamic properties (mean temperature, density and others) strongly vary with $M_w$ . Under proper scaling transformations, the mean velocity profiles for the compressible and incompressible cases collapse well and show a logarithmic region with the Kárman constant $\kappa =0.41$ . Compared with wall units, the semilocal units yield a better collapse for the profiles of the Reynolds stresses. While the wall-normal and spanwise Reynolds stress components slightly decrease in the near-wall region, the inner peak of the streamwise component notably increases with increasing $M_w$ – indicating that flow becomes more anisotropic when compressible. In addition, the near-wall turbulence production decreases as $M_w$ increases – due to rapid wall-normal changes of viscosity caused by viscous heating. The streamwise and spanwise energy spectra show that the length scale of near-wall coherent structures does not vary with $M_w$ in semilocal units. Consistent with those in incompressible flows, the superstructures (the large-scale streamwise rollers) with a typical spanwise scale of $\lambda _z/h\approx 1.5{\rm \pi}$ become stronger with increasing $Re_w$ . For the highest $Re_w$ studied, they contribute about $40\,\%$ of the Reynolds shear stress at the channel centre. Interestingly, flow visualization and correlation analysis show that the streamwise coherence of these structures degrades with increasing $M_w$ . In addition, at comparable $Re^*_{\tau,c}$ , the amplitude modulation of these structures on the near-wall small scales is quite similar between incompressible and compressible cases – but much stronger than that in plane Poiseuille flows.