Direct simulation of a supersonic round turbulent shear layer

Utilizing an optically index-matched facility and high-resolution particle image velocimetry measurements, this paper examines flow structure and turbulence in a rough-wall channel flow forReτin the 3520–5360 range. The scales of pyramidal roughness elements satisfy the ‘well-characterized’ flow conditions, withh/k≈ 50 andk+= 60 ~ 100, wherehis half height of the channel andkis the roughness height. The near-wall turbulence measurements are sensitive to spatial resolution, and vary with Reynolds number. Spatial variations in the mean flow, Reynolds stresses, as well as the turbulent kinetic energy (TKE) production and dissipation rates are confined toy< 2k. All the Reynolds stress components have local maxima at slightly higher elevations, but the streamwise-normal component increases rapidly aty<k, peaking at the top of the pyramids. The TKE production and dissipation rates along with turbulence transport also peak near the wall. The spatial energy and shear spectra show an increasing contribution of large-scale motions and a diminishing role of small motions with increasing distance from the wall. As the spectra steepen at low wavenumbers, they flatten and develop bumps in wavenumbers corresponding tok− 3k, which fall in the dissipation range. Instantaneous realizations show that roughness-scale eddies are generated near the wall, and lifted up rapidly by large-scale structures that populate the outer layer. A linear stochastic estimation-based analysis shows that the latter share common features with hairpin packets. This process floods the outer layer with roughness-scale eddies, in addition to those generated by the energy-cascading process. Consequently, although the imprints of roughness diminish in the outer-layer Reynolds stresses, consistent with the wall similarity hypothesis, the small-scale turbulence contains a clear roughness signature across the entire channel.

Direct numerical simulation databases have been used to study the effect of compressibility on mixing layers. The simulations cover convective Mach numbers from 0.2 to 1.2 and all contain a fully resolved turbulent energy cascade to small spatial scales. Statistical information is extracted from the databases to determine reasons for the reduced growth rate that is observed as the convective Mach number is increased. It is found that the dilatational contribution to dissipation is negligible even when eddy shocklets are observed in the flow. Also pressure-dilatation is not found to be significant. Using an accurate relation between the momentum thickness growth rate and the production of turbulence kinetic energy together with integrated equations for the Reynolds stress tensor it is shown that reduced pressure fluctuations are responsible for the changes in growth rate via the pressure–strain term. A deterministic model for the required pressure fluctuations is given based on the structure of variable-density vortices and the assumption that the limiting eddies are sonic. Simple anisotropy considerations are used to close the averaged equations. Good agreement with turbulence statistics obtained from the simulations is found.

The aim of this study is to clarify the streamwise variation of the production terms for the three-dimensional turbulent air jet issuing from a quasi two-dimensional nozzle affected by the additional strain rate caused by the rectangular notch, and to examine the advection transport of the mean flow and the turbulent kinetic energy affected by the inward secondary flow. The Reynolds number based on the nozzle width and the exit mean velocity, was kept constant 13 000 through this experiment. From this experiment, it was revealed that adding the rectangular notch to the two-dimensional jet, the region of |∂U/∂y|≅0 was generated on the rectangular notch axis in the upstream region, therefore the production of turbulent kinetic energy was suppressed there. Furthermore, the turbulent kinetic energy on the y axis was transported toward the jet center region by the turbulent advection term, this is a reason of that the turbulent kinetic energy on the x axis took the maximum value at the section of x/d =45 which is more downstream section compared to that of the two-dimensional jet.

Near‐bed sediment pickup is critical for predictions of intrawave suspension and in turn net sediment transport in coastal models. In the present study, numerical results from a two‐dimensional Reynolds‐averaged Navier‐Stokes model are used to assess the functional relationship of intrawave ripple‐averaged sediment pickup above steep ripples. The numerical model provides intrawave time histories of ripple‐averaged near‐bed velocities and turbulence, which are qualitatively interrogated to determine pickup functional relationships. Several specific sediment pickup formulations are implemented within the numerical model: expressions relating pickup to near‐bed velocity or near‐bed turbulent kinetic energy via the bed shear stress; and expressions relating pickup to near‐bed shear production of turbulent kinetic energy. These are then tested via model‐data comparisons of near‐bed suspended sediment concentration. The results show that the traditional functions relating sediment pickup to near‐bed velocity cannot lead to reasonable intrawave suspension predictions above vortex ripples under a ripple‐averaged framework. Instead, relating sediment pickup to near‐bed turbulence quantities, such as turbulent kinetic energy or shear production of turbulent kinetic energy, significantly improves the numerical predictions for these conditions.

A detailed experimental examination of the turbulent kinetic energy budgets in a fully pulsed air jet exhausting into still air is presented. Through the pulse hot-wire anemometer measurements were made to obtain estimates of all measurable terms in the energy budget of the intrinsic or phase averaged turbulent kinetic energy. The region of measurements ranged from 50≤x/d≤70 which was previously identified to be the transition from pulse domination to steady jet behaviour. Pulsing was at very low Strouhal numbers to be in the quasi-steady jet regime. Measurements identified significant regions of negative production of turbulent kinetic energy as well as a domination of the energy budget by the time dependent term which is balanced by the advection term during the pulse. The pressure diffusion term is seen to play a significant role, changing from a positive contribution to a negative one as downstream distance increases. Axial diffusion of turbulent energy varies strongly with x/d but radial diffusion is almost self-similar for the region investigated. Results obtained have significant implications for application of turbulence models which have not yielded satisfactory predictions to date. This may be partly due to the finding that the ratio of production of turbulent kinetic energy to dissipation rate is much higher during the pulse dominated part of a cycle than is the case for steady jets thus invalidating a quasi-steady jet assumption which is contained in many model equations.

A study of the neutrally-stratified flow within and over an array of three-dimensional buildings (cubes) was undertaken using simple Reynolds-averaged Navier—Stokes (RANS) flow models. These models consist of a general solution of the ensemble-averaged, steady-state, three-dimensional Navier—Stokes equations, where the k-e turbulence model (k is turbulence kinetic energy and e is viscous dissipation rate) has been used to close the system of equations. Two turbulence closure models were tested, namely, the standard and Kato—Launder k-e models. The latter model is a modified k-e model designed specifically to overcome the stagnation point anomaly in flows past a bluff body where the standard k-e model overpredicts the production of turbulence kinetic energy near the stagnation point. Results of a detailed comparison between a wind-tunnel experiment and the RANS flow model predictions are presented. More specifically, vertical profiles of the predicted mean streamwise velocity, mean vertical velocity, and turbulence kinetic energy at a number of streamwise locations that extend from the impingement zone upstream of the array, through the array interior, to the exit region downstream of the array are presented and compared to those measured in the wind-tunnel experiment. Generally, the numerical predictions show good agreement for the mean flow velocities. The turbulence kinetic energy was underestimated by the two different closure models. After validation, the results of the high-resolution RANS flow model predictions were used to diagnose the dispersive stress, within and above the building array. The importance of dispersive stresses, which arise from point-to-point variations in the mean flow field, relative to the spatially-averaged Reynolds stresses are assessed for the building array.

A two-dimensional (i.e., laterally averaged) numerical model of the circulation in Burrard Inlet and Indian Arm near British Columbia, Canada, is used to examine the sensitivity of deep-water renewal events in Indian Arm to the turbulent mixing in the lee of the narrow sills in Burrard Inlet. Horizontal variations in the flow field can have an important influence on the production of turbulent kinetic energy near the sills and therefore also on the renewal events in Indian Arm. An ad hoc modification to the expression for the production of turbulent kinetic energy, required to obtain an acceptable simulation downstream of Second Narrows in Burrard Inlet, also results in a reasonable simulation of the observed circulation in Indian Arm. The modified laterally averaged model can reproduce the main features of the circulation away from the narrow sills. However, it seems that a three-dimensional model will be required if the circulation is to be simulated with greater accuracy and without the ad hoc modification, which has a free parameter.

With increasing implementation of renewable energy, planetary boundary layer (PBL) processes, including the effects of wind farm (WF), are gaining great attention. This research focuses on the dynamic interaction between WF and the PBL using the Weather Research and Forecasting Model based on a large-eddy simulation (WRF-LES), incorporating WF representation via the actuator disc model. A range of stability conditions, from unstable to stable stratification, are examined along with various wind turbine arrangements.The results show a significant effect of WF on increasing turbulent kinetic energy (TKE) above the hub-height level under stably stratified to near-neutrally stratified conditions. In contrast, the effect is not profound in the case of unstable stratification.Three key WF impacts on TKE production can be identified: the effect on mean momentum equation, effect on TKE production due to the WF thrust term, and correction of the length scale. TKE budget analysis reveals that the direct effect of the WF thrust term to TKE production or dissipation is minimal. This implies that the WF effect on TKE production largely depends on the mean-wind profile modulation, increasing shear-production of the TKE. In the case of stably stratified and near-neutrally stratified conditions, the local wind deficits around WT hub height is large. In contrast, the wind speed is entirely decelerated over the boundary layer in case of unstable stratification. This explains why the WF effect is reduced under unstable stratification, where buoyancy-induced mixing dominates over mechanical shear. The length-scale characteristics of the PBL scheme are discussed in terms of how WF modify it.

Direct numerical simulations of high-speed mixing layers are used to characterize the effects of compressibility on the basis of local streamline topology and vortical structure. Temporal simulations of the mixing layers are performed using a finite volume gas-kinetic scheme for convective Mach numbers ranging from $M_{c}=0.2$ to $M_{c}=1.2$. The focus of the study is on the transient development and the main objectives are to (i) investigate and characterize the turbulence suppression mechanism conditioned upon local streamline topology; and (ii) examine changes in the vortex vector field – distribution, magnitude and orientation – as a function of Mach number. We first reaffirm that kinetic energy suppression with increasing Mach number is due to a decrease in pressure–strain redistribution. Then, we examine the suppression mechanism conditioned upon topology and vortex structure. Conditional statistics indicate that (i) at a given Mach number, shear-dominated topologies generally exhibit more effective pressure–strain redistribution than vortical topologies; and (ii) for a given topology, the level of pressure–strain correlation mostly decreases with increasing Mach number. At each topology, with increasing Mach number, there is a corresponding decrease in turbulent shear stress and production leading to reduced kinetic energy. Further, as $M_{c}$ increases, the proportion of vortex-dominated regions in the flow increases, leading to further reduction in the turbulent kinetic energy of the flow. Then, the orientation of vortical structures and direction of fluid rotation are examined using the vortex vector approach of Tian et al. (J. Fluid Mech., vol. 849, 2018, pp. 312–339). At higher $M_{c}$, the vortex vectors tend to be more aligned in the streamwise direction in contrast to low $M_{c}$ wherein larger angles with streamwise direction are preferred. The connection between vortex orientation and kinetic energy production is also investigated. The findings lead to improved insight into turbulence suppression dynamics in high Mach number turbulent flows.

We analyze a one-equation model for the turbulent kinetic energy of an open channel flow in the presence of suspension sediment. Engelund's pioneer analysis and his criterion for the threshold conditions for the initiation of suspension are revisited, and it is concluded that such criterion does not represent any physical response of the system under consideration, but rather appears to be an artifact of the mathematical manipulations of the turbulent energy equation. The present analysis indicates that the effect of the suspended sediment on the turbulent kinetic energy near the bed is to reduce such energy when the particle size is sufficiently small, and that the reduction increases with the sediment concentration and the particle settling velocity to flow shear velocity ratio. On the other hand, suspended particles of larger size can enhance the turbulence of the flow because of the production of turbulent kinetic energy through vortex shedding mechanisms. A criterion is proposed to estimate the conditions for which turbulent enhancement due to the presence of suspended sediment occurs.

This paper presents experimental investigation of upstream roughness and Reynolds number effects on the recirculation region over a smooth forward facing step. The upstream rough wall was produced from 1.5 mm sand grains and the Reynolds number based on step height, Reh, was varied from 2040 to 9130 for both the upstream smooth and rough walls. For the smooth wall, the reattachment length increased monotonically with Reh to an asymptotic value of 2.2 step heights for Reh ≥ 6380. Upstream roughness reduced the reattachment length by 44% because of larger momentum deficit and higher turbulence level in the rough wall boundary layer. The mean velocities and Reynolds stresses were also reduced by roughness. The Reynolds shear stress and production of turbulent kinetic energy showed high negative values at the leading edge of the step indicating counter-gradient diffusion. The implications of these results for standard eddy viscosity models are discussed.

A full Reynolds stress tensor model for rough wall turbulent flow is developed and presented in this paper. The basis for the model development is a two-phase averaging approach wherein the rough solid boundary is treated as the second phase. This approach leads to a set of averaged equations similar to the canonical Reynolds averaged equations, but which contain additional terms reflecting the inclusion of the roughness. The full stress model is developed from a variant of the Speziale, Sakar annd Gatski model. The primary modifications are the addition of a model for the production of turbulent stresses and kinetic energy by the roughness elements and a modification to the pressure strain modeling near the wall. The model is then reduceed to a k model. In the k model, the eddy viscosity model contain an additional term representing the roughness production of turbulence. The model is calibrated by reference to established equivalent sand grain roughness scaling.

Abstract. Observed and projected trends in large-scale wind speed over the oceans prompt the question: how do marine stratocumulus clouds and their radiative properties respond to changes in large-scale wind speed? Wind speed drives the surface fluxes of sensible heat, moisture, and momentum and thereby acts on cloud liquid water path (LWP) and cloud radiative properties. We present an investigation of the dynamical response of non-precipitating, overcast marine stratocumulus clouds to different wind speeds over the course of a diurnal cycle, all else equal. In cloud-system resolving simulations, we find that higher wind speed leads to faster boundary layer growth and stronger entrainment. The dynamical driver is enhanced buoyant production of turbulence kinetic energy (TKE) from latent heat release in cloud updrafts. LWP is enhanced during the night and in the morning at higher wind speed, and more strongly suppressed later in the day. Wind speed hence accentuates the diurnal LWP cycle by expanding the morning–afternoon contrast. The higher LWP at higher wind speed does not, however, enhance cloud top cooling because in clouds with LWP ⪆ 50 g m−2, longwave emissions are insensitive to LWP. This leads to the general conclusion that in sufficiently thick stratocumulus clouds, additional boundary layer growth and entrainment due to a boundary layer moistening arises by stronger production of TKE from latent heat release in cloud updrafts, rather than from enhanced longwave cooling. We find that large-scale wind modulates boundary layer decoupling. At nighttime and at low wind speed during daytime, it enhances decoupling in part by faster boundary layer growth and stronger entrainment and in part because shear from large-scale wind in the sub-cloud layer hinders vertical moisture transport between the surface and cloud base. With increasing wind speed, however, in decoupled daytime conditions, shear-driven circulation due to large-scale wind takes over from buoyancy-driven circulation in transporting moisture from the surface to cloud base and thereby reduces decoupling and helps maintain LWP. The total (shortwave + longwave) cloud radiative effect (CRE) responds to changes in LWP and cloud fraction, and higher wind speed translates to a stronger diurnally averaged total CRE. However, the sensitivity of the diurnally averaged total CRE to wind speed decreases with increasing wind speed.

Adverse pressure gradient (APG) effects are investigated for the turbulent boundary layer (TBL) developing over the suction side of a NACA0012 at 12 deg. angle of attack. Spatio-temporal data is obtained from a wall-resolved large-eddy simulation (LES) conducted at Reynolds number Re = 400,000 and freestream Mach number M=0.2, where the boundary layer is tripped near the leading edge to induce bypass transition. Despite the high angle of attack, the mean flow remains attached throughout the airfoil suction side. A quadrant-splitting analysis is performed to investigate the effects of coherent motions (sweeps, ejections, inward and outward interactions) on momentum balance and the production of turbulent kinetic energy (TKE). The results demonstrate that sweeps are the greatest contributor for the inner peak of TKE production and transport of momentum from the mean flow to the fluctuation field, while ejections affect mainly the outer region, near the boundary layer edge.

The oblique shock impinging on the supersonic turbulent boundary layer leads to a mixing layer and the emergence of large-scale coherent structures within the interaction zone which leave significant velocity defect and turbulence amplification downstream. In the present study, we investigate the turbulence recovery in the post-shock region by exploiting direct numerical simulation data of the oblique-shock/turbulent boundary layer interaction flow at the incoming Mach number of $2.28$ and the shock angle of $33.2^\circ$ , with special attention paid to the contribution of the mixing layer and large-scale structures to flow dynamics. For that purpose, we propose to split the mean velocity, Reynolds stresses and spanwise spectra into a canonical portion that is constructed according to the statistics of canonical turbulent boundary layers, and a mixing-layer-induced portion. We found that the hidden mixing layer grows with the boundary layer thickness and that the induced mean shear and Reynolds stresses decay at different rates. The mean velocity recovers to the canonical profiles at a distance of 13 boundary layer thicknesses downstream where the mixing-layer-induced mean shear ceases to have strong impacts. The recovery of Reynolds stresses requires 10 boundary layer thicknesses in the near-wall region but a much longer streamwise extent in the outer region due to the slow decay of large-scale motions. These large-scale motions superpose on the near-wall turbulence, intensifying the turbulent fluctuations, yet having a trivial impact on the skin friction, for the contribution of the mixing-layer-induced mean shear and Reynolds shear stress are balanced by the advection term. We further establish a simple physical model capable of approximately predicting the streamwise evolution of mixing-layer-induced mean shear and turbulent kinetic energy. This model suggests that the complete recovery of turbulence in the outer region requires a streamwise extent of approximately 50 boundary layer thicknesses.