Untitled

Abstract

Reynolds stress budgets for both Couette and boundary layer flows are evaluated and presented. Data are taken from direct numerical simulations of rotating and non-rotating plane turbulent Couette flow and turbulent boundary layer with and without adverse pressure gradient. Comparison of the total shear stress for the two types of flows suggests that the Couette case may be regarded as the high Reynolds number limit for the boundary layer flow close to the wall. The limit values of turbulence statistics close to the wall for the boundary layer for increasing Reynolds number approach the corresponding Couette flow values. The direction of rotation is chosen so that it has a stabilizing effect, whereas the adverse pressure gradient is destabilizing. The pressure-strain rate tensor in the Couette flow case is presented for a split into slow, rapid and Stokes terms. Most of the influence from rotation is located to the region close to the wall, and both the slow and rapid parts are affected. The anisotropy for the boundary layer decreases for higher Reynolds number, reflecting the larger separation of scales, and becomes close to that for Couette flow. The adverse pressure gradient has a strong weakening effect on the anisotropy. All of the data presented here are available on the web [36].

Reynolds number effects on the Reynolds-stress budgets in turbulent channels

“…Experimental difficulties prevented for a long time the determination of many of the quantities involved, and it was not until the first direct numerical simulation of a turbulent channel 1 that reliable budgets of the Reynolds-stress tensor could be obtained. 2 After that pioneering paper, budgets have been published for other numerical flows, [3][4][5][6][7][8][9] but they have usually been limited to relatively low Reynolds numbers by the resolution of the simulations.…”

Reynolds number effects on the fluctuating velocity distribution in wall-bounded shear layers

“…Örlü and Schlatter [11] attributed this effect to the growing influence of the large-scale turbulence structures and their impact on the wall-shear stress. By assessing various numerical simulation data of turbulent boundary layers, [47]; pentacle (☆), Wu and Moin [48]; circle (○), Schlatter and Örlü [30]; Channel flow DNS results: delta (Δ), Iwamoto et al [49]; gradient (∇), Hu et al [50]; right triangle (⊳), Abe et al [51]; left triangle (⊲), Del Alamo et al [52]; Turbulent boundary layer results: cross (+), PIV results by de Silva et al [13]; asterisk ( * ), Österlund [42] hot-wire results corrected by Örlü and Schlatter [11] showing the wall-shear stress fluctuation to increase at growing Reynolds number. However, due to the difficulty in measuring the wall-shear stress fluctuation accurately, only a few experimental investigations reported this effect.…”

“…Wall-shear stress fluctuation distribution as a function of the momentum thickness based Reynolds number Re θ . Turbulent boundary layer DNS results: diamond ( ⃟ ), Komminaho and Skote[47]; pentacle (☆), Wu and Moin[48]; circle (○), Schlatter and Örlü[30]; Channel flow DNS results: delta (Δ), Iwamoto et al[49]; gradient (∇), Hu et al[50]; right triangle (⊳), Abe et al[51]; left triangle (⊲), Del Alamo et al[52]; Turbulent boundary layer results: cross (+), PIV results by de Silva et al[13]; asterisk ( * ), Österlund[42] hot-wire results corrected by Örlü and Schlatter[11]; red bullet point (•), present µ-PTV results, error bar indicates the standard deviation of /…”

A general optimal formulation for the dynamic Smagorinsky subgrid-scale stress model

“…Turbulent Couette ow is a canonical test problem for wall-bounded anisotropic turbulence, which has been studied both experimentally [38][39][40][41][42][43] and numerically [13,[43][44][45][46][47][48][49]. The transitional Reynolds number (lowest Reynolds number for which turbulence can be sustained) for Couette ow is Re T ≈ 600 according to Leutheusser and Chu [39], while Re T ≈ 720 (or Re T ≈ 26) according to other studies [42][43][44][45].…”

“…By substituting the above equation into Equation (43) and averaging the result in the homogeneous plane, the following discrete system can be obtained: which can be readily solved using the conventional tri-diagonal matrix algorithm (TDMA). Here, A J q and S J represent the coe cients and source term contained in Equation (49). The boundary condition is set as C S = 0 at the wall.…”