A turbulence velocity scale for curved shear flows

1975 ◽  
Vol 70 (1) ◽  
pp. 37-57 ◽  
Author(s):  
Ronald M. C. So
Keyword(s):  
Reynolds Stress ◽  
Shear Flows ◽  
Turbulent Energy ◽  
Streamline Curvature ◽  
Velocity Scale ◽  
Dimensional Boundary ◽  
Free Constant ◽  
Turbulence Velocity ◽  
Turbulence Length ◽  
Energy Balances

Assuming the turbulence length scale to be unaffected by streamline curvature, a turbulence velocity scale for curved shear flows is derived from the Reynolds-stress equations. Closure of the equations is obtained by using the scheme of Mellor & Herring (1973), and the Reynolds-stress equations are simplified by invoking the two-dimensional boundary-layer approximations and assuming that production of turbulent energy balances viscous dissipation. The resulting formula for the velocity scale has one free parameter, but this can be determined from data for non-rotating unstratified plane flows. Consequently there is no free constant in the derived expression. A single value of the constant is found to give good agreement between calculated and measured values of the velocity scale for a wide variety of curved shear flows.The result is also applied to test the validity and extent of the analogy between the effects of buoyancy and streamline curvature. This is done by comparing the present result with that obtained by Mellor (1973). Excellent agreement is obtained for the range −0·21 [les ]Rif[les ] 0·21. Therefore the present result provides direct evidence in support of the use of a Monin–Oboukhov (1954) formula for curved shear flows as proposed by Bradshaw (1969).

A Numerical Investigation to Study Roughness Effects in Oscillatory Flows

2017 ◽  
Author(s):  
Chaitanya D. Ghodke ◽  
Sourabh V. Apte
Keyword(s):  
Shear Rate ◽  
Reynolds Stress ◽  
Large Diameter ◽  
Turbulent Energy ◽  
Sand Particle ◽  
Roughness Effects ◽  
Oscillatory Flows ◽  
Wake Field ◽  
Double Averaging ◽  
Acceleration Cycle

Effects of roughness on the near-bed turbulence characteristics in oscillatory flows are studied by means of particle-resolved direct numerical simulations (DNS). Two particle sizes of diameter 375 and 125 in wall units corresponding to the large size gravel and the small size sand particle, respectively, in a very rough turbulent flow regime are reported. A double-averaging technique is employed to study the nature of the wake field, i.e., the spatial inhomogeneities at the roughness length scale. This introduced additional production and transport terms in double-averaged Reynolds stress budget, indicating alternate pathways of turbulent energy transfer mechanisms. Budgets of normal components of Reynolds stress reveal redistribution of energy from streamwise component to other two components and is attributed to the work of pressure in both flow cases. It is shown that the large diameter gravel particles significantly modulate the near-bed flow structures, leading to pronounced isotropization of the near-bed flow; while in the sand case, elongated horseshoe structures are found as a result of high shear rate. Effect of mean shear rate on the near-bed anisotropy is significant in the sand case, while it is minimal for the gravel-bed. Redistribution of energy in the gravel case showed reduced dependence on the flow oscillations, while for the sand particle it is more pronounced towards the end of an acceleration cycle.

scholarly journals Simulating Real Atmospheric Boundary Layers at Gray-Zone Resolutions: How Do Currently Available Turbulence Parameterizations Perform?

Atmosphere ◽  
2020 ◽  
Vol 11 (4) ◽  
pp. 345 ◽  
Author(s):  
Paula Doubrawa ◽  
Domingo Muñoz-Esparza
Keyword(s):  
Boundary Layer ◽  
Turbulent Transport ◽  
Model Performance ◽  
Wrf Model ◽  
Turbulent Energy ◽  
Complex Problem ◽  
Gray Zone ◽  
Horizontal Structure ◽  
One Dimensional ◽  
Dimensional Boundary

Recent computational and modeling advances have led a diverse modeling community to experiment with atmospheric boundary layer (ABL) simulations at subkilometer horizontal scales. Accurately parameterizing turbulence at these scales is a complex problem. The modeling solutions proposed to date are still in the development phase and remain largely unvalidated. This work assesses the performance of methods currently available in the Weather Research and Forecasting (WRF) model to represent ABL turbulence at a gray-zone grid spacing of 333 m. We consider three one-dimensional boundary layer parameterizations (MYNN, YSU and Shin-Hong) and coarse large-eddy simulations (LES). The reference dataset consists of five real-case simulations performed with WRF-LES nested down to 25 m. Results reveal that users should refrain from coarse LES and favor the scale-aware, Shin-Hong parameterization over traditional one-dimensional schemes. Overall, the spread in model performance is large for the cellular convection regime corresponding to the majority of our cases, with coarse LES overestimating turbulent energy across scales and YSU underestimating it and failing to reproduce its horizontal structure. Despite yielding the best results, the Shin-Hong scheme overestimates the effect of grid dependence on turbulent transport, highlighting the outstanding need for improved solutions to seamlessly parameterize turbulence across scales.

A Three Equation Curvature and Rotation Sensitive Variant of the SST K-Omega Turbulence Model

2010 ◽  
Author(s):  
Tej Prasad Dhakal ◽  
D. Keith Walters
Keyword(s):  
Transport Equation ◽  
Eddy Viscosity ◽  
Reynolds Stress Model ◽  
Turbulent Velocity ◽  
Turbulence Structure ◽  
New Model ◽  
Streamline Curvature ◽  
History Effects ◽  
System Rotation ◽  
Velocity Scale

To date, eddy viscosity models are the most accepted and widely used RANS-based turbulence closures, attributable to their computational efficiency and relative robustness. One notable shortcoming of these models is their insensitivity to system rotation and streamline curvature. In this article, we present a variation of the SST k-ω model properly sensitized to system rotation and streamline curvature. The new model is based on a direct simplification of the Reynolds Stress Model under weak equilibrium conditions. To enhance stability and include history effects, an additional transport equation for a transverse turbulent velocity scale is added to the model. The new transport equation incorporates the physical effect of curvature and rotation on the turbulence structure. The eddy viscosity is then redefined based on the new turbulent velocity scale. The model is calibrated based on rotating homogeneous shear flow and implemented for a number of test cases including rotating channel, U-duct, and hump model flow. Compared to popular two equation models, the new model shows improved performance in system rotation and/or streamline curvature dominated flows.

Turbulence characteristics of the boundary layer on a rotating disk

1994 ◽  
Vol 266 ◽  
pp. 175-207 ◽  
Author(s):  
Howard S. Littell ◽  
John K. Eaton
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Reynolds Stress ◽  
Structural Model ◽  
Rotating Disk ◽  
Two Dimensional ◽  
Mean Flow ◽  
Velocity Correlation ◽  
Dimensional Boundary ◽  
The Mean

Measurements of the boundary layer on an effectively infinite rotating disk in a quiescent environment are described for Reynolds numbers up to Reδ2 = 6000. The mean flow properties were found to resemble a ‘typical’ three-dimensional crossflow, while some aspects of the turbulence measurements were significantly different from two-dimensional boundary layers that are turned. Notably, the ratio of the shear stress vector magnitude to the turbulent kinetic energy was found to be at a maximum near the wall, instead of being locally depressed as in a turned two-dimensional boundary layer. Also, the shear stress and the mean strain rate vectors were found to be more closely aligned than would be expected in a flow with this degree of crossflow. Two-point velocity correlation measurements exhibited strong asymmetries which are impossible in a two-dimensional boundary layer. Using conditional sampling, the velocity field surrounding strong Reynolds stress events was partially mapped. These data were studied in the light of the structural model of Robinson (1991), and a hypothesis describing the effect of cross-stream shear on Reynolds stress events is developed.

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