Effect of compressibility on inhomogeneous planar shear flows: Reynolds stress evolution dynamics

2018 ◽  
Author(s):  
Rebecca L. Bertsch ◽  
Divya Sri Praturi ◽  
Sharath S. Girimaji
Keyword(s):  
Reynolds Stress ◽  
Shear Flows ◽  
Stress Evolution ◽  
Planar Shear ◽  
Evolution Dynamics

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).

scholarly journals Spanwise-localized solutions of planar shear flows

2014 ◽  
Vol 745 ◽  
pp. 25-61 ◽  
Author(s):  
J. F. Gibson ◽  
E. Brand
Keyword(s):  
Channel Flow ◽  
Shear Flows ◽  
Travelling Wave ◽  
Wall Region ◽  
Travelling Wave Solutions ◽  
Simulation Data ◽  
Localized Solutions ◽  
Wave Solutions ◽  
Planar Shear ◽  
Near Wall

AbstractWe present several new spanwise-localized equilibrium and travelling-wave solutions of plane Couette and channel flows. The solutions exhibit concentrated regions of vorticity that are centred over low-speed streaks and flanked on either side by high-speed streaks. For several travelling-wave solutions of channel flow, the vortex structures are concentrated near the walls and form particularly isolated and elemental versions of coherent structures in the near-wall region of shear flows. One travelling wave appears to be the invariant solution corresponding to a near-wall coherent structure educed from simulation data by Jeong et al. (J. Fluid Mech., vol. 332, 1997, pp. 185–214) and analysed in terms of transient growth modes of streaky flow by Schoppa & Hussain (J. Fluid Mech., vol. 453, 2002, pp. 57–108). The solutions are constructed by a variety of methods: application of windowing functions to previously known spatially periodic solutions, continuation from plane Couette to channel flow conditions, and from initial guesses obtained from turbulent simulation data. We show how the symmetries of localized solutions derive from the symmetries of their periodic counterparts, analyse the exponential decay of their tails, examine the scale separation and scaling of their streamwise Fourier modes, and show that they develop critical layers for large Reynolds numbers.

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