NUMERICAL COMPUTATION OF
TURBULENT SHEAR FLOWS'
1. 1 NTRODUCTION
In this paper, we report simulations of turbulent shear flows by direct
numerical solution of the three-dimensional Navier-Stokes equations. This
approach provides several advantages over more conventional approaches.
First, the complete flow field is obtained at all times so that detailed flow
characteristics may be obtained that would be difficult to measure in the
laboratory. Second. initial conditions can be accurately controlled so that
their effect may be determined. Third, numerical simulations are convenient
experiments to assess the effect of various physical processes, like chemical
reactions, on turbulence and vice versa. Fourth, the simulation results can be
used to test and suggest various statistical hypotheses involved in turbulence
models and theories.
The present work is an extension to inhomogeneous shear flows of the
t hrec-dimensional. homogeneous, isotropic turbulence simulations reported
by Orszag and Patterson (1972). In this earlier work. simulations using up to
(32)j Fourier modes to represent each velocity component were performed
at microscale Reynolds numbers 20-50 (grid Reynolds numbers
5000 30,000), corresponding to moderate Reynolds number grid turbulence.
The results of these homogeneous turbulence simulations agreed well with
both turbulence theory (e.g., the direct interaction approximation) and laboratory experiments. Simulations have also been made of two-dimensional
"turbuleiice" using up to (128)' Fourier modes (Herring et al., 1974) with
successful comparisons with the results of turbulence theories. These successful simulations gave impetus to the present extension to shear flows.
Jn the homogeneous turbulence simulations, it was observed that some
important features of the flows were Reynolds number independent (Herring
er ul., 1974). so that there is basis for assuming that the large-scale features of
' 'This work is supported by Fluid Dynamics Branch, Office of Naval Research under Navy
('ontract No. NOOO14-72-C-0355, ONR Task No. NR 062-464 and the Climatic Impact
Awwncnt Prngram, Ikpartment of Transportation under Contract DOT-AS-30041.
225
TURBULENT SHEAR FLOWS'
1. 1 NTRODUCTION
In this paper, we report simulations of turbulent shear flows by direct
numerical solution of the three-dimensional Navier-Stokes equations. This
approach provides several advantages over more conventional approaches.
First, the complete flow field is obtained at all times so that detailed flow
characteristics may be obtained that would be difficult to measure in the
laboratory. Second. initial conditions can be accurately controlled so that
their effect may be determined. Third, numerical simulations are convenient
experiments to assess the effect of various physical processes, like chemical
reactions, on turbulence and vice versa. Fourth, the simulation results can be
used to test and suggest various statistical hypotheses involved in turbulence
models and theories.
The present work is an extension to inhomogeneous shear flows of the
t hrec-dimensional. homogeneous, isotropic turbulence simulations reported
by Orszag and Patterson (1972). In this earlier work. simulations using up to
(32)j Fourier modes to represent each velocity component were performed
at microscale Reynolds numbers 20-50 (grid Reynolds numbers
5000 30,000), corresponding to moderate Reynolds number grid turbulence.
The results of these homogeneous turbulence simulations agreed well with
both turbulence theory (e.g., the direct interaction approximation) and laboratory experiments. Simulations have also been made of two-dimensional
"turbuleiice" using up to (128)' Fourier modes (Herring et al., 1974) with
successful comparisons with the results of turbulence theories. These successful simulations gave impetus to the present extension to shear flows.
Jn the homogeneous turbulence simulations, it was observed that some
important features of the flows were Reynolds number independent (Herring
er ul., 1974). so that there is basis for assuming that the large-scale features of
' 'This work is supported by Fluid Dynamics Branch, Office of Naval Research under Navy
('ontract No. NOOO14-72-C-0355, ONR Task No. NR 062-464 and the Climatic Impact
Awwncnt Prngram, Ikpartment of Transportation under Contract DOT-AS-30041.
225