9.3 Large Eddy Simulation (LES)
291
''A(,
l,l).fina~
Fig. 9.9. The stationary Richardson number as a function of the Reynolds number
of the turbulence), tends to become asymptotically constant with a value
of approximately 6 in homogeneous stratified sheared turbulence, at high
Reynolds numbers and for Richardson numbers below the stationary value.
For unstratified flow, this relation can be derived by assuming that production and dissipation are equal and the fact that, in shear flows, the structure
function b l 3 = iiZ/q2 tends to take a constant value of approximately 0.15.
These properties can be extremely useful in the construction of parameterization~ for these flows.
It also turns out that the gradient Richardson number is not a particularly good parameter for describing the local state of a stratified flow. The
turbulent F'roude number, defined by
performs better in this regard. It is therefore important to note that the turbulent F'roude number also tends asymptotically to a constant in stationary
stratified sheared homogeneous turbulence. This actually follows from the
facts that S* becomes constant and that the gradient Richardson number is
constant. This was demonstrated recently by Shih et al. (2000) and should
be useful in modeling. These authors also showed that the asymptotic value
of Frt is very close to the one which maximizes the mixing efficiency, the
fraction of the kinetic energy that is converted to potential energy.
291
''A(,
l,l).fina~
Fig. 9.9. The stationary Richardson number as a function of the Reynolds number
of the turbulence), tends to become asymptotically constant with a value
of approximately 6 in homogeneous stratified sheared turbulence, at high
Reynolds numbers and for Richardson numbers below the stationary value.
For unstratified flow, this relation can be derived by assuming that production and dissipation are equal and the fact that, in shear flows, the structure
function b l 3 = iiZ/q2 tends to take a constant value of approximately 0.15.
These properties can be extremely useful in the construction of parameterization~ for these flows.
It also turns out that the gradient Richardson number is not a particularly good parameter for describing the local state of a stratified flow. The
turbulent F'roude number, defined by
performs better in this regard. It is therefore important to note that the turbulent F'roude number also tends asymptotically to a constant in stationary
stratified sheared homogeneous turbulence. This actually follows from the
facts that S* becomes constant and that the gradient Richardson number is
constant. This was demonstrated recently by Shih et al. (2000) and should
be useful in modeling. These authors also showed that the asymptotic value
of Frt is very close to the one which maximizes the mixing efficiency, the
fraction of the kinetic energy that is converted to potential energy.