TURBULENCE MODELS FOR WIND STORMS INDUCED BY GRAVITY WAVES

In this paper, the atmospheric code SUBMESO which resolves the compressible Navier Stokes equat ions with turbulence models adapted to stably stratified flows is applied on the Boulder wind storm, 1972 (Lilly and Zipse r, 1972). We take particular care over the reduction of the discretisation errors (not shown here).

I. Turbulence models for stably stratified flows

Two new type of statistical first-order closure models have been developed in Abart and Sini, 1997
aimed to predict the intense impact of stable stratification on turbulence. The method to build the present turbulence mod
els is based on the modelling of the turbulence anisotropy due to stratification and the exchange of turbulent kinetic ene
rgy and potential energy by means of the vertical heat flux. The first closure model for stable stratification is composed
by five prognostic equations for the turbulent kinetic energy k, its dissipation range e, the
vertical turbulent kinetic energy , the vertical heat flux and the potential energy . The three last equations are issued
from the quadratic second order model of Craft and Launder,1991. The bidimensionalisation properties of the turbulence ob
served in stably stratified flows are used to close the other turbulence correlations (Reynolds stresses and heat fluxes).
The difference between this first model and the new k-e-Ri_{u} one consists in the use
of an experimental correlation based on the experiment of Yoon and Warhaft, 1990. This correlation prescribe the ratio be
tween and by use of the horizontal turbu
lent Richardson number where is the hor
izontal turbulence length scale defined as . To add, is closed by an algebraic formulation without need of .

These two first-order models have been validated on flows where stratification is dynamically activ e. They are some valuable competitive of the second-order models because of their physical accuracy, their lower CPU time consumption and higher numerical stability than those lasts.

II. The Boulder wind storm, 1972

On January 1972, the eastern slope of the Rocky Mountains experienced a severe Chinook windstorm du e to gravity waves induced by stable stratification. Wind speeds higher than 50 m/s were recorded in the populated areas o f Boulder. Compared to the measurements and the previous simulations of this storm (the more recent is Thunis, 1997), SUBM ESO achieves rather good results thanks to its new discretisation schemes and to the turbulence models. It describes the u nstationarity and the intensity of the storm (see Figure 1). The choice of the turbulence model is particularly important in the breaking zone (see Figure 2).

References

B. Abart and J.-F. Sini, "New first-order closure models for stably stratified flows," *Proceedin
gs of Eleventh Symposium on Turbulent Shear Flows*, p. 2-1 (1997).

T.J. Craft and B.E. Launder, "Computation of impinging flows using second-moment closures," *Proceedi
ngs of Eighth Symposium on Turbulent Shear Flows*, p. 8-5-1 (1991).

K. Yoon and Z. Warhaft, "The evolution of grid-generated turbulence under conditions of stable thermal stratification," J. Fluid Mech. 215, 601 (1990).

G.L. Mellor and T. Yamada, "Development of a turbulence closure model for geophysical fluid problems," Reviews of Geophysics and Space Physics 20, p. 851 (1982).

G. Schayes, P. Thunis and R. Bornstein, "Topographic Vorticity-Mode Mesoscale-b (TVM) Model. Part I: Fo rmulation," J. Applied Meteorology 35, p. 1815-1823 (1996).

D.K. Lilly and E.J. Zipser, "The front range wind storm of 11 January 1972. A meteorological narrative, " Weatherwise 25, p 56-63.

P. Thunis, "Formulation of a nonhydrostatic vorticity model (TVM), and application to topographic waves and to the 1972 Boulder wind storm, " modified to J. Atmospheric Sciences (June 1997).

Figure 1: From top to bottom: 221*43 grid; horizontal velocity and potential temperature after 1h; then the same after 2h (time of maximum of wind intensity on Boulder).

Figure 2: Turbulent kinetic energy from k-e-Ri_{u} model after 1h an
d 2h of integration.