Studies on Turbulence Parametrizations
for Flows with Helicity¹

R. Cieszelski

Institute for Tropospheric Research, Permoserstrasse 15, 04303 Leipzig, Germany

Received January 6, 1998; in final form, July 28, 1998

Abstract—A new class of turbulent kinetic energy (TKE) parametrization schemes is derived, which takes the
total of both the kinetic energy and helicity conservation of the mesoscale regime and of the subgrid turbulence
regime into account. The experiences with the new TKE parametrization scheme when applied in a nonhydro-
static mesoscale model are reported. The Reynolds tensor divergence of the grid-volume averaged form of the
Navier–Stokes equation is parametrized as suggested by Lautenschlager et al. (1988). For the subgrid turbu-
lence regime an equation of TKE following Mellor et al. (1974) is adapted and a novel equation of turbulent
helicity is derived. The resulting closed turbulent kinetic energy and helicity (TKEH) parametrization scheme
allows one to calculate the spectral fluxes of kinetic energy and of helicity between the mesoscale regime and
the subgrid turbulence regime interactively in a grid point model. The capabilities of the TKEH parametrization
scheme are demonstrated by two series of model calculations with a nonhydrostatic mesoscale model. With
TKEH parametrization schemes, features of the spectral processes of spectral kinetic energy cascade stabiliza-
tion and of large scale structure preservation can be successfully reestablished. It is demonstrated that calcu-
lated mesoscale vortices are stabilized by their self-sustained fields of TKE and of turbulent helicity, which
could not be realized with recent TKE parametrization schemes.

Pleiades Publishing home page | journal home page | top

If you have any problems with this server, contact webmaster.