78
Jm6T A. BLJSINGER A N D S. P. S. ARYA
demonstrated. There are some problems which have to be resolved before
this method can be successfully employed for determining the detailed structure of the stable atmospheric boundary layer. For example, very little is
known about the proma of tramition franr turbulent to laminar flow due to
increasing stability. Thc usual clmure assumptions are not expected to
remain valid near the critical conditions.
The steady-state barotropic boundary layer is described by the following
equations of motion:
Here, a right-handed coordinate system is used for the Northern Hemisphere with s axis oriented in the direction of surface shear and z axis in the
vertical; ii and Z are the mean vclocity components in x and y directions;
uI = -( l/pf) 2p@y a d 3 = ( 1! [ $) ?p/ax are the two components of the
geostrophic wind; and u'w' and u'w' arc the components of thc momentum
flux.
Introducing an eddy viscosity K, such that
Eqs. (15) and (16). after differentiation ottce with respect to z, can be written
(19)
K, dZT,/dt2 + Tp = 0
as
(20)
K, d2Ty/dr2 - T, 91 0
in which the various dimensionkss variables are defined as
-
T, -u'w'/u:
-(21)
(22)
7 = -vpw'/u:
The dimensionless eddy viscosity K, is expected to be a function of { as
well as of stability. In many eddy viscosity models K,,, is prescribed explicitly
and somewhat arbitrarily. A more rational approach is to use the turbulent
energy equation for deriving an equation for K, (see. e.g., Monin, 1950;
Rlacklidar, 1962; Bobylcva et al., 1967; Peterson, 1969). This usually requires gross simplification or neglect of the turbulent transport terms and
parametrization of the energy dissipation in tttms of some length and velo-
Jm6T A. BLJSINGER A N D S. P. S. ARYA
demonstrated. There are some problems which have to be resolved before
this method can be successfully employed for determining the detailed structure of the stable atmospheric boundary layer. For example, very little is
known about the proma of tramition franr turbulent to laminar flow due to
increasing stability. Thc usual clmure assumptions are not expected to
remain valid near the critical conditions.
The steady-state barotropic boundary layer is described by the following
equations of motion:
Here, a right-handed coordinate system is used for the Northern Hemisphere with s axis oriented in the direction of surface shear and z axis in the
vertical; ii and Z are the mean vclocity components in x and y directions;
uI = -( l/pf) 2p@y a d 3 = ( 1! [ $) ?p/ax are the two components of the
geostrophic wind; and u'w' and u'w' arc the components of thc momentum
flux.
Introducing an eddy viscosity K, such that
Eqs. (15) and (16). after differentiation ottce with respect to z, can be written
(19)
K, dZT,/dt2 + Tp = 0
as
(20)
K, d2Ty/dr2 - T, 91 0
in which the various dimensionkss variables are defined as
-
T, -u'w'/u:
-(21)
(22)
7 = -vpw'/u:
The dimensionless eddy viscosity K, is expected to be a function of { as
well as of stability. In many eddy viscosity models K,,, is prescribed explicitly
and somewhat arbitrarily. A more rational approach is to use the turbulent
energy equation for deriving an equation for K, (see. e.g., Monin, 1950;
Rlacklidar, 1962; Bobylcva et al., 1967; Peterson, 1969). This usually requires gross simplification or neglect of the turbulent transport terms and
parametrization of the energy dissipation in tttms of some length and velo-