HEIGHT OF THE MIXED LAYER IN THE
STABLY STRATIFIED PLANETARY
BOUNDARY LAYER
JWST A. BLJSINGER AND s. P. s. ARYA
Drpurfwnr of Atmospheric Sciences
L’niivrsitv of Washirylton, Swtle, Washington 98195. U.S.A.
1. INTRODUCTION
The modeling of the stable boundary layer is difficult because usually a
transition from turbulent to laminar flow takes place with increasing height.
Consequent I). because the processes under laminar conditions are very
slow, steady state is usually not reached in the laminar region but may be
approached in the turbulent region. Complex transient interactions between
the laminar and turbulent regimes may occur. In this paper an attempt is
made to formulate a steady-state stable boundary layer which in reality may
occur only after a very long time, possibly during the polar night in the
arctic. Nevertheless, it is felt that having a reasonable steady-state model
may help us in understanding the more complex real case in a qualitative
way.
2. DIAtiNOSTIC ELEMENTS TO THE PROBLEM
The entire boundary layer may be laminar provided the stratification is
sufficiently stable. This requires a rather extreme condition if we assume that
the Richardson number must be larger than 0.25. To illustrate this point, let
us assume a light geostrophic wind G = 1 m sec-’. The maximum shear
which occurs at the surface is then
(1)
(fi/&)o = ( f l 2 ~ ) ’ ’ ~ G
where /’is the Coriolis parameter (about 10 -'set- I ) and 11 is the kinematic
viscosity for air (about 0.15 cm2 sec-I). In order that
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