A multi-limit formulation for the equilibrium depth of a stably stratified boundary layer |
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| Authors: | Sergej Zilitinkevich Dmitrii V Mironov |
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| Institution: | (1) Alfred Wegener Institute for Polar and Marine Research, Am Handelshafen 12, 27570 Bremerhaven, Germany;(2) Max Planck Institute for Meteorology, Bundesstr. 55, 20146 Hamburg, Germany |
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| Abstract: | Currently no expression for the equilibrium depth of the turbulent stably-stratified boundary layer is available that accounts
for the combined effects of rotation, surface buoyancy flux and static stability in the free flow. Various expressions proposed
to date are reviewed in the light of what is meant by the stable boundary layer. Two major definitions are thoroughly discussed.
The first emphasises turbulence and specifies the boundary layer as a continuously and vigorously turbulent layer adjacent
to the surface. The second specifies the boundary layer in terms of the mean velocity profile, e.g. by the proximity of the
actual velocity to the geostrophic velocity. It is shown that the expressions based on the second definition are relevant
to the Ekman layer and portray the depth of the turbulence in the intermediate regimes, when the effects of static stability
and rotation essentially interfere. Limiting asymptotic regimes dominated by either stratification or rotation are examined
using the energy considerations. As a result, a simple equation for the depth of the equilibrium stable boundary layer is
developed. It is valid throughout the range of stability conditions and remains in force in the limits of a perfectly neutral
layer subjected to rotation and a rotation-free boundary layer dominated by surface buoyancy flux or stable density stratification
at its outer edge. Dimensionless coefficients are estimated using data from observations and large-eddy simulations. Well-known
and widely used formulae proposed earlier by Zilitinkevich and by Pollard, Rhines and Thompson are shown to be characteristic
of the above interference regimes, when the effects of rotation and static stability (due to either surface buoyancy flux,
or stratification at the outer edge of the boundary layer) are roughly equally important. |
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| Keywords: | Stable Boundary Layer Boundary-Layer Depth |
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