Abstract
Within the framework of a mixed layer (ML) containing a zero-order jump, the concept of ML is generalized for the case of horizontal non-homogeneity on the assumption that not only potential temperature, but also the wind does not change with height. It turns out that the components of the vertical turbulent stresses are quadratic functions of height.
For such a well-mixed layer (WML), bounded below by uneven terrain with an adjacent surface layer, and above — by a stably stratified quasigeostrophic baroclinic atmosphere, a consistent system of equations with all terms independent of height, is obtained. This can be considered as a meteorological generalization of the known shallow-water equations.
As an example of the use of these equations, an analytical solution of the large-scale one-dimensional steady-state problem concerning the development of the WML in a stable stratified barotropic air mass moving over a heated horizontal surface has been found.
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Gutman, L.N., Berkofsky, L. On the theory of the well-mixed layer containing a zero-order jump. Boundary-Layer Meteorol 31, 287–301 (1985). https://doi.org/10.1007/BF00120897
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DOI: https://doi.org/10.1007/BF00120897