HELMHOLTZ WAVES IN A LINEAR TEMPERATURE FIELD WITH VERTICAL WIND SHEAR

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Abstract
Solberg's theory of oscillations and waves of short wave length unaffected by the earth's rotation in an atmosphere with a linear temperature field is extended for a vertical wind shear. Under normal conditions in the atmosphere this extension means only a small and insignificant correction of Solberg's theory provided the wind velocity is different from the wave velocity. If the wave velocity is equal to the wind velocity in a particular level then the theory presented in this paper requires an adiabatic or superadiabatic temperature gradient in the layer containing this particular level. This theory, applied to the theory of billow clouds generalized for the case when the sharp discontinuity is replaced by a transition layer with continuous distribution of wind velocity, provides not only the necessary conditions for the existence of billow clouds, requiring a neutral (adiabatic) or unstable stratification in the transition layer, but also determines the form of the cellular pattern of such wav... Abstract Solberg's theory of oscillations and waves of short wave length unaffected by the earth's rotation in an atmosphere with a linear temperature field is extended for a vertical wind shear. Under normal conditions in the atmosphere this extension means only a small and insignificant correction of Solberg's theory provided the wind velocity is different from the wave velocity. If the wave velocity is equal to the wind velocity in a particular level then the theory presented in this paper requires an adiabatic or superadiabatic temperature gradient in the layer containing this particular level. This theory, applied to the theory of billow clouds generalized for the case when the sharp discontinuity is replaced by a transition layer with continuous distribution of wind velocity, provides not only the necessary conditions for the existence of billow clouds, requiring a neutral (adiabatic) or unstable stratification in the transition layer, but also determines the form of the cellular pattern of such wav...

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