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An Efficient Solution Method for the Buoyancy Wave Equation at Variable Wind and Temperature

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  • 1 Tartu University, Tartu, Estonia
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Abstract

To solve a horizontally spectral, vertically discrete buoyancy wave equation in conditions of arbitrary wind and temperature distribution with height, a novel method is applied, which consists of a presentation of the solution in the form of a cumulative product of complex decrease factors. For decrease factors, a nonlinear, inhomogeneous, two-member recurrence formula follows that is initiated, assuming the radiative condition at the top. Singularities of the wave equation, corresponding to a critical layer in the vicinity of evanescent wind, are eliminated by turbulent friction. The estimation of minimal vertical resolution is derived, enabling solution stability and accuracy. The areas of application of the developed numerical scheme are the high-precision modeling of orographic waves for arbitrary orography in general atmospheric stratification conditions and testing of adiabatic kernels of numerical weather prediction models.

Corresponding author address: Rein Rõõm, Institute of Environmental Physics, Tartu University, Ülikooli 18, Tartu 50090, Estonia. Email: rein.room@ut.ee

Abstract

To solve a horizontally spectral, vertically discrete buoyancy wave equation in conditions of arbitrary wind and temperature distribution with height, a novel method is applied, which consists of a presentation of the solution in the form of a cumulative product of complex decrease factors. For decrease factors, a nonlinear, inhomogeneous, two-member recurrence formula follows that is initiated, assuming the radiative condition at the top. Singularities of the wave equation, corresponding to a critical layer in the vicinity of evanescent wind, are eliminated by turbulent friction. The estimation of minimal vertical resolution is derived, enabling solution stability and accuracy. The areas of application of the developed numerical scheme are the high-precision modeling of orographic waves for arbitrary orography in general atmospheric stratification conditions and testing of adiabatic kernels of numerical weather prediction models.

Corresponding author address: Rein Rõõm, Institute of Environmental Physics, Tartu University, Ülikooli 18, Tartu 50090, Estonia. Email: rein.room@ut.ee

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