Commun. Comput. Phys., 2 (2007), pp. 993-1006. |
Amplitude Factorization Method in the Atmospheric Gravity-Wave Equation Rein Rõõm ^{1*}, Marko Zirk ^{1} 1 Institute of Environmental Physics, Tartu University, Ulikooli 18, Tartu 50090, Estonia.Received 29 September 2006; Accepted (in revised version) 24 January, 2007 Available online 18 April 2007 Abstract A novel amplitude factorization method is applied to solve a discrete buoyancy wave equation with arbitrary wind and temperature height distribution. The solution is given in the form of a cumulative product of complex factors, which are computed by a nonlinear, inhomogeneous, two-member recurrence formula, initiated from a radiative condition on top. Singularities of the wave equation due to evanescent winds are eliminated by turbulent friction. The method provides an estimation of the minimal vertical resolution, required to attain a stable accurate solution. The areas of application of the developed numerical scheme are high resolution modelling of orographic waves for arbitrary orography in general atmospheric stratification conditions, and testing of adiabatic kernels of numerical weather prediction models. AMS subject classifications: 83C35, 35L05, 81T80 PACS: 47.35.Bb, 92.60.hh, 47.11.-j Key words: Atmospheric gravity waves, linear buoyancy wave equation, arbitrary stratification, numerical solution, amplitude factorization method. *Corresponding author. Email: Rein.Room@ut.ee (R. Rõõm), Marko.Zirk@ut.ee (M. Zirk) |