Group seminar on 9. January, 14:15 CET
Energy transfers between normal modes in a spherical rotating shallow-water model
Katharina Holube
The rotating shallow-water (RSW) equations describe the horizontal structure of atmospheric processes in an idealized framework. The solutions of the RSW equations in spherical geometry, linearized around a state of rest, are the Hough harmonics. These can be identified with Rossby, inertia-gravity, MRG and Kelvin waves. The wave-wave and wave-mean flow interactions involving these waves are studied in numerical simulations with the model TIGAR, which solves the nonlinear rotating shallow-water equations on the sphere using Hough harmonics as basis functions. In the linear framework, the energy of each mode, which is the sum of kinetic energy and available potential energy, can be calculated from the square of the absolute values of the Hough expansion coefficients. In physical space, the kinetic energy is proportional to the integral of the squared velocity vector, multiplied by the mean depth, over the sphere. In the nonlinear system, the squared velocity vector is instead multiplied with the space-dependent shallow-water depth, so that the energy is a third-order quantity. The impact of this difference increases with the deviations from the mean depth. In this seminar, I will discuss energy transfers between waves and the mean flow in TIGAR simulations and compare this ongoing work with literature findings.