Study of nonlinear trapped lee waves in the modified β-plane approximation

Abstract

In the modified β-plane approximation, we derive exact solutions to the nonlinear governing equations of three-dimensional trapped lee waves influenced by Coriolis forces or Coriolis forces and centripetal forces, respectively. Further, we obtain the dispersion relation and qualitatively analyze the pressure, density, and vorticity in two cases. In this process, we find more accurate representations of solutions caused by the incorporation of a gravitational-correction term and investigate the influence of centripetal forces on trapped lee waves.