In this thesis, an initial value problem is presented and we consider the problem analytically. We define a vortex with a circular motion in a configuration for an inviscid fluid flow on a horizontal plane under the influence of the Coriolis force. We consider a wave generated by a specified initial condition which gives an initial value problem. We obtain a nonlinear equation which we solve by looking for a perturbation series solution. The nonlinear wave interactions give rise to a wave-induced mean flow component, which modifies the background vortex flow, as well as a higher wavenumber component. We also find additional terms with a wavenumber of one which represents the beta-gyre effect.