Using initial value problem approach the evolution of linearized disturbances in a stratified shear flow is studied. The resulting equation in time posed by using Fourier transform is solved for the Fourier amplitudes with a point source of the field of transverse velocity and density as initial disturbances. The disturbances are resolved into rotational and irrotational components. The rotational solution is obtained for small values of frequency. The irrotational solution in each layer is specified uniquely by satisfying the interfacial conditions and boundary conditions at a wall or at infinity. The velocity and density plots are drawn for different values of frequency.

Stratified shear flow, initial value problem, Fourier transform, Squire transform, Brunt frequency.