Vertical Structure of Internal Modes in Stratified Flows

An analytic solution of the linearized two-dimensional equations for stably stratified flows driven by a surface shear stress which is periodic in the horizontal direction, and in time, is developed. The solution is based on the assumptions of a fluid with infinite Prandtl number and a linear thermal stratification which is constant in each horizontal plane. The analytic solution is used to examine the joint effect of the viscosity value, the frequency of the driving force and the intensity of the stratification on the vertical structure of the internal modes. It is shown that as the viscosity value increases, the formation of higher-order modes is prohibited. The validity of the assumptions of the analytic solution is tested by comparing it with numerical solutions of the same problem.