Power and Energy Characteristics of the Internal Wave Beams in a Continuously Stratified Fluid

AbstractAnalytic linear theory of disturbances generated by an oscillating compact source in a viscous continuously stratified fluid was constructed. Exact solution of the emission internal waves was constructed taking into account diffusivity effects. Analy- sis is based on set of fundamental equations of incompressible flows. The linearized problem of periodic flows in a continu- ously stratified fluid, generated by an oscillating part of the inclined plane was solved by methods of singular perturbation theory. Source (rectangular or disc) oscillating linearly in a longitudinal and lateral direction. The solutions include regularly perturbed on dissipative component functions (internal waves) and singularly perturbed functions. Only one of the singular components of the flow has an analogue in the homogeneous fluid that is a periodic or Stokes’ flow. Its thickness is defined by a universal micro scale depending on kinematics viscosity coefficient and a buoyancy frequency with a factor depending on the wave slope. Other singular perturbed functions are specific for stratified flows and don’t have analogue in homogene- ous fluid. Their thickness are defined the diffusion coefficient, kinematic viscosity and additional factor depending on geome- try of the problem. We have shown that for real stratified fluid is necessary to consider influence of all dissipative factors (viscosity, stratification, diffusion)