INTERNAL WAVES AROUND A DISTURBANCE IN A FLUID WITH ARBITRARY STRATIFICATION AND BACKGROUND SHEAR-FLOW

A three-dimensional ray theory is presented for calculating the phase configuration of internal waves around a moving disturbance in a flow with arbitrary stratification and background shear. The theory is appl ied to two-dimensional stratified shear flows which have been produced in the laboratory and good agreement is shown between the theoretical and experimental phase configurations. Good agreement is also shown w hen caustics and critical levels are present. This paper includes the wave systems arising from a combined translation and oscillatory motio n of a source and it shows how distinct systems of waves arise from ea ch type of motion under different background conditions. This paper sh ows that for two-dimensional steady wave systems the critical level is at a well defined height which is independent of wavenumber but in th ree dimensions the critical height can in general van, with wavenumber .