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 applied 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 when caustics and critical levels are present. This paper includes the wave systems arising from a combined translation and oscillatory motion of a source and it shows how distinct systems of waves arise from each, type of motion under different background conditions. This paper shows that for two-dimensional steady wave systems the critical level is at a well defined height which is independent of wavenumber but in three dimensions the critical height can in general vary with wavenumber.