The structure of the internal wave Mach front generated by a point source moving in a stratified fluid

The height and velocity of an internal wave (IW) generated by a point fluid source moving horizontally in a stratified fluid have been calculated at asymptotically large distances behind the source. Particular emphasis has been given to the region near the Mach front, defined by the offtrack angle Theta M = sin-1 (cM/V), where cM is the speed of the fastest IW and V is the source velocity. To elucidate the asymptotic IW profile in that regime, a novel uniform asymptotic expansion was developed that is valid on both sides of the Mach front. It was found that the asymptotic approximation for the IW height, as well as for all its derivatives, is continuous at that front, and, furthermore, that all these IW profiles are remarkably smooth and slowly varying functions of offtrack distance in that regime.