Geometry and energetics of beams of internal waves

The Boussinesq approximation is used to investigate the propagation and reflection of beams of internal gravity waves in a viscous exponentially stratified fluid. A propagator is constructed that relates the vertical displacements in arbitrary transverse sections of a propagating or a reflecting beam. On the basis of the propagator, the Huygens principle is formulated for wave packets. The energy density per unit length and the energy flux in a beam are calculated. The coefficients of energy losses, a fraction of the energy of an incident beam transferring to the boundary flow, are obtained. Under typical laboratory conditions, they prove to be about 2% for a vertical wall, 60% for a horizontal wall, and 20% for intermediate positions of the reflecting rigid plane.