A numerical investigation of solitary internal waves with trapped cores formed via shoaling. (English) Zbl 1009.76010

Lamb, Kevin G.

J. Fluid Mech. 451, 109-144 (2002).

Summary: The formation of solitary internal waves with trapped cores via shoaling is investigated numerically. For density fields for which the buoyancy frequency increases monotonically towards the surface, sufficiently large solitary waves break as they shoal and form solitary-like waves with trapped fluid cores. Properties of large-amplitude waves are shown to be sensitive to the near-surface stratification. For the monotonic stratifications considered, waves with open streamlines are limited in amplitude by the breaking limit (maximum horizontal velocity equals wave propagation speed). When an exponential density stratification is modified to include a thin surface mixed layer, wave amplitudes are limited by the conjugate flow limit, in which case waves become long and horizontally uniform in the centre. The maximum horizontal velocity in the limiting wave is much less than the wave’s propagation speed, and, as a consequence, waves with trapped cores are not formed in the presence of the surface mixed layer.

MSC:

76B25	Solitary waves for incompressible inviscid fluids
76B70	Stratification effects in inviscid fluids
76B55	Internal waves for incompressible inviscid fluids

Keywords:

solitary internal waves; trapped cores; shoaling; large-amplitude waves; near-surface stratification; exponential density stratification; thin surface mixed layer; maximum horizontal velocity