Nonlinear interfacial progressive waves near a boundary in a Boussinesq fluid
Abstract
The behavior of nonlinear progressive waves at the interface between two inviscid fluids in the presence of an upper free boundary is studied as a model of waves on the thermocline. A set of relationships between the integral properties of bounded waves in a general twofluid model is first developed and the Stokes expansion to third order is derived. The exact free boundary problem for the wave profile is then formulated within the Boussinesq approximation as a nonlinear integral equation, which is solved numerically using two different numerical methods. For finite velocity difference across the twofluid interface bifurcation of solutions into upper and lower branch wave profiles with quite different properties is obtained. Numerically calculated wave shapes and integral properties show good agreement with thirdorder Stokes expansion predictions in the weakly nonlinear regime for waves which are not too long. Very long waves were found to exhibit distinct solitary wavelike features.
 Publication:

Physics of Fluids
 Pub Date:
 April 1983
 DOI:
 10.1063/1.864239
 Bibcode:
 1983PhFl...26..897P
 Keywords:

 Boussinesq Approximation;
 Computational Fluid Dynamics;
 Free Boundaries;
 Thermoclines;
 Two Fluid Models;
 Wave Interaction;
 Integral Equations;
 Internal Waves;
 Nonlinear Equations;
 Stokes Law (Fluid Mechanics);
 Fluid Mechanics and Heat Transfer