SOLITARY WAVES IN COMPRESSIBLE DEEP FLUIDS

Solitary waves in incompressible deep fluids are described to the first order in the wave amplitude by the Benjamin-Davis-Ono equation [J. Fluid Mech. 29, 559 (1967); J. Fluid Mech. 29, 593 (1967); J. Phys. Soc. Jpn. 39, 1082 (1975)]. This equation describes the balance between dispersion and weak nonlinear effects for long internal waves in a density stratified layer of fluid confined in an infinitely deep fluid. A solution of this equation is the so-called algebraic solitary wave. In the present paper the modifications of this wave due to the compressibility of the fluid are investigated. It is found that the linear (eigenvalue) problem, determining the modal function and the possible phase speeds, as well as the coefficients of the Benjamin-Davis-Ono equation, change due to the compressibility. These changes are discussed considering three special cases in detail. © 1990 American Institute of Physics.