On the maximal form of internal solitary waves

W. A. B. Evans,
Physics Laboratory, University of Kent,
Canterbury, Kent CT2 7NR, UK.



Recent integral equation computations (Evans and Ford 1996bTurner and Vandenbroeck 1988) of large amplitude internal waves under oceanic conditions, $\rho_2/\rho_1\lesssim 1$, have suggested a form with fixed maximal depth and of arbitrary, very large width in accord with Benjamin (1966)'s concept of `conjugate flow'. Here we explore the `conjugate flow' picture for both ``rigid-lid'' and ``free top surface'' boundary conditions. We discuss the limitations of this kind of extremal form - especially for cases where $\rho_2/\rho_1\ll 1$.