A Model for Large-Amplitude Internal Waves with Finite-Thickness Pycnocline
We derive a new model of internal solitary wave propagation governed by the Euler equations for a continuously stratified, incompressible fluid in the Boussinesq approximation. The model is derived by a systematic joint asymptotic expansion for long wavelengths and thin pycnoclines. The resulting solutions extend those of the strongly nonlinear two-layer system (Choi and Camassa in J. Fluid Mech. 396:136, 1999) to continuous stratifications, and capture non-trivial features of the internal pycnocline structure. These solutions can be used, among other applications, to perform shear instability calculations in analytic form.
solitary internal waves asymptotic models closed form solutions