On the nonlinear internal waves propagating in an inhomogeneous shallow sea

SummaryA concept of conservation of energy flux for the internal waves propagating in an inhomogeneous shallow water is examined. The emphasis is put on an application of solution of the Korteweg–de Vries (KdV) equation in a prescribed form of the cnoidal and solitary waves. Numerical simulations were applied for the southern Baltic Sea, along a transect from the Bornholm Basin, through the Słupsk Sill and Słupsk Furrow to the Gdańsk Basin. Three-layer density structure typical for the Baltic Sea has been considered. An increase of wave height and decrease of phase speed with shallowing water depth was clearly demonstrated. The internal wave dynamics on both sides of the Słupsk Sill was found to be different due to different vertical density stratification in these areas. The bottom friction has only negligible influence on dynamics of internal waves, while shearing instability may be important only for very high waves. Area of possible instability, expressed in terms of the Richardson number Ri, is very small, and located within the non-uniform density layer, close to the interface with upper uniform layer. Kinematic breaking criteria have been examined and critical internal wave heights have been determined.