Interfacial solitons propagating through a background shear current

Nonlinear internal solitary waves (ISWs) propagating through a two-layer stratified system, in the presence of a shear background current, are theoretically investigated. We implement a new version of the Miyata-Choi-Camassa model with mobile layers (MCC-ML), by considering an asymptotic, uniform velocity distribution for each layer. To investigate the typical geophysical flow conditions observed in the coastal oceans, we focused on theoretical predictions for a density ratio between the two layers set to 0.99. A rigid-lid at the top of the theoretical domain is considered since it represents a good approximation under the Boussinesq condition. By varying the ratio of the undisturbed layer thickness from 0.1 to 10, we considered ISWs with both positive and negative polarities, when the background fluid is at rest. For increasing velocity differences between the two layers, ISWs tend to broaden (steepen) when the background velocities assume the same (opposite) direction of those induced by the wave. We show that the polarity conversion can be easily predicted since it directly depends on both stratification features and ambient velocities. The shear current affects also the wave celerity: for increasing background shear, upstream-propagating solitons reach a critical condition for which the wave celerity is equal to zero. We found that this occurrence is associated with a well-defined value of the wave amplitude. For even larger background shears, the waves are observed to change their direction of propagation. By linear analysis, we finally obtained the limiting background shear current for which the MCC-ML model does not provide any solution.