Shoaling Mode-2 Internal Solitary-Like Waves

They owe their existence to a balance between nonlinear wave steepening and linear wave dispersion. In linear theory, sets of modal solutions exist for large amplitude ISWs propagating in bounded, stratified fluids but, for most cases of geophysical interest, over 90% of kinetic energy of the nonlinear baroclinic modes is contained within the first two modes. Mode-1 ISWs displace isopycnals in one direction only and can be waves of depression or elevation. Mode-2 ISWs on the other hand, displace isopycnals in opposite directions and can be convex or concave in form. 

Laboratory investigation and numerical simulation of the propagation of mode-2 ISWs over a uniformly sloping, solid topographic boundary, will be presented. The waves are generated by a lock-release method. Features of their shoaling include (i) formation of an oscillatory tail, (ii) degeneration of the wave form, (iii) wave run up, (iv) boundary layer separation, (v) vortex formation and re-suspension at the bed and (vi) a reflected wave signal. In shallow slope cases, the wave form is destroyed by the shoaling process; the leading mode-2 ISW degenerates into a train of mode-1 waves of elevation and little boundary layer activity is seen. For steeper slopes, boundary layer separation, vortex formation and re-suspension at the bed are observed. The boundary layer dynamics is shown (numerically) to be dependent on the Reynolds number of the flow.

Reference: Carr et al. J. Fluid Mech. (2019), vol. 879, pp. 604632