Non-linear internal waves in two-layer stratified flows

We consider an analytical model of internal waves propagating in a weakly stratified two-layer fluid. A new model equation extents the long-wave approximation suggested in [1,2] for the non-linear Dubreil-Jacotin - Long equation. This model takes into account a slight density gradient in stratified layers, which can be comparable with the density jump at the interface between layers. Parametric range of solitary waves is determined in the framework of considered mathematical model. We demonstrate that solitary wave modes can be subject to the Kelvin-Helmholtz instability arising due to wave-induced velocity shear in layered flow. Such a marginal stability of internal waves could explain the formation mechanism of billow trains leading to the mixing in abyssal near-bottom flows.

This work was supported by the grant of the Russian Science Foundation (Project No 21-71-20039).

References

[1] Makarenko N.I., Maltseva J.L., Morozov E.G., Tarakanov R.Yu., Ivanova K.A. Internal waves in marginally stable abyssal stratified flow, Nonlin. Proc. Geophys. 2018, 25, 659-669

[2] Makarenko N.I., Maltseva J.L., Morozov E.G., Tarakanov R.Yu., Ivanova K.A.  Steady internal waves in deep stratified flow, J. Appl. Mech. Tech. Phys. 2019, 60(2), 248-256