Simulation of internal solitary waves with negative polarity in slowly varying medium

Abstract

We consider the propagation of an internal solitary wave over two different types of varying depth regions, i.e. a gentle monotonic bottom slope connecting two regions of constant depth in two-layer fluid flow and a smooth bump. Here, we let the depth of the upper layer is smaller than the lower layer such that an internal solitary wave of negative polarity is generated. The appropriate model for this problem is the variable-coefficient extended Korteweg-de Vries equation, which is then solved numerically using the method of lines. Our numerical results show different types of transformation of the internal solitary wave when it propagates over the varying depth region depending on the depth of the lower layer after the varying depth region including generation of solitary wavetrain, adiabatic and non-adiabatic transformation of the internal solitary wave.

Simulation of Internal Undular Bores of Depression Propagating over a Slowly Varying Region

“…In previous studies, the MOL is widely used in solving many KdV-type equations, e.g. constant-coefficient eKdV equation [30], variable-coefficient eKdV equation [31], forced KdV equation [32], and forced KdV-Burgers equation [33]. First, the veKdV Eq.…”

Simulation of Internal Undular Bores Propagating over a Slowly Varying Region

“…The MOL is widely used in solving many partial differential equations, e.g. the eKdV equation [20][21], KdV equation with forcing term [22], and forced KdVB equation [23]. To begin, we rewrite veKdV equation as follows…”

Simulation of Internal Undular Bores in Rapidly Varying Topography

“…Here, the internal undular bore is propagating over a rapidly increasing depth region, where the lower layer on the new constant region has a smaller or equal depth to the upper layer, 11 hH  . In this case, there is no polarity change in the internal undular bores, which is determined by the value of  in Eq (1).…”

“…These effects include the formation of a trailing shelf which would then decomposes into a secondary wavetrain, the generation of an internal solitary wave of opposite polarity, etc. [3][4][9][10][11]. Furthermore, internal solitary waves will evolve or fission into several solitons when they propagate over a step or rapidly changing bottom, i.e.…”