Internal solitary waves propagating through variable background hydrology and currents

Hihglights
- An omitted term representing non-conservative effects in Korteweg-de Vries equation can make some difference.
- It arises from dissipative or forcing terms when the hydrology varies in the horizontal direction.
- The overall structure of the wave evolution remains basically the same and this term is mainly to change the amplitude.

Large-amplitude, horizontally-propagating internal wave trains are commonly observed in the coastal ocean, fjords and straits. They are long nonlinear waves and hence can be modelled by equations of the Korteweg-de Vries type. However, typically they propagate through regions of variable background hydrology and currents, and over variable bottom topography. Hence a variable-coefficient Korteweg-de Vries equation is needed to model these waves. Although this equation is now well-known and heavily used, a term representing non-conservative effects, arising from dissipative or forcing terms in the underlying basic state, has usually been omitted. In particular this term arises when the hydrology varies in the horizontal direction. Our purpose in this paper is to examine the possible significance of this term. This is achieved through analysis and numerical simulations, using both a two-layer fluid model and a re-examination of previous studies of some specific ocean cases.