Abstract
Large amplitude, horizontally propagating internal waves are commonly observed in the coastal ocean. They are often modelled by a variable-coefficient Korteweg–de Vries equation to take account of a horizontally varying background state. Although this equation is now well-known, a term representing non-conservative effects, arising from horizontal variation in the underlying basic state density stratification and current, has often been omitted. In this paper, we examine the possible significance of this term using climatological data for several typical oceanic sites where internal waves have been observed.
Highlights
Large amplitude internal solitary waves are commonly observed in the coastal ocean
As they are long waves with wavelengths greater than the relevant vertical scale, it is widely accepted that the basic paradigm for the description of these waves is based on the Korteweg–de Vries (KdV) equation, first derived in this context by Benney [8] and Benjamin [9] and subsequently by many others
An outline of the derivation of (1) was given by Liu et al [12] and for convenience is briefly summarised here in Section 2, emphasising how the “new” term ση arises. It is present because the variable-coefficientKorteweg–de Vries (vKdV) Equation (1) describes the evolution of a wave field about a basic state which may not be in exact equilibrium due to the inhomogeneous background state
Summary
Large amplitude internal solitary waves are commonly observed in the coastal ocean (see the reviews by Grimshaw [1], Holloway et al [2], Ostrovsky and Stepanyants [3], Helfrich and Melville [4,5], Grimshaw et al [6] and the book by Vlasenko et al [7]) As they are long waves with wavelengths greater than the relevant vertical scale, it is widely accepted that the basic paradigm for the description of these waves is based on the Korteweg–de Vries (KdV) equation, first derived in this context by Benney [8] and Benjamin [9] and subsequently by many others (see the aforementioned references). An outline of the derivation of (1) was given by Liu et al [12] and for convenience is briefly summarised here, emphasising how the “new” term ση arises It is present because the vKdV Equation (1) describes the evolution of a wave field about a basic state which may not be in exact equilibrium due to the inhomogeneous background state. In the Appendices A and B, we examine the possible effects of bottom friction and the earth’s background rotation, neglected in the main body of the paper
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