Modelling internal solitary waves on the Australian North West Shelf

Abstract

Abstract:The transformation of the nonlinear internal tide and the consequent development of internal solitary waves on the Australian North West Shelf is studied numerically in the framework of the generalized rotation-modified Korteweg-de Vries equation. This model contains both nonlinearity (quadratic and cubic), the Coriolis effect, depth variation and horizontal variability of the density stratification. The simulation results demonstrate that a wide variety of nonlinear wave shapes can be explained by the synergetic action of nonlinearity and the variability of the hydrology along the wave path.2

Modelling Internal Solitary Waves in the Coastal Ocean

“…Beginning with the seminal paper by Benney (1966) there have been many derivations of a (constant-coefficient) KdV equation suitable for the description of internal solitary waves, see, for instance, Lee and Beardsley (1974), Ostrovsky (1978), Maslowe and Redekopp (1980), Grimshaw (1981), Tung et al (1981), and the recent articles by Apel et al (2007), Holloway et al (1997Holloway et al ( , 1999Holloway et al ( , 2001, Grimshaw (2001Grimshaw ( , 2005, Grimshaw et al (2006), Helfrich and Melville (2006) and Ostrovsky and Stepanyants (2005) which review the literature in this area. However, in the present oceanic framework, the waves are propagating on a background whose properties vary in the wave propagation direction.…”

“…The final term mA represents nonconservative effects arising from dissipative or forcing terms in the underlying basic state. Extra terms can also be added to represent dissipative effects on the wave itself (see Grimshaw et al 2003), and Coriolis effects due to the Earth's rotation (see Grimshaw et al 1998bGrimshaw et al , 2006, but these will not be considered here. The variable-coefficient KdV equation for water waves was developed by Ostrovsky and Pelinovsky (1970) and later systematically derived by Johnson (1973b), while Grimshaw (1981) gave a detailed derivation for internal waves (see also Zhou and Grimshaw 1989;Grimshaw 2001).…”

“…Equations 3, 6, sometimes with various modifications such as with an additional dissipative term, or with a term taking account of the Earth's rotation, have been applied to the study of internal solitary wave wave transformation in the coastal zone by many authors (for instance Cai et al 2002;Djordjevic and Redekopp 1978;Grimshaw et al , 2006Holloway et al 1997Holloway et al , 1999Hsu et al 2000;Liu et al 1988Liu et al , 1998Liu et al , 2004Orr and Mignerey 2003;Small 2001aSmall , b, 2003. In Sect.…”

Internal solitary waves: propagation, deformation and disintegration

“…Equations (3) and (6), sometimes with various modifications such as with an additional dissipative term, or with a term taking account of the Earth's rotation, have been applied to the study of internal solitary wave wave transformation in the coastal zone by many authors (for instance Cai et al, 2002;Djordjevic and Redekopp, 1978;Grimshaw et al, , 2006Grimshaw et al, , 2007Holloway et al, 1997Holloway et al, , 1999Hsu et al, 2000;Liu et al, 1988Liu et al, , 1998Liu et al, , 2004Orr and Mignerey, 2003;Shroyer et al, 2009and Small, 2001a, b, 2003. In Sect.…”

Internal waves and coastal currents: a special research forum in honour of Peter Holloway

“…The other is by Antenucci and Ivey (2006), from the University of Western Australia, where there has been a recent upsurge of interest again in internal waves. It is pleasing to see a paper on non-linearities from Grimshaw et al (2006), who were all active collaborators with Peter, Pelinovsky and Talipova co-authoring at least six papers with him. The final two papers are on dynamics associated with Australia's two major coastal current systems: the East Australian Current (Mata et al 2006) and the Leeuwin Current (Woo et al 2006).…”