Abstract
Abstract. We present high-resolution, three-dimensional simulations of rotation-modified mode-2 internal solitary waves at various rotation rates and Schmidt numbers. Rotation is seen to change the internal solitary-like waves observed in the absence of rotation into a leading Kelvin wave followed by Poincaré waves. Mass and energy is found to be advected towards the right-most side wall (for a Northern Hemisphere rotation), leading to increased amplitude of the leading Kelvin wave and the formation of Kelvin–Helmholtz (K–H) instabilities on the upper and lower edges of the deformed pycnocline. These fundamentally three-dimensional instabilities are localized within a region near the side wall and intensify in vigour with increasing rotation rate. Secondary Kelvin waves form further behind the wave from either resonance with radiating Poincaré waves or the remnants of the K–H instability. The first of these mechanisms is in accord with published work on mode-1 Kelvin waves; the second is, to the best of our knowledge, novel to the present study. Both types of secondary Kelvin waves form on the same side of the channel as the leading Kelvin wave. Comparisons of equivalent cases with different Schmidt numbers indicate that while adopting a numerically advantageous low Schmidt number results in the correct general characteristics of the Kelvin waves, excessive diffusion of the pycnocline and various density features precludes accurate representation of both the trailing Poincaré wave field and the intensity and duration of the Kelvin–Helmholtz instabilities.
Highlights
Over recent decades non-linear internal solitary waves (ISWs) have been the subject of continuing research due, in part, to their common presence in coastal waters (Shroyer et al, 2010; Lamb, 2004; Zhang et al, 2015) and estuaries (Bourgault and Kelley, 2003), and an expanding set of applications, such as plankton and krill transport (Scotti and Pineda, 2004; Cuypers et al, 2010) or cross-shelf transport (Hosegood and van Haren, 2004)
Both authors found that though the wave amplitude increased at the channel wall with increasing rotation rate, the phase speed and shape were comparable to waves of similar amplitude in the presence of no rotation
Since direct numerical simulations (DNSs) at these values are unattainable due to the resolution required, here we provide a short description of the impact that various Schmidt numbers have on the results presented far
Summary
Over recent decades non-linear internal solitary waves (ISWs) have been the subject of continuing research due, in part, to their common presence in coastal waters (Shroyer et al, 2010; Lamb, 2004; Zhang et al, 2015) and estuaries (Bourgault and Kelley, 2003), and an expanding set of applications, such as plankton and krill transport (Scotti and Pineda, 2004; Cuypers et al, 2010) or cross-shelf transport (Hosegood and van Haren, 2004). The dominant laboratory insights on Kelvin waves in channel geometry come from the experimental work of Maxworthy (1983) and Renouard et al (1987) These authors performed lab-scale experiments in which mode-2 (Maxworthy, 1983) and mode-1 (Renouard et al, 1987) Kelvin waves were generated in a rectangular domain. Both authors found that though the wave amplitude increased at the channel wall with increasing rotation rate, the phase speed and shape were comparable to waves of similar amplitude in the presence of no rotation. The authors described how the wave amplitude decayed exponentially away from the wall, how the wave front was curved backwards, and how the waves decayed as they propagated away from the generation site due to the generation of inertial waves. Melville et al (1989) followed this by showing that Poincaré waves of comparable phase speed to a Kelvin wave will naturally resonant with the Kelvin wave, causing the curvature of the wave front and the amplitude decay away from the side wall
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