Analysis of asymmetries in propagating mode-2 waves

Abstract

Abstract.Using numerical simulations performed with a pseudo-spectral incompressible Navier-Stokes solver, we describe the asymmetries that arise in the recirculating core of mode-2 internal, solitary-like waves. The waves are generated in a manner consistent with many laboratory studies, namely via the collapse of a region of mixed fluid. Analysis of the simulations reveals that asymmetries across both the wave crest and the pycnocline centre develop in the spatial distribution of density, kinetic energy and a passive tracer transported by the mode-2 waves. The simulations are extended to three-dimensions to allow for the formation of spanwise instabilities. We find that three-dimensionalization modifies the structure and energetics of the core, but that the majority of the results obtained from two dimensional simulations remain valid. Taken together, our simulations demonstrate that the cores of solitary-like mode-2 waves are different then their counterparts for mode-1 waves and that their accurate characterization on both lab and field scales should account for the core asymmetry across the pycnocline centre.

The evolution of mode-2 internal solitary waves modulated by background shear currents

“…Similar to the case 1, the characteristics and energy loss of the amplitude-modulated wave packet for the case 5 were also similar with the breather definition. Noted that the breather solution exist only if the cubic nonlinearity coefficients in Gardner equation is positive (Lamb et al, 2007), but the configuration of the stratification in our simulation results a negative cubic nonlinearity coefficient in Gardner equation (Grimshaw et al, 2010;Talipova et al, 2011) and it means the breather is not allowed The oscillating tail was frequently observed in similar studies (Carr et al, 2015;Olsthoorn et al, 2013;Stastna et al, 2015). Its generation was related to the shear, and the tail was sustained by continuous energy input.…”

“…Between 10 T and 38 T, ~20% of mode-2 ISW total energy lost，it was a 15 little smaller than the typical observation results. Relatively high energy loss rate and a large amplitude oscillating tail in the third transect of the field observations could be probably attributed to the effect of a shoaling pycnocline (Shroyer et al, 2010) and thus the enhancement of the asymmetries in stratification, which could increase the energy loss of the wave during the propagation of mode-2 ISWs (Carr et al, 2015;Olsthoorn et al, 2013). …”

“…Those wave forms are common in the adjustment of mode-2 ISWs (Carr et al, 2015;Olsthoorn et al, 2013;Terletska et al, 2016), but the generation mechanism of amplitude-modulated wave packet requires further examination.…”

Multi-scale phenomena of rotation-modified mode-2 internal waves

“…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.…”

“…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.…”