Flows induced by Coriolis-influenced vertically propagating two-dimensional internal gravity wave packets

Abstract

Theory is developed to predict the flows induced by small-amplitude two-dimensional vertically propagating internal wavepackets under the influence of rotation. While the long wave response originally predicted by Bretherton [J. Fluid Mech. 36, 785-803 (1969)] dominates if the influence of background rotation is negligible, the induced waves are found to be evanescent if the Coriolis parameter is sufficiently large. Explicitly, evanescent induced flows dominate if the Coriolis parameter is greater than the forcing frequency, which is set by the ratio of the vertical group velocity of the wavepacket divided by the vertical scale of modulation of the wavepacket. The predicted structure of the induced flow is confirmed by numerical simulations. For an up-and rightward propagating Gaussian wavepacket that dominantly induces a long wave response, the flow is rightward across the upper flank and leftward across the lower flank of the wavepacket. In contrast, the induced flow for a dominantly evanescent response is negative over the middle of the wavepacket. This qualitative change in structure is anticipated to influence the modulational stability of moderately large amplitude wavepackets.

Rising and settling 2-D cylinders with centre-of-mass offset

“…2017) or, as previously mentioned, the spread of micro plastics in our oceans (Sutherland et al. 2023).…”

“…Therefore, a complete solution or model of these systems remains elusive in many cases such that new insights rely on empirical results and parameter studies based on experiments or numerical simulations. Understanding and modelling of particle dynamics is important in many fields, for instance, to predict the spread of (plastic) pollutants in the ocean (Sutherland et al 2023).…”

“…Understanding and modelling of particle dynamics is important in many fields, for instance, to predict the spread of (plastic) pollutants in the ocean (Sutherland et al. 2023).…”

Propagation and overturning of three-dimensional Boussinesq wave packets with rotation

“…Neglecting to superimpose the initial predicted induced mean flow results in an "error flow" [9], an unphysical "deficit" [25], or residual flow that remains at the initial location of the wave packet, and is of equal magnitude but opposite sign of the predicted induced mean flow (see also Refs. [7,8]). Although small-amplitude wave packets initially induce a mean flow of negligible magnitude, for consistency across simulations such wave packets were nonetheless initialized to include their Bretherton flow.…”

“…It has been shown [5][6][7] that the induced mean flow manifests as long, hydrostatic waves that propagate far streamwise and vertically below an upward-propagating wave packet. Conversely, two-dimensional wave packets induce an evanescent long wave response [8] if the Coriolis parameter is of greater magnitude than the forcing frequency (set by the ratio of the wave packet's vertical group speed to its vertical scale of modulation). Three-dimensional wave packets again induce qualitatively distinct mean flows [5][6][7].…”