Internal solitary wave energy transformations under ridged ice cover

Propagation of internal solitary waves (ISW) under the edge of the ice cover may lead to their
destabilization through overturning and breaking events. Factors such as ice cover depth, ridging
intensity, and internal wave amplitudes play crucial roles in the evolution and disintegration of ISW
beneath the ice cover. In the study, a numerical investigation of the transformation of ISW
propagating from open water in the stratified sea under ridged ice cover is carried out. A
nonhydrostatic numerical model, that is based on the Reynolds averaged Navier-Stokes equations in
the Boussinesq approximation for a continuously stratified fluid, was used in the investigation. The
study focused on an idealized scenario with a vertical distribution of potential density anomalies
designed to replicate the summer profile of potential density observed over the Yermak Plateau in
the Arctic Ocean. In the numerical experiments, number of ice keels were placed beneath a
uniform-thickness ice layer. The ice keel shape was approximated by the Versoria function. It is
carried out calculations with a different ridging intensity, that is, the ratio of the maximum height of
the keel to the distance between the keels. In present calculations, it varies from 1/1000 for
moderately ridged ice to 1/20 for heavily ridged ice, which is broadly consistent with the ocean
values. The transformation of ISW of depression is additionally governed by the blocking
parameter β for a single keel, which is the ratio of the height of the minimum thickness of the upper
layer under the ice keel to the incident wave amplitude. An important characteristic of the ISW-
ridged ice interaction is the loss of kinetic and available potential energy during the ISW
transformation. Energy transformation due to mixing leads to the transition of energy to background
potential energy and energy dissipation. To characterize the dependence of energy loss on keel
height and distance between keels, we introduced the parameter, which is the ratio of the sum of
submerged ice thickness and maximal keel penetration to the distance between keels. An energy
loss was estimated based on a budget of depth-integrated pseudoenergy before and after the wave
transformation. The results revealed that the energy loss increases with a decrease in distance
between keels or an increase in keel height. The level of energy loss is highest for β values near
zero. For values β greater than 0.8, interaction is moderate or weak, and distance between the keels
no longer affects energy loss.