Asymmetric Holmboe instabilities in arrested salt-wedge flows

Abstract

The asymmetric Holmboe instabilities that form on an arrested salt wedge are investigated in the laboratory. The flow is characterized by three regions. Near the tip of the salt wedge, there is little wave activity; immediately downstream, mostly positive waves form; further downstream, both positive and negative waves are present. The appearance of these regions is determined by the spatial variation in the thickness of the saline layer, the shear layer thickness, and the offset between the density interface and velocity interface. We predict the growth of the instabilities by applying linear stability theory to the mean flow field. The predicted initial growth rate is consistent with the laboratory measurements until the Holmboe wave reaches a steepness ratio of 5–7 %. Then, the growth of the Holmboe wave is nonlinear. We found that the Holmboe wavelength increases downstream along the salt wedge. This wave stretching is related to the increase in the shear layer thickness and is supported by the gradual acceleration of the upper layer fluid. Eventually, the growth of the wave amplitude and the wave stretching balance a maximum wave steepness ratio of 10%. Although the wave is nonlinear, the predicted wave speed and wavelength are consistent with the laboratory measurements.