Instabilities in an Internal Solitary-like Wave on the Oregon Shelf

Abstract

Abstract Observations of internal solitary-like waves (ISWs) on the Oregon Shelf suggest the presence of Kelvin–Helmholtz billows in the pycnocline and larger-scale overturns at the back of the wave above the pycnocline. Numerical simulations designed to explore the mechanisms responsible for these features in one particular wave reveal that shear instabilities occur when (i) the minimum Richardson number Ri in the pycnocline is less than about 0.1; (ii) Lx/λ > 0.8, where Lx is the length of the unstable region with Ri < 0.25 and λ is a half wavelength of the wave; and (iii) a linear spatial stability analysis predicts that ln(af/ai) >≈ 4, where ai and af are the amplitudes of perturbations entering and leaving the unstable region. The maximum energy loss rate in our simulations is 50 W m−1, occurring at a frequency 8% below that with the maximum spatial growth rate. The observations revealed the presence of anomalously light fluid in the center of the wave above the pycnocline. Simulations of a wave encountering a patch of light surface water were used to model this effect. In the presence of a background current with near-surface shear, the simulated ISW has a trapped surface core. As this wave encounters a patch of lighter surface water, the light surface water at first passes beneath the core. Convective instabilities set in and the light fluid is entrained into the core. This results in the formation of overturning features, which exhibit some similarities with the observed overturns.