Abstract
Abstract. Large-amplitude internal waves in the ocean propagate in a dynamic, highly variable environment with changes in background current, local depth, and stratification. The Dubreil–Jacotin–Long, or DJL, theory of exact internal solitary waves can account for a background shear, doing so at the cost of algebraic complexity and a lack of a mathematical proof of algorithm convergence. Waves in the presence of shear that is strong enough to preclude theoretical calculations have been reported in observations. We report on high-resolution simulations of stratified adjustment in the presence of strong shear currents. We find instances of large-amplitude solitary-like waves with recirculating cores in parameter regimes for which DJL theory fails and of wave types that are completely different in shape from classical internal solitary waves. Both are spontaneously generated from general initial conditions. Some of the waves observed are associated with critical layers, but others exhibit a propagation speed that is very near the background current maximum. As such they are not freely propagating solitary waves, and a DJL theory would not apply. We thus provide a partial reconciliation between observations and theory.
Highlights
Large-amplitude internal waves, often referred to as internal solitary-like waves or ISWs, are a well-studied coherent, nonlinear phenomenon accessible via field measurements, laboratory experiments, and simulations of density stratified fluids
ISWs were described by approximate perturbation theories that lead to an equation of Korteweg–de Vries (KdV) type for the temporal–horizontal portion of the object (Talipova et al, 1999; Helfrich and Melville, 2006)
The velocity range is chosen to be symmetric in order to demonstrate that the background current is always greater than or equal to zero
Summary
Large-amplitude internal waves, often referred to as internal solitary-like waves or ISWs, are a well-studied coherent, nonlinear phenomenon accessible via field measurements, laboratory experiments, and simulations of density stratified fluids. The vertical component is described by solving a linear ordinary differential eigenvalue problem. This is generally referred to as the weakly nonlinear description, or WNL. Exact ISWs are solutions of the nonlinear elliptic eigenvalue problem referred to as the Dubreil–Jacotin–Long (DJL) equation. This equation is formally equivalent to the full stratified Euler equations (in a frame moving with the wave), and this theory is referred to as fully nonlinear or exact
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