David Deepwell | Applied Math, University of Waterloo
High resolution simulations of mode-2 internal waves: transport, shoaling, and the influence of rotation
Internal waves are a universal feature in stratified flows. Of particular interest are Internal Solitary and Solitary-like Waves (ISWs) which may persist for long periods of time and travel great distances. In the ocean ISWs are energetically dominated by mode-1 waves for which all lines of constant density are displaced together in a direction from their rest height. The literature on higher modes, the second mode in particular, is less developed than that for the first mode. However, over the last decade multiple observations of the mode-2 ISWs have been made throughout the world's oceans, which has lead to a renewed interest in studying the second mode in theoretical and practical applications.
We present high resolution numerical simulations of mode-2 ISWs on a laboratory scale. We have used the pseudo-spectral model SPINS on the high-performance computing cluster SHARCNET. We have added diagnostics (specifically, energy budgets) into this model to help in reporting the accuracy and efficacy of each simulation. Laboratory experiments were also completed to make a comparison to particular numerical results.
Most previous numerical simulations of mode-2 ISWs have used symmetry arguments to simplify the domain into a two-dimensional half-depth region. These choices reduce the computational requirements but remove the ability for certain instabilities to form. Rather we have used full three-dimensional domains to study the generation and evolution of mode-2 ISWs in laboratory environments under various conditions.
We present results for three specific experiments: the mass transport efficiency of a mode-2 ISW in a variety of stratifications, the adjustment of a mode-2 ISW in a channel influenced by rotation, and the interaction with topography during the propagation of mode-2 ISWs over an isolated ridge. We find that mass transport is primarily affected by instabilities on the lee side of an ISW, rotation modifies the ISW into Kelvin waves and Poincare waves, and a ridge is able to extract mass from the core of the ISW when the interaction is strong while also inducing cross-boundary layer transport.