JP6.16 Secondary instabilities in the breaking of inertia gravity waves

Thursday, 11 June 2009
Stowe Room (Stoweflake Resort and Confernce Center)
Mark Furman, Goethe Universität, Frankfurt am Main, Germany; and U. Achatz

The three-dimensionalization of turbulence in a breaking inertia-gravity wave is investigated through singular vector analysis.

Earlier work has analyzed the breaking of an inertia gravity wave and the development of turbulence using a high resolution nonlinear 2-d Boussinesq model initialized with a single inertia-gravity wave and one of its leading singular vectors or fastest growing normal modes. This 2-d approach is computationally economical enough to easily explore the parameter space and yields results comparable to fully 3-d simulations in terms of energy conversion and stabilization of the initial wave.

It is known however that in the transition to turbulence in a breaking wave, the flow becomes strongly three dimensional. A tangent-linear model is used to find the leading singular vectors orthogonal to the plane containing the wave vectors of the breaking wave and primary perturbation, and thus shed light on the dynamics of the initial three-dimensionalization of the flow.

The talk will focus on the cases of a statically and dynamically stable vertically propagating inertia-gravity wave perturbed by its leading transverse singular vector and a statically unstable high frequency gravity wave perturbed by its leading normal mode. Secondary instabilities are concentrated near regions of strong gradients in the breaking wave. Location, structure, and growth mechanisms of the leading secondary perturbations will be discussed.

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