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• W2912510183 endingPage "729" @default.
• W2912510183 startingPage "702" @default.
• W2912510183 abstract "We study the evolution of three-dimensional (3-D), small-scale, small-amplitude perturbations on a plane internal gravity wave using the local stability approach. The plane internal wave is characterised by its non-dimensional amplitude, $A$ , and the angle the group velocity vector makes with gravity, $unicode[STIX]{x1D6F7}$ . For a given $(A,unicode[STIX]{x1D6F7})$ , the local stability equations are solved on the periodic fluid particle trajectories to obtain growth rates for all two-dimensional (2-D) and 3-D perturbation wave vectors. For small $A$ , the local stability approach recovers previous results of 2-D parametric subharmonic instability (PSI) while offering new insights into 3-D PSI. Higher-order triadic resonances, and associated deviations from them, are also observed at small $A$ . Moreover, for small $A$ , purely transverse instabilities resulting from parametric resonance are shown to occur at select values of $unicode[STIX]{x1D6F7}$ . The possibility of a non-resonant instability mechanism for transverse perturbations at finite $A$ allows us to derive a heuristic, modified gravitational instability criterion. We then study the extension of small $A$ to finite $A$ internal wave instabilities, where we recover and build upon existing knowledge of small-scale, small-amplitude internal wave instabilities. Four distinct regions of the $(A,unicode[STIX]{x1D6F7})$ -plane based on the dominant instability modes are identified: 2-D PSI, 3-D oblique, quasi-2-D shear-aligned, and 3-D transverse. Our study demonstrates the local stability approach as a physically insightful and computationally efficient tool, with potentially broad utility for studies that are based on other theoretical approaches and numerical simulations of small-scale instabilities of internal waves in various settings." @default.
• W2912510183 created "2019-02-21" @default.
• W2912510183 creator A5010177196 @default.
• W2912510183 creator A5084913330 @default.
• W2912510183 date "2019-01-29" @default.
• W2912510183 modified "2023-09-25" @default.
• W2912510183 title "Three-dimensional small-scale instabilities of plane internal gravity waves" @default.
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• W2912510183 doi "https://doi.org/10.1017/jfm.2018.921" @default.
• W2912510183 hasPublicationYear "2019" @default.
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