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• W2897908265 abstract "In this work, we study the nonlinear travelling waves in density stratified fluids with piecewise-linear shear currents. Beginning with the formulation of the water-wave problem due to Ablowitz et al. ( J. Fluid Mech. , vol. 562, 2006, pp. 313–343), we extend the work of Ashton & Fokas ( J. Fluid Mech. , vol. 689, 2011, pp. 129–148) and Haut & Ablowitz ( J. Fluid Mech. , vol. 631, 2009, pp. 375–396) to examine the interface between two fluids of differing densities and varying linear shear. We derive a systems of equations depending only on variables at the interface, and numerically solve for periodic travelling wave solutions using numerical continuation. Here, we consider only branches which bifurcate from solutions where there is no slip in the tangential velocity at the interface for the trivial flow. The spectral stability of these solutions is then determined using a numerical Fourier–Floquet technique. We find that the strength of the linear shear in each fluid impacts the stability of the corresponding travelling wave solutions. Specifically, opposing shears may amplify or suppress instabilities." @default.
• W2897908265 created "2018-10-26" @default.
• W2897908265 creator A5008168238 @default.
• W2897908265 creator A5062707088 @default.
• W2897908265 date "2018-10-12" @default.
• W2897908265 modified "2023-10-16" @default.
• W2897908265 title "Nonlinear travelling internal waves with piecewise-linear shear profiles" @default.
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• W2897908265 doi "https://doi.org/10.1017/jfm.2018.679" @default.
• W2897908265 hasPublicationYear "2018" @default.
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