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dc.contributor.authorCarr, Magda
dc.contributor.authorKing, Stuart Edward
dc.contributor.authorDritschel, David Gerard
dc.identifier.citationCarr , M , King , S E & Dritschel , D G 2011 , ' Numerical simulation of shear-induced instabilities in internal solitary waves ' , Journal of Fluid Mechanics , vol. 683 , pp. 263-288 .
dc.identifier.otherPURE: 4156981
dc.identifier.otherPURE UUID: 8ea58242-9417-45c6-8f1a-279b3ca2af9d
dc.identifier.otherScopus: 80053166478
dc.identifier.otherWOS: 000295715900010
dc.identifier.otherORCID: /0000-0001-6489-3395/work/64697739
dc.descriptionThis work was supported by the UK Engineering and Physical Sciences Research Council [grant number EP/F030622/1]en
dc.description.abstractA numerical method that employs a combination of contour advection and pseudo-spectral techniques is used to simulate shear-induced instabilities in an internal solitary wave (ISW). A three-layer configuration for the background stratification, in which a linearly stratified intermediate layer is sandwiched between two homogeneous ones, is considered throughout. The flow is assumed to satisfy the inviscid, incompressible, Oberbeck–Boussinesq equations in two dimensions. Simulations are initialized by fully nonlinear, steady-state, ISWs. The results of the simulations show that the instability takes place in the pycnocline and manifests itself as Kelvin–Helmholtz billows. The billows form near the trough of the wave, subsequently grow and disturb the tail. Both the critical Richardson number (Ric) and the critical amplitude required for instability are found to be functions of the ratio of the undisturbed layer thicknesses. It is shown, therefore, that the constant, critical bound for instability in ISWs given in Barad & Fringer (J. Fluid Mech., vol. 644, 2010, pp. 61–95), namely Ric = 0.1 ± 0.01 , is not a sufficient condition for instability. It is also shown that the critical value of Lx/λ required for instability, where Lx is the length of the region in a wave in which Ri < 1/4 and λ is the half-width of the wave, is sensitive to the ratio of the layer thicknesses. Similarly, a linear stability analysis reveals that δiTw (where δi is the growth rate of the instability averaged over Tw, the period in which parcels of fluid are subjected to Ri < 1/4) is very sensitive to the transition between the undisturbed pycnocline and the homogeneous layers, and the amplitude of the wave. Therefore, the alternative tests for instability presented in Fructus et al. (J. Fluid Mech., vol. 620, 2009, pp. 1–29) and Barad & Fringer (J. Fluid Mech., vol. 644, 2010, pp. 61–95), respectively, namely Lx/λ ≥ 0.86 and δiTw > 5 , are shown to be valid only for a limited parameter range.
dc.relation.ispartofJournal of Fluid Mechanicsen
dc.rightsThis is the author's version of this article. The published version (c)Cambridge University Press is available from http://journals.cambridge.orgen
dc.subjectInternal wavesen
dc.subjectSolitary wavesen
dc.subjectStratified flowsen
dc.subjectQA Mathematicsen
dc.titleNumerical simulation of shear-induced instabilities in internal solitary wavesen
dc.typeJournal articleen
dc.contributor.institutionUniversity of St Andrews. Applied Mathematicsen
dc.contributor.institutionUniversity of St Andrews. Scottish Oceans Instituteen
dc.contributor.institutionUniversity of St Andrews. Marine Alliance for Science & Technology Scotlanden
dc.description.statusPeer revieweden

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