Internal solitary wave-induced flow over a corrugated bed |
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Authors: | Magda Carr Marek Stastna Peter A Davies |
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Institution: | (1) School of Mathematics & Statistics, University of St Andrews, St Andrews, KY16 9SS, UK;(2) Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada;(3) Department of Civil Engineering, University of Dundee, Dundee, DD1 4HN, UK |
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Abstract: | A combined numerical and experimental study of the propagation of an internal solitary wave (ISW) over a corrugated bed is
presented, in which the amplitude and the wavelength of the corrugated bed, together with the wave amplitude and wave speed
of the ISW, have been varied parametrically. Both ISWs of elevation and depression have been considered. The wave-induced
currents over the corrugated bed cause flow separation at the apex of the corrugations and a sequence of lee vortices forms
as a result. These vortices develop fully after the main wave has passed over the topographic feature, resulting in deformation
of the overlying pycnocline and, in some instances, significant vertical mixing. It is found that the intensity of the vortex
formation is dependent on both the amplitude and wavelength of the bottom topography. In the case of an ISW of depression,
the generation of vertically (upward)-propagating vortices is seen to result in entrainment of fluid from a bottom boundary
jet (Carr and Davies, Phys Fluids 18:016601, 2006), while, in the elevation case, a second mechanism is present to induce significant turbulent mixing in the water column.
It occurs when the bottom corrugations reach into, or are very near, the pycnocline at rest. Large waves of elevation that
are stable on approach to the corrugations exhibit evidence of a spatio-temporally developing shear instability as they interact
with the bottom corrugation. The shear instability takes the form of billows that have a vertical extent that can reach 50%
of the wave amplitude. |
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