2 results
Boundary-layer-separation-driven vortex shedding beneath internal solitary waves of depression
- Payam Aghsaee, Leon Boegman, Peter J. Diamessis, Kevin G. Lamb
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- Journal:
- Journal of Fluid Mechanics / Volume 690 / 10 January 2012
- Published online by Cambridge University Press:
- 24 November 2011, pp. 321-344
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We investigate global instability and vortex shedding in the separated laminar boundary layer beneath internal solitary waves (ISWs) of depression in a two-layer stratified fluid by performing high-resolution two-dimensional direct numerical simulations. The simulations were conducted with waves propagating over a flat bottom and shoaling over relatively mild and steep slopes. Over a flat bottom, the potential for vortex shedding is shown to be directly dependent on wave amplitude, for a particular stratification, owing to increase of the adverse pressure gradient ( for leftward propagating waves) beneath the trailing edge of larger amplitude waves. The generated eddies can ascend from the bottom boundary to as high as 33 % of the total depth in two-dimensional simulations. Over sloping boundaries, global instability occurs beneath all waves as they steepen. For the slopes considered, vortex shedding begins before wave breaking and the vortices, shed from the bottom boundary, can reach the pycnocline, modifying the wave breaking mechanism. Combining the results over flat and sloping boundaries, a unified criterion for vortex shedding in arbitrary two-layer continuous stratifications is proposed, which depends on the momentum-thickness Reynolds number and the non-dimensionalized ISW-induced pressure gradient at the point of separation. The criterion is generalized to a form that may be readily computed from field data and compared to published laboratory experiments and field observations. During vortex shedding events, the bed shear stress, vertical velocity and near-bed Reynolds stress were elevated, in agreement with laboratory observations during re-suspension events, indicating that boundary layer instability is an important mechanism leading to sediment re-suspension.
Breaking of shoaling internal solitary waves
- PAYAM AGHSAEE, LEON BOEGMAN, KEVIN G. LAMB
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- Journal:
- Journal of Fluid Mechanics / Volume 659 / 25 September 2010
- Published online by Cambridge University Press:
- 15 July 2010, pp. 289-317
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The breaking of fully nonlinear internal solitary waves of depression shoaling upon a uniformly sloping boundary in a smoothed two-layer density field was investigated using high-resolution two-dimensional simulations. Our simulations were limited to narrow-crested waves, which are more common than broad-crested waves in geophysical flows. The simulations were performed for a wide range of boundary slopes S ∈ [0.01, 0.3] and wave slopes extending the parameter range to weaker slopes than considered in previous laboratory and numerical studies. Over steep slopes (S ≥ 0.1), three distinct breaking processes were observed: surging, plunging and collapsing breakers which are associated with reflection, convective instability and boundary-layer separation, respectively. Over mild slopes (S ≤ 0.05), nonlinearity varies gradually and the wave fissions into a train of waves of elevation as it passes through the turning point where solitary waves reverse polarity. The dynamics of each breaker type were investigated and the predominance of a particular mechanism was associated with a relative developmental time scale. The breaking location was modelled as a function of wave amplitude (a), characteristic wave length and the isopycnal length along the slope. The breaker type was characterized in wave slope (Sw = a/Lw, where Lw is a measure of half of the wavelength) versus S space, and the reflection coefficient (R), modelled as a function of the internal Iribarren number, was in agreement with other studies. The effects of grid resolution and wave Reynolds number (Rew) on R, boundary-layer separation and the evolution of global instability were studied. High Reynolds numbers (Rew ~ 104) were found to trigger a global instability, which modifies the breaking process relative to the lower Rew case, but not necessarily the breaking location, and results in a ~ 10 % increase in R, relative to the Rew ~ 103 case.