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Dec 2007

Volume 19, Issue 12, Articles (12xxxx)

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Phys. Fluids 19, 124102 (2007); http://dx.doi.org/10.1063/1.2813548 (11 pages)

J. P. Wilkinson and J. W. Jacobs
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back to top Geophysical Flows

Waves on unsteady currents

Merrick C. Haller and H. Tuba Özkan-Haller

Phys. Fluids 19, 126601 (2007); http://dx.doi.org/10.1063/1.2803349 (12 pages) | Cited 2 times

Online Publication Date: 3 December 2007

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Models for surface gravity wave propagation in the presence of currents often assume the current field to be quasi-stationary, which implies that the absolute wave frequency is time invariant. However, in the presence of unsteady currents or time-varying water depth, linear wave theory predicts a time variation of the absolute wave frequency (and wavenumber). Herein, observations of wave frequency modulations from a large-scale laboratory experiment are presented. In this case, the modulations are caused by both unsteady depths and unsteady currents due to the presence of low-frequency standing waves. These new observations allow a unique and detailed verification of the theoretical predictions regarding variations in the absolute wave frequency. In addition, analytic solutions for the variations in frequency and wave height induced by the unsteady medium are found through a perturbation analysis. These solutions clarify the dependency of the wave frequency/wave height modulations on the characteristics of the unsteady medium. We also find that analytic solutions for simplified basin configurations provide an order of magnitude estimate of the expected frequency modulation effect. Finally, the importance of this phenomenon in natural situations is discussed.
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47.35.Bb Gravity waves

Interactions of two vortices near step topography

A. K. Hinds, E. R. Johnson, and N. R. McDonald

Phys. Fluids 19, 126602 (2007); http://dx.doi.org/10.1063/1.2793140 (17 pages)

Online Publication Date: 4 December 2007

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The general motion of a pair of point vortices of arbitrary circulations in two-dimensional ideal shallow water near topography in the form of rectilinear step is found using Hamiltonian techniques. Paths are determined by the constants of motion: energy, linear impulse, and circulation. The behavior of vortex patches in the same geometry is computed using contour dynamics. Comparisons of point vortex and patch trajectories are found to be close provided the vortex patch centroids are sufficiently far away from the escarpment. For special values of the constants of motion, vortex pairs that propagate steadily parallel to the escarpment without deformation are found (that is, vortex pair equilibrium states) and exist even when the circulation of each vortex has the same sign.
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47.32.cb Vortex interactions

Vorticity dynamics of a dipole colliding with a no-slip wall

W. Kramer, H. J. H. Clercx, and G. J. F. van Heijst

Phys. Fluids 19, 126603 (2007); http://dx.doi.org/10.1063/1.2814345 (13 pages) | Cited 5 times

Online Publication Date: 11 December 2007

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The active role of vorticity in the collision of a Lamb-like dipole with a no-slip wall is studied for Re values ranging between 625 and 20000. The initial approach of the dipole does not differ from the stress-free case or from a point-vortex model that incorporates the diffusive growth of the dipole core. When closer to the wall, the detachment and subsequent roll-up of the boundary layer leads to a viscous rebound, as was observed by Orlandi [Phys. Fluids A 2, 1429 (1990)] in numerical simulations with Re up to 3200. The net translation of the vortex core along the wall is strongly reduced due to the cycloid-like trajectory. For Re ⩽ 2500 wall-generated vorticity is wrapped around the separate dipole halves, which hence become (partially) shielded monopoles. For Re≳O(104), however, a shear instability causes the roll-up of the boundary layer before it is detached from the wall. This leads to the formation of a number of small-scale vortices, between which intensive, narrow eruptions of boundary-generated vorticity occur. Quantitative measures are given for the influx of vorticity at the wall and the consequent increase of boundary layer vorticity and enstrophy.
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47.20.Ib Instability of boundary layers; separation
47.20.-k Flow instabilities
47.32.C- Vortex dynamics
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