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Aug 2008

Volume 20, Issue 8, Articles (08xxxx)

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Phys. Fluids 20, 086604 (2008); http://dx.doi.org/10.1063/1.2968451 (9 pages)

Y. D. Afanasyev, P. B. Rhines, and E. G. Lindahl
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back to top Geophysical Flows

Reflection and diffraction of internal waves analyzed with the Hilbert transform

Matthieu J. Mercier, Nicolas B. Garnier, and Thierry Dauxois

Phys. Fluids 20, 086601 (2008); http://dx.doi.org/10.1063/1.2963136 (10 pages) | Cited 17 times

Online Publication Date: 5 August 2008

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We apply the Hilbert transform to the physics of internal waves in two-dimensional fluids. Using this demodulation technique, we can discriminate internal waves propagating in different directions: This is very helpful in answering several fundamental questions in the context of internal waves. We focus more precisely in this paper on phenomena associated with dissipation, diffraction, and reflection of internal waves.
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47.35.-i Hydrodynamic waves
47.55.Hd Stratified flows
02.30.Uu Integral transforms

Driven chirped vorticity holes

M. A. Borich and L. Friedland

Phys. Fluids 20, 086602 (2008); http://dx.doi.org/10.1063/1.2964361 (11 pages)

Online Publication Date: 12 August 2008

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The formation and control of m-fold symmetric vorticity hole structures in a two-dimensional vortex patch with a line vortex core is studied within an adiabatic contour dynamics theory. The holes are formed by subjecting an initially circular vortex patch to an m-fold symmetric, oscillating, chirped frequency straining flow. The theory uses adiabatic invariants associated with the boundaries of the patch and describes all stages of evolution in the driven system, i.e., the emergence of the m-fold symmetric V-state, resonant passage through the boundary of the V-state, formation of vorticity holes, and autoresonant dynamics of the driven holes inside the vortex structure. The results of the theory are in a good agreement with the fast multipole-type simulations. In contrast to free (unstrained) m-fold symmetric vorticity hole structures, where only m = 1 case is stable, resonantly driven phase-locked m>1 vorticity holes can be stabilized by the external strain. More complex, stable m-fold symmetric vorticity structures with local minima in vorticity distributions can be formed from initially axisymmetric distributions by external, chirped frequency strains.
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47.32.-y Vortex dynamics; rotating fluids

Dam-break flows with resistance as agents of sediment transport

M. Emmett and T. B. Moodie

Phys. Fluids 20, 086603 (2008); http://dx.doi.org/10.1063/1.2967534 (20 pages) | Cited 2 times

Online Publication Date: 12 August 2008

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When a semi-infinite body of fluid initially at rest behind a vertical retaining wall is suddenly released by the removal of the barrier, the resulting flow over either a horizontal or a sloping bed is referred to as a dam-break flow. When resistance to the flow is neglected, the exact solution in the case of a horizontal bed with or without “tail water” may be obtained on the basis of shallow-water theory via the method of characteristics, and the results are well known. The inclusion of the effects of resistance in the form of basal friction that are needed in order to bring the mathematical solutions into closer harmony with the experimental results modifies the wave speed and flow profile near the head of the wave significantly and the simple exact solution of the shallow-water equations can no longer be employed as a reasonable description of the flow field. It is our intention here to study dam-break flows as agents of sediment transport taking into account basal friction and the attendant changes in depth profiles near the head, as well as the effects of particle concentrations on the flow dynamics including both erosion and deposition of particles arising through the interaction of the flow with the bed material. We shall consider shallow flows over dry beds and investigate the effects of changes in the depositional and erosional models employed as well as in the nature of the drag acting on the flow. These models offer some insight into the transport of sediment in the worst case scenario of complete and instantaneous collapse of a dam. They are also anticipated to provide information on other sheet flow events where particle transport plays a significant role in the flow dynamics.
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47.57.ef Sedimentation and migration
47.55.Hd Stratified flows
47.11.-j Computational methods in fluid dynamics
92.40.Gc Erosion and sedimentation; sediment transport

Vortices and Rossby waves in cylinder wakes on a parabolic β-plane observed by altimetric imaging velocimetry

Y. D. Afanasyev, P. B. Rhines, and E. G. Lindahl

Phys. Fluids 20, 086604 (2008); http://dx.doi.org/10.1063/1.2968451 (9 pages) | Cited 2 times

Online Publication Date: 15 August 2008

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Intense vortices in the wake of a circular cylinder are investigated in a rotating parabolic (polar) β-plane fluid. This system has a background potential vorticity (PV) field that supports Rossby waves and causes vortices to migrate and radiate. A method for imaging rotating flows, which we call “altimetric imaging velocimetry” is employed. Optical color coding of slopes of the free-surface elevation field yields the pressure, geostrophic and gradient wind velocity, and potential vorticity fields with very high spatial resolution, limited largely by the pixel resolution of the available imaging sensors. Cylinder wakes on the polar β-plane exhibit strikingly different regimes as it is translated azimuthally, eastward or westward. Self-arrangement of vortices after the cylinder was stopped drives an intense eastward jet formed by the rows of anticyclones and cyclones on its flanks. In agreement with the idea of a PV staircase, this jet has a strong PV gradient at its center, while PV is homogenized by the vortices on either side. A slowly translating cylinder generates Rossby waves with phase propagation locked to the cylinder, and intermediate cases show a widespread vortex/wave interaction.
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47.32.cb Vortex interactions
47.80.Jk Flow visualization and imaging
47.35.-i Hydrodynamic waves

Regimes of near-wall vortex dynamics in potential flow through gaps

V. G. Makarov and S. N. Bulgakov

Phys. Fluids 20, 086605 (2008); http://dx.doi.org/10.1063/1.2969471 (11 pages) | Cited 3 times

Online Publication Date: 29 August 2008

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A two-dimensional problem of the motion of a single vortex near an infinite straight wall with singular gaps is solved both analytically, using a point-vortex approach, and numerically based on the method of contour surgery for a vortex patch. The background irrotational flow was generated by a balanced point source-sink system located at the gaps. Three different regimes of vortex evolution were detected and studied in detail: (i) Complete or partial transit, i.e., continuation of the motion along the wall; (ii) complete destruction, i.e., the “penetration” through the sink gap; and (iii) capture in a certain area against the wall between the gaps. These regimes are controlled by three parameters: the ratio of the vortex size and the distance between the gaps, the remoteness of the vortex trajectory from the wall, and the ratio of the intensities of the background flow and the vortex. A bifurcational character of the transition between the regimes was observed. Steady-state solutions were found numerically, including the orbital O state, where the vortex's centroid moves along a constant orbit, while the shape of the vortex changes periodically. Capturing the vortex was usually carried out in a form close to this state.
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47.32.C- Vortex dynamics
47.60.-i Flow phenomena in quasi-one-dimensional systems
47.20.Ky Nonlinearity, bifurcation, and symmetry breaking
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