Bulletin of the American Physical Society
2005 58th Annual Meeting of the Division of Fluid Dynamics
Sunday–Tuesday, November 20–22, 2005; Chicago, IL
Session LL: Waves III |
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Chair: Andre Nachbin, Instituto Nacional de Matematica Pura e Aplicada Room: Hilton Chicago Astoria |
Tuesday, November 22, 2005 8:00AM - 8:13AM |
LL.00001: Improved Boussinesq models over highly variable topographies Andre Nachbin Recently a weakly nonlinear, weakly dispersive terrain-following Boussinesq system was formulated [SIAP 2003] in order to study solitary waves over highly variable (random) topographies. The modeling allows for multiply-valued topography profiles. In this presentation we will give an overview of very recent theoretical results performed with this equation. The apparent diffusion [SIAP 2004, Physica D 2004], eddy viscosity [PRL 2004b] and time-reversed waveform inversion [PRL 2004a] are illustrated through computational experiments. Finally we introduce a new, fully dispersive, Boussinesq system [PRL 2004c] that generalizes the terrain-following system mentioned above. The full linear dispersion relation is entirely retained by constructing a Dirichlet-to-Neumann (DtN) map along the top boundary of the highly corrugated strip representing the channel. [Preview Abstract] |
Tuesday, November 22, 2005 8:13AM - 8:26AM |
LL.00002: Asymptotic calculation of the velocity field for shallow- water waves Alexander Sachs, Shiu-Chin Tsai An approximate calculation is made of the velocity field for the propagation of a soliton on the surface of a fluid in a channel of constant depth, The time evolution equation for the stream function for a viscous fluid described by the Navier-Stokes equation is solved for large distances from the crest of the soliton. Boundary conditions at the bottom and at the free surface are included. The results for the velocity field are in fairly good agreement with the numerical calculation of C.J. Tang et al. (1) \newline \newline (1) C.J. Tang,V.C. Patel and L. Landweber, J.Comut. Phys. \textbf{88}, 86 (1990) [Preview Abstract] |
Tuesday, November 22, 2005 8:26AM - 8:39AM |
LL.00003: Progressive internal waves of permanent form John McHugh Progressive internal waves of permanent form in a semi-infinite layer of stratified fluid are considered. Such waves were previously considered in a layer of finite depth by Thorpe (1968) and Yih (1974). Both of these previous studies have difficulty with uniform validity, which becomes critically important in the unbounded layer. New results are obtained here using a different expansion, still assuming small wave amplitude. A model equation is useful in directing the choice of expansion. Long's equation is used for the governing equation. The upstream velocity is assumed constant and equal to the wave speed, making the problem steady. The upstream density profile is chosen to have constant Brunt-Vaisala frequency, however for nonlinear waves, the upstream density profile must be adjusted to avoid mass transport through a streamline, as demonstrated by Yih (1974). This adjustment involves non-Boussinesq effects. The results show that the wave amplitude can reach a maximum at a finite altitude, depending on the background state. [Preview Abstract] |
Tuesday, November 22, 2005 8:39AM - 8:52AM |
LL.00004: Stokes waves with viscosities Jin Wang We study the influence of viscosities on travelling Stokes waves of permanent form. Our numerical results suggest that slight viscous effects on a Stokes wave merely cause the wave to dissipate while remaining a member of the family. This observation is justified by performing formal asymptotic analysis. [Preview Abstract] |
Tuesday, November 22, 2005 8:52AM - 9:05AM |
LL.00005: Conservation laws for the Rossby wave system Francois van Heerden, Alexander Balk It is known that the Rossby wave system possesses an extra motion invariant (in addition to energy and enstrophy). This yields an approximate conservation law, conserved up to third order of smallness in amplitude. We investigate whether the conservation can be extended to an exact conservation law. [Preview Abstract] |
Tuesday, November 22, 2005 9:05AM - 9:18AM |
LL.00006: Nonlinear and breaking micron waves at the edge of laser-liquified indium pool Stjepan Lugomer, Norman Zabusky We have discovered solidified fossils of micron-sized nonlinear and breaking surface waves of 10 micron depth on the edge of a liquid indium pool. These are likely the result of driven capillary-gravity waves. These results were obtained with a 30 nanosecond laser beam interacting with a thin indium target. The laser fluence varied around 4.25 J/cm$^{2}$ . As the fluence is increased, the waves ``break-and-spill'' and elongated fingers and spherical bubbles appear more frequently on the fossil surface. [Preview Abstract] |
Tuesday, November 22, 2005 9:18AM - 9:31AM |
LL.00007: WITHDRAWN: Stochastically Forced Surface Waves Kristjan Onu, N. Sri Namachchivaya We consider the long term evolution of surface waves under the influence of small amplitude stochastic forcing. The waves are enclosed in a cylindrical container. Our starting point is a Hamiltonian formulation of the equations of motion that govern the motion of two wave modes near resonance with one another, a four dimensional system. We then establish two integrals of motion for the surface waves system and describe how, in the presence of small amplitude stochastic forcing and small viscous damping, the two integrals of motion evolve as a two-dimensional Markov process. Stochastic averaging is performed to characterize the generator of the Markov process. Due to the structure of the phase space of the surface waves, the stochastic averaging is ``non-standard'' and the transition of the probabilistic Markov process from one region of phase space to another must be carefully specified. Knowing the generator of the Markov process, it becomes possible to calculate stationary probability density functions of the surface wave system by solving the Fokker-Planck equation. The probability densities thus obtained are validated against those obtained by directly modeling the stochastic ordinary differential equations governing the evolution of the original two wave modes, using a Monte Carlo method. [Preview Abstract] |
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