Bulletin of the American Physical Society
60th Annual Meeting of the Divison of Fluid Dynamics
Volume 52, Number 12
Sunday–Tuesday, November 18–20, 2007; Salt Lake City, Utah
Session NP: Waves II |
Hide Abstracts |
Chair: A. Tabaei, Massachusetts Institute of Technology Room: Salt Palace Convention Center 251 D |
Tuesday, November 20, 2007 11:35AM - 11:48AM |
NP.00001: Effects of Dissipation on Multiple Resonant Scattering of Monochromatic Waves by an Array of Cylinders Ali Tabaei, Yile Li, Chiang Mei As in crystallography and photonic physics, multiple scattering of incident waves by a periodic array of scatterers can induce Bragg resonance and bandgaps. Extending the asymptotic theory of Li and Mei (2007) for water waves passing an array of vertical cylinders, we consider the additional effects of viscous dissipation. Two types of the dissipation are treated. One is that in a laminar Stokes boundary layer near the cylinder; the results are relevant to sound waves scattering. The second is due to vortex shedding common around offshore structures. Starting from the resonance criterion known in solid state physics, asymptotic techniques are employed to derive two-dimensional coupled-mode equations for the envelopes of the scattered waves. Cylinders are assumed to be much smaller than the incident wavelength which is comparable to the cylinder spacing. To account for the effect of vortex shedding, the method of equivalent linearization is employed to model the nonlinear separation losses in the vicinity of cylinders. Analytical solutions are found for a long strip of cylinder array and the effects of dissipation loss on the attenuation of wave amplitudes throughout the strip are discussed. [Preview Abstract] |
Tuesday, November 20, 2007 11:48AM - 12:01PM |
NP.00002: Stability of Gravity--Capillary Lumps T.R. Akylas, Yeunwoo Cho Lumps are fully localized nonlinear waves of permanent form. In the classical water-wave problem, such waves are possible only when both gravity and surface tension are present. Shallow- water lumps, in particular, are known to arise in the strong- surface-tension regime and have been studied extensively. Here, we are concerned with a new class of lumps, found recently on water of finite or infinite depth. These lumps bifurcate at the minimum gravity--capillary phase speed and, in the small-amplitude limit, resemble locally confined wavepackets with envelope corresponding to the ground state of a steady elliptic-- elliptic Davey--Stewartson (EEDS) equation system. We examine the stability of lumps of this type. We find that exchange of stabilities occurs when the energy is stationary as a function of the wave speed. This criterion predicts that small-amplitude lumps are unstable while finite-amplitude lumps are stable. Numerical simulations indicate that the instability results in the formation of a finite-amplitude lump, thus interpreting the focusing singularity (wave collapse) predicted by the EEDS equations. [Preview Abstract] |
Tuesday, November 20, 2007 12:01PM - 12:14PM |
NP.00003: Along-track Gradients and Stratified Wake Green Functions David Vasholz In the context of linear stratified equilibrium wakes an approximation that consists of removing the along-track gradient term from the source equation is considered. An analysis is carried out in terms of Green functions and a formal solution is derived that directly displays the simplifying effects of this approximation. A complementary analysis is performed that reinterprets the modal expansion appearing in the formal solution in terms of critical speed eigenvalues. It is then shown how the neglect of the along-track gradient amounts to a high Froude number approximation. Detailed results are shown for the case of a uniform buoyancy frequency, where the validity of the high Froude number approximation is examined as a function of source speed. [Preview Abstract] |
Tuesday, November 20, 2007 12:14PM - 12:27PM |
NP.00004: Jetting from parametrically forced gravity waves in a circular cylinder Shyama Prasad Das, Emil J. Hopfinger We present results on parametrically forced gravity waves in a circular cylinder of 5cm diameter in the limit of large fluid depth. The stability threshold forcing amplitude and the wave breaking threshold have been determined in a frequency range near the natural frequency of the lowest axi-symmetric wave mode. The wave amplitude response curves of stable wave motions exhibit wave amplitude modulations and bifurcations to other wave modes of frequencies neighbouring the axi-symmetric mode frequency. The amplitude modulations are either on a slow time scale or period tripling and intermittently period tripling without wave breaking. In the unstable regime a finite time singularity occurs with intense geyser or jet formation, a phenomenon demonstrated by Zeff et al. (\textit{Nature} v. 403, 2000) in fluids of high viscosity and large surface tension. Here, this singular behaviour is demonstrated for a low viscosity and low kinematic surface tension liquid. The jet velocity seems to scale with kinematic surface tension and container radius. Especially the importance of the singularity and maximum jet velocity is radius dependent. A correlation containing all the parameters is proposed. [Preview Abstract] |
Tuesday, November 20, 2007 12:27PM - 12:40PM |
NP.00005: Correction of Lamb's dissipation calculation for the effects of viscosity on capillary-gravity waves Juan C. Padrino, Daniel D. Joseph Purely irrotational theories of the flow of a viscous liquid are applied to model the effect of viscosity on the decay and oscillation of capillary-gravity waves. In particular, the dissipation approximation used in this analysis gives rise to a viscous correction of the frequency of the oscillations which was not obtained by Lamb`s [H. Lamb, Hydrodynamics (Cambridge University Press, Cambridge, UK, 1932) (reprinted in 1993)] dissipation calculation. Moreover, our dissipation method goes beyond Lamb's in the sense that it yields an eigenvalue relation for the entire continues spectrum of wave numbers. Comparisons are presented between the purely irrotational theories and Lamb`s exact solution, showing good to reasonable agreement for long, progressive waves and for short, standing waves, even for very viscous liquids. The performance of the irrotational approximations deteriorates within an interval of wave numbers containing the cutoff where traveling waves become standing ones. [Preview Abstract] |
Tuesday, November 20, 2007 12:40PM - 12:53PM |
NP.00006: Normal modes of a rectangular tank with corrugated bottom Jie Yu, Louis Howard We study some effects of regular bottom corrugations on water waves in a long rectangular tank with vertical end walls and open top. In particular, we consider motions which are normal modes of oscillation in such a tank. Attention is focused on the modes whose internodal spacing, in the absence of corrugations, would be near the wavelength of the corrugations. In these cases, the perturbation of the eigenfunctions (though not of their frequencies) can be significant, e.g. the amplitude of the eigenfunction can be greater by a factor of ten or more near one end of the tank than at the other end. This is due to a cooperative effect of the corrugations, called Bragg resonance. We first study these effects using an asymptotic theory, which assumes that the bottom corrugations are of small amplitude and that the motions are slowly-varying everywhere. We then present an exact theory, utilizing continued fractions. This allows us to deal with the rapidly varying components of the flow. The exact theory confirms the essential correctness of the asymptotic results for the slowly varying aspects of the motions. The rapidly varying parts (evanescent waves) are, however, needed to accurately satisfy the true boundary conditions, hence of importance to the flow near the end walls. [Preview Abstract] |
Tuesday, November 20, 2007 12:53PM - 1:06PM |
NP.00007: Harmonic and Subharmonic Surface Wave Dynamics in Horizontally Vibrated Rectangular Containers Jeff Porter, Carlos Lopez, Ana Laveron We discuss the theoretical background and preliminary results from a recently initiated experimental study of surface wave dynamics in open, horizontally vibrated containers. Recent theory by Varas and Vega (J. Fluid Mech. 579, 2007) indicates how rich this system can be. The container walls, acting as wavemakers, generate harmonic surface waves that may be localized near these walls or extended; a multiplicity of states leads to hysteresis depending strongly on the Bond number and container size. Additionally, the horizontally vibrated walls generate an oscillatory bulk flow, and hence an oscillatory normal pressure gradient at the free surface, whose effect is analogous to Faraday (vertical) excitation and leads, for sufficient amplitude, to subharmonic instability. We investigate this mechanism, and a range of competing instabilities and mode interactions, in low viscosity silicone oil (DC 200/10) for frequencies of 10-50 Hz. [Preview Abstract] |
Tuesday, November 20, 2007 1:06PM - 1:19PM |
NP.00008: Numerical analysis of thermal wave behavior by the CESE Method Yin Chou, Ruey Jen Yang In this study, we simulate the behavior of Dual Phase Lag (DPL) thermal wave with a pulsed temperature condition in one dimension and two dimension domain by applying an extension of the Space-Time Conservation Element and Solution Element (CESE) numerical method. Both the temperature and heat flux distributions in a finite medium subject to various non-Fourier heat conduction models are calculated. In every case, the thermal waves are simulated with respect to time as the thermal wave propagates through the medium with a constant velocity. Calculations performed to exhibit various lagging thermal behavior of conduction heat transfer, such as wave, wavelike, and diffusive behavior. In general, the simulation results are found to be in good agreement with the exact analytical solutions. Furthermore, it is shown that the CESE method yields low numerical dissipation and dispersion errors and accurately models the propagation of the wave form even in its discontinuous portions. [Preview Abstract] |
Follow Us |
Engage
Become an APS Member |
My APS
Renew Membership |
Information for |
About APSThe American Physical Society (APS) is a non-profit membership organization working to advance the knowledge of physics. |
© 2024 American Physical Society
| All rights reserved | Terms of Use
| Contact Us
Headquarters
1 Physics Ellipse, College Park, MD 20740-3844
(301) 209-3200
Editorial Office
100 Motor Pkwy, Suite 110, Hauppauge, NY 11788
(631) 591-4000
Office of Public Affairs
529 14th St NW, Suite 1050, Washington, D.C. 20045-2001
(202) 662-8700