Bulletin of the American Physical Society
62nd Annual Meeting of the APS Division of Fluid Dynamics
Volume 54, Number 19
Sunday–Tuesday, November 22–24, 2009; Minneapolis, Minnesota
Session LS: Waves I |
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Chair: Jim Duncan, University of Maryland Room: 200G |
Monday, November 23, 2009 3:35PM - 3:48PM |
LS.00001: Resonantly Forced Gravity--Capillary Lumps on Deep Water T.R. Akylas, Yeunwoo Cho A theoretical study is made of the wave disturbance generated by
a locally confined external pressure on the surface of deep
water moving with speed $V$ near the minimum gravity--capillary
phase speed, $c_{min}$. According to linear inviscid theory, the
response when $V$ coincides with $c_{min}$ is unbounded, and the
interplay of nonlinear and damping effects is crucial close to
this resonance. The analysis is based on an approximate model
that combines the linear dispersion relation in the vicinity of
$c_{min}$ with quadratic and cubic nonlinearity as well as
viscous damping. For $V$ well below $c_{min}$, the transient
response from rest approaches the small-amplitude steady state
predicted by linear theory, but nonlinear effects come into play
at a certain forcing speed, $c_{crit} |
Monday, November 23, 2009 3:48PM - 4:01PM |
LS.00002: An Experimental Investigation of the Wave Pattern Generated by a Moving Pressure Source: Solitary Capillary-Gravity Waves J.H. Duncan, J.D. Diorio, A. Lisiewski, R. Harris The wave pattern generated by a small pressure source moving across a water surface at speeds less than the minimum phase speed for linear gravity-capillary waves (c$_{min}$ = 23 cm/s) was investigated experimentally. The resulting wave pattern was measured using cinematic shadowgraph and laser-induced fluorescence (LIF) techniques. The results show the existence of several distinct behavioral states. At low speeds, no wave behavior is observed and the pattern resembles the symmetric stationary condition. However, at a critical speed, but still below c$_{min}$, the pattern undergoes a sudden transition to an asymmetric state with a stationary, 2D solitary wave that forms behind the pressure source. This solitary wave is elongated in the cross-stream relative to the stream-wise direction and resembles gravity-capillary ``lumps'' observed in previous numerical calculations. As the translation speed approaches c$_{min}$, another time-dependent behavior is observed characterized by periodic ``shedding'' from a V-shaped solitary wave pattern. This work will be discussed in conjunction with the recent numerical calculations of T. Akylas and his research group. [Preview Abstract] |
Monday, November 23, 2009 4:01PM - 4:14PM |
LS.00003: Internal Waves in Shear Flow Scott Wunsch, Alan Brandt Internal waves propagating through a shear flow can exchange energy with the mean flow. Waves may be reflected or transmitted through the shear, gaining or losing energy by exchange with the mean flow field. This effect is most pronounced at a ``critical level,'' a depth where the wave horizontal phase velocity matches the local mean flow speed. Laboratory experiments are underway to study internal waves interacting with shear using the synthetic schlieren measurement technique. Particular interest is on conditions leading to internal wave amplification, which based on theory should occur when the Richardson number is less than 1/4. Experimental results indicate that, as the stratified shear flow is subject to instabilities as Richardson number approaches 1/4, internal wave interactions are more complex than the idealized theories predict. [Preview Abstract] |
Monday, November 23, 2009 4:14PM - 4:27PM |
LS.00004: Propagation of internal waves through time-dependent shear profiles in the ocean and atmosphere Julie Vanderhoff Internal wave breaking in the ocean and atmosphere leads to mixing of pollutants and nutrients, contributes to the global mixing budget, and is necessary for the overall global circulation. Locations and magnitudes of this breaking are not fully understood. Internal waves are constantly being generated throughout the ocean and atmosphere. These waves can propagate long distances before breaking and dissipating. They will interact with other flow phenomenon as they propagate, including strong shear profiles, inertial scale waves, and vortex dipoles, as examples of a few. These interactions may lead to breaking, change the physical parameters of the short wave (including wavenumber and amplitude), change their direction of propagation (turning points), or shift them hundreds of kilometers from their original path. Ray tracing and numerical simulations are used to better understand the three-dimensional dynamics of these types of interactions. Results will be compared to previous experimental work and ocean observations from the Hawaiian Ocean Mixing Experiment. The results of these interactions further our knowledge of the evolution of the energy spectrum and give insight into how locally generated internal waves can contribute to the global energy budget. [Preview Abstract] |
Monday, November 23, 2009 4:27PM - 4:40PM |
LS.00005: Internal wave structure emitted by a horizontally oscillating sphere Evguenyi Ermanyuk, Jan-Bert Flor, Bruno Voisin An oscillating body in a stratified fluid generates a double cone-shaped internal-wave pattern, the 3D analogue of the classic St.Andrew-cross. For sufficiently low frequency and large amplitude oscillations, higher-order wave harmonics may be generated along with the fundamental one. We present an experimental study of the 3D structure of first- and second-order wave fields emitted by a {\it horizontally} oscillating sphere. In contrast to the axisymmetric wave pattern found for a {\it vertically} oscillating sphere, for {\it horizontal} oscillations, the first- and higher-order-harmonic waves have different distributions of wave amplitudes in the azimuthal direction. The amplitude of the first-order waves is shown to follow the cosine dependence on the azimuthal angle, in accordance with theoretical predictions. The azimuthal distribution of the amplitude of the second-order waves gives evidence of a quadrupolar distribution, with four preferential directions of wave radiation in a horizontal plane, along the direction of oscillation and normal to it. Noteworthy is that the amplitudes of these second-order waves may exceed the amplitude of first-order waves. [Preview Abstract] |
Monday, November 23, 2009 4:40PM - 4:53PM |
LS.00006: A Model for Large-Amplitude Internal Solitary Waves with Trapped Cores Karl Helfrich, Brian White Large-amplitude internal solitary waves in continuously stratified systems can be found by solution of the Dubreil-Jacotin-Long (DJL) equation. For finite ambient density gradients at the surface (bottom) for waves of depression (elevation) these solutions may develop recirculating cores for wave amplitudes above a critical value. These recirculating cores contain densities outside the ambient range, may be statically unstable, and thus are physically questionable. To address these issues the problem for trapped-core solitary waves is reformulated. A finite core of uniform density and velocity, but unknown shape, is assumed. The core density is arbitrary, but generally set equal to the ambient density on the streamline bounding the core. The uniform core velocity set to the wave phase speed. The exterior flow satisfies the DJL equation and pressure continuity is imposed at the core boundary. Simultaneous numerical solution of the DJL equation and the core condition gives the exterior flow and the core shape. Numerical solutions of time-dependent nonhydrostatic equations with the theoretical solutions as initial conditions show that the waves are stable up to a critical amplitude above which shear instability destroys the initial wave. Trapped-core waves formed by lock-release initial conditions also agree well with the theoretical wave properties despite differences in the core circulation. [Preview Abstract] |
Monday, November 23, 2009 4:53PM - 5:06PM |
LS.00007: The Cross-Stream Structure of the Crests of Breaking Waves J.D. Diorio, X. Liu, J.H. Duncan The cross-stream profiles of spilling breaking waves (wavelengths 80-120 cm) are investigated experimentally. A programmable wave maker is used to generate Froude scaled wave packets (central frequencies 1.15 - 1.40 Hz and various wave maker amplitudes) that create breakers via dispersive focusing. A cinematic 2D LIF technique is used to measure the crest profile histories both in stream-wise and cross-stream planes. It is found that the cross-stream averaged amplitude undergoes periodic oscillations due to the passage of large streamwise (oriented parallel to the wave crest) ripples. Cross-stream ripples, while initially small, grow rapidly as breaking develops. These cross-stream ripples are in the range of 1-4 cm in wavelength and can have amplitudes comparable in size to the streamwise ripples. The amplitude of the cross-stream ripples grows with the gravity wavelength to the third power and shows periodic peaks that coincide with the troughs of the streamwise ripples. The cross-stream surface gradients show thin persistent surface ``scars'' that appear to be generated in the troughs of the streamwise ripples. The connection between these observations and a possible vortical model is discussed. [Preview Abstract] |
Monday, November 23, 2009 5:06PM - 5:19PM |
LS.00008: Air Bubble Entrainment by Breaking Ship Bow Waves M. Tavakolinejad, M. Shakeri, D. Hadschiev, J.H. Duncan Air entrainment induced by breaking bow waves simulated with a 2D+T technique was studied experimentally in a tank that is 14.8m long, 1.15m wide, and 2.2m deep with a water depth of 1.85m. In the 2D+T technique, a two-dimensional wave maker moves horizontally and deforms in a manner that approximates the time varying intersection of one side of the hull of the three-dimensional ship and a fixed vertical plane oriented normal to the ship's path. The experiments were performed in simulated seawater and the bubble sizes and velocities in the streamwise plane were measured with a double-pulsed shadowgraph technique. In cases with plunging breakers, the primary mechanisms for air entrainment are the entrapment of a tube of air in the crest during the impact of the plunging jet and the turbulent fluid motion in the splash region create by the plunging jet impact. Two equivalent ship model forward speeds, one with a very weak plunging breaker and one with a very strong plunging breaker, were studied. Bubble size distributions, void fractions and bubble velocity distributions at times corresponding to the passage of the ship stern will be presented. [Preview Abstract] |
Monday, November 23, 2009 5:19PM - 5:32PM |
LS.00009: Experimental observation of trapped modes in a water wave channel Pablo Cobelli, Vincent Pagneux, Agn\`es Maurel, Philippe Petitjeans The fluid around a free surface piercing circular cylinder in a long narrow wave tank can exhibit a local oscillation that does not propagate down the channel but is confined to the vicinity of the cylinder. This is a manifestation of the so-called trapped modes, bound states occurring in a wide variety of situations in physics. In this study, we present the first whole-field time resolved measurements for the free surface deformation obtained by a Fourier transform profilometry technique. The scattering characteristics of the cylinder and consequently the behavior of the trapped mode frequency are determined. The experimental results show good agreement with the predictions arising from linear water-wave theory. [Preview Abstract] |
Monday, November 23, 2009 5:32PM - 5:45PM |
LS.00010: 2D plus time analogy of corner waves downstream partially submerged bodies Pablo Martinez-Legazpi, Javier Rodriguez-Rodriguez, Juan Lasheras We have studied experimentally and numerically the expansion flow developing downstream the corner of a partially submerged vertical plate. In this flow configuration, a steady wave remains attached to the corner of the plate. Theoretical analysis shows that, taking advantage of the slender nature of the flow, the 3D steady problem can be transformed into a 2D+time one that resembles some important features of deep-water breaking waves. The resulting simplified problem is then solved using a boundary element method. Finally, the results of simulations are compared with experimental measurements. [Preview Abstract] |
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