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 GL: Waves I |
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Chair: Triantaphyllos Akylas, Massachusetts Institute of Technology Room: Hilton Chicago Astoria |
Monday, November 21, 2005 10:34AM - 10:47AM |
GL.00001: A model for nonlinear wave-current interaction Wooyoung Choi, David Lyzenga, Caleb Schillinger We study interaction of surface gravity-capillary waves with surface currents using a system of coupled nonlinear evolution equations for two surface variables: the free surface elevation and the velocity potential at the free surface. Results of our numerical simulations found via a pseudo-spectral method are compared with solutions of the wave action equation. Both narrow- and wide-band initial wave spectra are considered and special attention is paid to nonlinear effects on their evolution. [Preview Abstract] |
Monday, November 21, 2005 10:47AM - 11:00AM |
GL.00002: A model for the generation of solitary waves by reflections of tidal wave beams at the ocean thermocline T.R. Akylas, Roger Grimshaw There is evidence from field observations that, apart from direct forcing by ocean-floor topography, internal solitary waves can also arise from the interaction with the ocean thermocline of tidal internal wave beams. A theoretical model is presented in support of this generation mechanism. The thermocline is modelled as a sharp interface between a shallow homogeneous layer on top of a deep weakly stratified fluid. A propagating internal wave beam in the lower fluid impinging on the interface generates a reflected wave beam as well as a weakly dispersive interfacial disturbance, which evolves into a series of solitary waves if nonlinear wave steepening is strong enough to overcome radiation damping into the lower fluid. Sample numerical results reveal that this mechanism is robust and can play an important part in the field. [Preview Abstract] |
Monday, November 21, 2005 11:00AM - 11:13AM |
GL.00003: Turbulence measurements under unsteady deep-water breaking waves David Drazen, Ken Melville We present results of laboratory experiments on turbulence in deep-water unsteady breaking waves. Through the use of a 10 megapixel 3 Hz digital camera we conducted Digital Particle Image Velocimetry (DPIV) measurements on a large scale, approximately 1.8~m x 0.6~m. Using both instantaneous full-field measurements, and mosaic reconstructions of the flow field (Melville, Veron, and White, 2002), we present results of measurements in both the stream-wise and cross-stream planes. We present results on the evolution of horizontal and vertical wavenumber spectra in both planes. The suite of experiments discussed covers a spectral range of $kl\rightarrow O(k\eta)$, where $l$ is the integral length scale of the flow and $\eta$ is the Kolmogorov length scale. Additionally, evolution of the turbulent kinetic energy density will be presented with an emphasis on the rate of dissipation for times soon after breaking. The use of these results for modeling breaking-induced turbulence will be discussed. [Preview Abstract] |
Monday, November 21, 2005 11:13AM - 11:26AM |
GL.00004: Micro-scale breaking from wave blocking on strong opposing currents Chin Wu, Aifeng Yao Blocking of surface water waves by strong opposing currents is one of intriguing phenomena in wave-current interactions. In this study, the effects of spectral bandwidth and nonlinearity on wave blocking or/and breaking processes are examined. Well-controlled laboratory experiments on varying amplitudes of monochromatic, narrow-banded, and broad-banded waves on strong spatially varying opposing currents achieved by a raised bottom were conducted. For narrow-banded or monochromatic waves of lower incident amplitudes, the spatial wave profile showed that a series of short capillary waves at the front of the blocked wave appeared and the amplitude of capillary waves significantly decreased due to viscous damping. With increasing amplitudes, the reflected waves became higher and pushed the blocking point further downstream, indicating the importance of wave nonlinearity. The wave profile was replaced by a short wave with parasitic capillary waves riding on the forward face of the crest. The growth and the relative motion of the parasitic capillary waves on the underlying crest led to a so called micro-scale breaking during the wave blocking process. For broad-banded waves, so-called partial blocking was observed. [Preview Abstract] |
Monday, November 21, 2005 11:26AM - 11:39AM |
GL.00005: Disintegration (or not) of the nonlinear internal tide Karl Helfrich The disintegration of a low-mode internal tide into high-frequency solitary-like waves is re-examined in the fully-nonlinear regime. As with weakly nonlinear models, the disintegration is inhibited by rotation. Using a two-layer fully-nonlinear long-wave model with rotation, it is shown that underlying periodic fully-nonlinear hydrostatic waves act as attractors that prevent the complete disintegration of a general (e.g. sinusoidal) initial tide. In the hydrostatic limit the initial tide will steepen to breaking, dissipate energy and eventually settle onto a nonlinear periodic solution. When weak nonhydrostatic dispersion is included, excess energy in the initial tide is shed as a packet of high-frequency waves; however, the underlying long tidal wave is the same. While qualitatively similar to results from weakly nonlinear theory, there are substantial quantitative differences related to the properties of both the underlying low and high-frequency waves. The periodic nonlinear tide solutions are extended to continuously stratified systems and it is shown via numerical solutions of the Euler equations that these tidal solutions are generally robust to weak nonhydrostatic effects. [Preview Abstract] |
Monday, November 21, 2005 11:39AM - 11:52AM |
GL.00006: Internal Wave Transmission Across Critical Levels Geoff L. Brown, Bruce R. Sutherland We study the transmission of internal gravity waves through non-uniformly stratified fluid with vertically varying background shear. The appropriate value for the transmission coefficient in this case is the ratio of the flux of transmitted to incident pseudoenergy. We derive an analytic prediction for the transmission coefficient of waves incident upon a piecewise-linear shear flow in which the fluid is unstratified over the depth of the shear and is uniformly stratified above and below the shear-layer. Such a basic state is unstable but with vanishingly small growth rate as the bulk Richardson number becomes larger. In the limit of infinitely large Richardson number (no shear), we recover the tunnelling prediction of Sutherland \& Yewchuk (JFM, 2004). In weak shear, there is no transmission if the phase speed of the incident waves matches the speed of the flow on the other flank of the shear layer, but weak transmission can occur otherwise, even if the phase speed of the waves matches the speed of flow within the shear layer. In strong shear, a transmission peak occurs where the wavenumber and frequency of the incident waves is close to the wavenumber and frequency associated with the most unstable mode and, hence, with overreflected waves. [Preview Abstract] |
Monday, November 21, 2005 11:52AM - 12:05PM |
GL.00007: On the Geometrical Characteristics of the Breaking Bow Waves M. Shakeri, M. Tavakolinejad, J.R. Walters, J.H. Duncan Simulated breaking bow waves were generated using a 2D+T wave maker in a 14.8-m-long tank with a water depth of 1.83 m. The wave maker motion simulates the passage of a ship model with a length, beam, and draft of 21.03, 2.82, and .91 m, respectively. The profile histories of the breaking bow waves were measured with an LIF technique. Geometric characteristics the water surface/hull contact line, the wave crest, and the plunging jet were measured as a function of the equivalent forward speed of the ship model. It was found that the maximum height of the free surface contact line and the main wave crest increases with equivalent 3D ship model speed. The main wave crest moves at a speed of 45\% of the speed of the equivalent 3D ship model. The horizontal trajectories of the point of the maximum height of the wave crest are converted into an equivalent 3D ship model system where they are straight lines and make an almost constant angle with the ship centerline. The jet created by the breaking wave impacts the front face of the wave at a speed of about 50\% of the speed of the equivalent 3D ship model. [Preview Abstract] |
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