Bulletin of the American Physical Society
61st Annual Meeting of the APS Division of Fluid Dynamics
Volume 53, Number 15
Sunday–Tuesday, November 23–25, 2008; San Antonio, Texas
Session HU: Surface Waves |
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Chair: Lian Shen, Johns Hopkins University Room: 204B |
Monday, November 24, 2008 10:30AM - 10:43AM |
HU.00001: Forced nonlinear gravity-capillary waves near the minimum phase speed T.R. Akylas, Y. Cho For Bond number less than 1/3, the minimum gravity-capillary phase speed, Cmin, is known to be the bifurcation point of wavepacket-type plane as well as fully localized solitary waves (lumps) on water of finite or infinite depth. Also, according to linear inviscid theory, the steady-state forced response to a moving 2-D or 3-D disturbance (Rayleigh's solution) becomes singular when the speed of the forcing approaches Cmin. We examine the role that plane solitary waves and lumps play in the nonlinear forced response near this critical speed, using as a model a forced fifth-order KP equation with an additional term representing the effect of dissipation. For sub-critical forcing speed, there are multiple steady-state finite-amplitude response branches. Moreover, for a range of transcritical forcing speeds, it is possible for the response, rather than reaching steady state, to remain transient owing to periodic shedding of solitary waves. The results are discussed in connection with experiments on forced deep-water gravity- capillary waves conducted by Prof J. Duncan's group. [Preview Abstract] |
Monday, November 24, 2008 10:43AM - 10:56AM |
HU.00002: Evolution of Modulated Gravity Waves in Water of Finite Depth David Rollins, Bhimsen Shivamoggi Evolution of a gravity wavetrain in water of finite depth is considered. It is shown that the dynamics can be distinguished as pseudo-infinite depth like and finite-depth like in the weakly-nonlinear limit. Two specific aspects of the weakly-nonlinear dynamics, namely, the linear instability and the long-time evolution of the linearly-unstable modulation of a gravity wavetrain are considered. [Preview Abstract] |
Monday, November 24, 2008 10:56AM - 11:09AM |
HU.00003: An Experimental Investigation of the Free Surface Profiles Generated by a Moving Pressure Source: Solitary Capillary-Gravity Waves J.D. Diorio, N. Watkins, J. Zuech, J.H. Duncan There have been several recent numerical investigations that have shown the existence of three-dimensional nonlinear solitary surface wave patterns that propagate with speeds less than the minimum wave phase speed prescribed by linear theory (23 cm/s for clean water). In the present study, wave patterns were generated by translating a small-diameter region of high pressure across a water surface. The high-pressure region was created by forcing air through a small-diameter vertically oriented tube attached to a carriage that propelled it horizontally at speeds near 23 cm/s. The wave pattern was measured with a cinematic LIF technique. It was found that a steady solitary wave pattern can exist at speeds below the linear-theory minimum phase speed, while for speeds above the minimum, a pattern of gravity-capillary waves was produced. The solitary wave pattern, which only appeared when the pressure forcing was large, dissipated rapidly when the forcing was turned off. The streamwise dimension of the solitary wave was much smaller than the transverse dimension. [Preview Abstract] |
Monday, November 24, 2008 11:09AM - 11:22AM |
HU.00004: A train of solitary waves breaking on a plane beach Yong Sung Park, Philip Liu Traditionally, researches on breaking waves in the near-shore region have focused on mean flow fields of periodic incident waves or a single runup-rundown process of a solitary wave. In these approaches, however, interactions between successively breaking waves are obscure or absent, and it is our objective to investigate the interactions using a train of solitary waves. With the newly built long-stroke wavemaker in the DeFrees Hydraulics Laboratory at Cornell University, we can control the number of the solitary waves as well as separation between waves. Particle Image Velocimetry (PIV) technique with fluorescent seeding particles and an optical filter to exclude scattered laser light from broken surface and air bubbles is employed and the flow field in the surf zone is obtained. So far two-wave cases have been conducted and it is found that as long as the two waves are close enough, they merge into one lump of water body in the surf zone and only one reflected wave is observed in the offshore region. Detailed measurements on water surface profiles, instantaneous velocity fields, depth-averaged velocities and bed shear stresses under breaking waves and the resulting turbulent bores are reported. Hydraulic jumps during rundown are carefully observed and their relevance to the offshore vortices is discussed. Further experimental results with three or more waves in a train will be conducted and presented. [Preview Abstract] |
Monday, November 24, 2008 11:22AM - 11:35AM |
HU.00005: Resonance tongues for higher order Bragg reflection of water waves Jie Yu, Louis Howard It is well-known that a series of corrugations on the bottom of a layer of water of otherwise uniform depth can have a cooperative effect on incident water waves whose wavelength is close to twice the spacing of the corrugations. This is called Bragg reflection or Bragg resonance. We report here a study of similar effects when the spacing of corrugations is an integer (greater than 1) multiple of half the water wavelength. Using the exact theory formulated, we can readily construct the solution regimes, i.e. resonance tongues, within which the water wave amplitudes are exponentially modulated in space. These results are applied to study the effect of bottom corrugations on the normal modes of a rectangular tank. [Preview Abstract] |
Monday, November 24, 2008 11:35AM - 11:48AM |
HU.00006: Interaction between deformable free surface and homogeneous turbulence Xin Guo, Lian Shen In order to understand the dynamics of free-surface turbulence, we perform direct numerical simulation for isotropic turbulence, which is generated and maintained by a random force method, interacting with a free surface with appreciable surface deformations. A wide range of Froude number and Weber number values are considered in our simulation. It is found that waves are generated at the surface, of which the low wave number components are controlled by the turbulence underneath. Splat and antisplat events are prominent features of this type of flows. Towards the free surface, the isotropic turbulence becomes axisymmetric and disk-like within the surface blockage layer. By examining the turbulence structure, turbulence intensity, vorticity fluctuation, and turbulence length scales, we find that the blockage effect of the free surface on the turbulence is sensitive to the Froude and Weber numbers. We also investigate water concentration, velocity fluctuation, and budgets of turbulence kinetic energy and enstrophy within the air-water intermittency layer, of which the results shed lights on turbulence modeling. [Preview Abstract] |
Monday, November 24, 2008 11:48AM - 12:01PM |
HU.00007: A Numerical Study of Wind-Wave Interaction Di Yang, Xin Guo, Lian Shen The problem of wind interacting with water waves is important to many air-sea interaction applications. In this study, we perform direct simulation of turbulent flows over water waves for a mechanistic study of this problem. For motions of the air, the unsteady, three-dimensional momentum equations in the primitive form are simulated with a hybrid pseudo-spectral and finite-difference method on a boundary-fitted grid that fits the surface wave profile. The evolution of the water wave can be either prescribed based on wave theory, or simulated dynamically and coupled with wind motions. Through systematic simulations with a wide range of wave conditions, we investigate the flow structure in detail. It is found that the mean flow, turbulence intensity, Reynolds stress, and vortical structures in the air are strongly dependent on the wave motion, mainly in terms of wave phase, wave age, and wave nonlinearity. The wind input to waves is also quantified based on the simulation results, which compares well with our direct simulation of wind-wave growth. [Preview Abstract] |
Monday, November 24, 2008 12:01PM - 12:14PM |
HU.00008: Laboratory Measurements of Droplets Generated by Breaking Water Waves X. Liu, J.H. Duncan The sizes and motions of droplets that are generated by single breaking water waves are explored in a wave tank that is 11.8 m long, 1.1 m wide and 2.2 m high (0.91 m water depth). A programmable wave maker is used to generate wave packets (central frequency 1.15 Hz) that create breakers by dispersive focusing. Different amplitudes of the wave maker motion are used to generate various breaking waves ranging from weakly spilling breakers to plunging breakers. The profile histories of the breaking wave crests along the center plane of the tank are measured with a cinematic LIF technique. The droplets at various heights and positions above the crests of the breaking waves are measured with a shadowgraph technique that uses a double-pulsed laser, a long-distance microscope lens and a CCD camera. These two measurement systems are mounted on an instrument carriage that moves along the tank with the speed of the breaking crests. The results include the size distributions of the droplets, the variations of the droplet number with height above the wave crest and the velocities of the droplets. The effects of the intensity of the breaking waves on the dynamics of the droplets are discussed. [Preview Abstract] |
Monday, November 24, 2008 12:14PM - 12:27PM |
HU.00009: Air bubble Entrainment by Breaking Waves M. Tavakolinejad, M. Shakeri, J.H. Duncan Air entrainment induced by plunging breaking bow waves simulated by a 2D+T wave maker was studied experimentally in a tank that is 14.8 m long, 1.15 m wide, and 2.2 m deep with a water depth of 1.85 m. In the 2D+T simulation, the sequence of shapes of the flexible surface (wave board) of the wave maker reproduces the time varying intersection of one side of the ship hull with a vertical plane oriented normal to the ship's track as the ship moves at constant speed. The experiments were performed in simulated seawater and the bubble sizes and velocities in the streamwise plane were measured with a double-pulsed shadowgraph method. Two equivalent ship model forward speeds, one with a very weak plunging breaker and one with a very strong plunging breaker, were studied. In the weak plunging breaker, a fairly uniform layer of bubbles is formed along the water surface. In the strong plunging breaker, many of the bubbles are found in two vortical regions: one from the air entrapped in the wave crest by the impact of the wave's plunging jet and one entrapped by the splash resulting from the jet impact. Bubble size distributions and bubble velocity distributions at times corresponding to the passage of the ship stern will be presented. [Preview Abstract] |
Monday, November 24, 2008 12:27PM - 12:40PM |
HU.00010: Solitary water wave interactions in a wave channel Jose Alberto Morales, Maria del Carmen Jorge, Panayiotis Panayotaros, Rodolfo Silva, Edgar Mendoza Experimental research on the interaction of two co-propagating solitary water waves was carried out, comparing it with the KdV Equation two-soliton solution. Experiments were conducted in a wave channel of width 0.8m, with a 30m length available for the interactions, at a water depth of $h=0.16$m. Solitary waves were generated using a piston wave maker. The higher wave height $a_2$ was fixed, with the parameter $\alpha_2=a_2/h\approx 0.5$; several lower wave heights were used, with $\alpha_1\in(0.1,0.3)$. Surface displacements were measured in fixed locations by resistive probes. The interactions were found to be solitonic, which is predicted by KdV theory. Graphs of surface level vs. time were compared with the KdV two-soliton solutions fitted to the initial wave profiles. Experimental graphs generally differed with theoretical on phases. When heights $a_1$, $a_2$ were comparable, KdV theory acceptably described the qualitative behavior of the interaction. However, when $a1/a2$ was relatively low, the second half of the interaction was more complicated experimentally than theoretically. [Preview Abstract] |
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