Bulletin of the American Physical Society
67th Annual Meeting of the APS Division of Fluid Dynamics
Volume 59, Number 20
Sunday–Tuesday, November 23–25, 2014; San Francisco, California
Session L16: Waves I: Surface Waves |
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Chair: Francesco Fedele, Georgia Institute of Technology Room: 2000 |
Monday, November 24, 2014 3:35PM - 3:48PM |
L16.00001: Quasi-periodic water wave dynamics Jon Wilkening We present a framework for computing quasi-periodic solutions of the free-surface Euler equations with spectral accuracy. Some of the new solutions are hybrid traveling-standing waves that return to a spatial translation of their initial condition at a later time. Others are nonlinear superpositions of several standing waves with irrationally related periods. We also present a Floquet analysis of the stability of pure standing waves. When they are stable, generic perturbations appear to yield quasi-periodic solutions that remain close to nearby pure standing waves. [Preview Abstract] |
Monday, November 24, 2014 3:48PM - 4:01PM |
L16.00002: Lensing of Oceanic Gravity Waves: Theory and Experiment Mohammad-Reza Alam, Ryan Blake Elandt, Mostafa Shakeri In this talk we show that small features embedded to the seafloor can result in a lensing effect for overpassing oceanic surface waves, similar to how glass lenses focus or defocus light. These seafloor features are typically in the shape of curved periodic sandbars, and the effect is a result of a nonlinear interaction between surface waves and seabed undulations which is known as ``Bragg Resonance.'' We further show that for a broadband incident wave spectrum (i.e. a wave group composed of multitude of different-frequency waves) a polychromatic topography (occupying no more than the area required for a monochromatic lens) can achieve a broadband lensing effect. Gravity wave lenses can be utilized to create localized high-energy wave zones (e.g. for wave energy harvesting or creating artificial surf zones) as well as to disperse waves in order to create protected areas (e.g. harbors or areas near important offshore facilities). In reverse, lensing of oceanic waves may be caused by natural seabed features and may explain the frequent appearance of very high amplitude waves at certain bodies of water. [Preview Abstract] |
Monday, November 24, 2014 4:01PM - 4:14PM |
L16.00003: Perfect Broadband Cloaking of shallow water Waves via Nonlinear Medium Transformation Ahmad Zareei, M.-Reza Alam The major obstacle in achieving a perfect cloaking for shallow water waves is that the linear transformation media scheme (aka transformation optics) requires variations of two independent medium properties. These two medium properties for the case of electromagnetic waves are permittivity and permeability. Designing a medium with a variable permittivity and permeability is difficult to achieve. For gravity waves, the two required spatially variable properties are the water depth and the gravity acceleration, but here changing of the gravity acceleration is simply impossible. Here we present a nonlinear transformation that only requires the change in one of the medium properties, i.e., in the case of shallow water waves just the water depth, and hence enables us to design a perfect cloak for long gravity waves. We show that with this nonlinear transformation an object can be cloaked for any wave satisfying merely the shallow water condition. The presented transformation can as well be applied for the design of non-magnetic optical cloak for electromagnetic waves. [Preview Abstract] |
Monday, November 24, 2014 4:14PM - 4:27PM |
L16.00004: Ocean crest slowdown and geometric phases Francesco Fedele Several studies over the past two decades suggest that the initial speed of breaking crests of dominant open ocean wave groups, or breaker speeds, are typically 20{\%} lower than expected from linear wave theory (Rapp {\&} Melville, 1990). A recent multifaceted study in Banner et al. (PRL, 2014) explains the reduced breaker speed by means of the crest slowdown, a new fundamental property of non-breaking ocean waves as they occur naturally, not as uniform wavetrains, but within evolving groups. Before the focusing point, the crest of the largest wave in the group slows down as it advances leaning forward, and it becomes symmetrical as the maximum height is approached. As the wave decays after focus, the crest accelerates as it leans backward. In this talk, I will show that the crest slowdown and the associated forward/backward leaning are generic features of each crest of water wave groups. They are associated with the energy convergence in the neighborhood of the focal region, irrespective of whether the wave evolves to break or not (Fedele, JFM 2014). In particular, I will show that the crest slowdown is induced by the natural dispersion of unsteady wave groups. Drawing from quantum mechanics and differential geometry, it can be explained in terms of geometric phases associated with the wave motion with U(1) group symmetry (e.g. Berry 1984). The theoretical findings are in fair agreement with ocean field observations off the Venice coast, Italy, obtained by state-of-the-art stereo imaging techniques. [Preview Abstract] |
Monday, November 24, 2014 4:27PM - 4:40PM |
L16.00005: Wave Impact on a Wall: Comparison of Experiments with Similarity Solutions A. Wang, J.H. Duncan, D.P. Lathrop The impact of a steep water wave on a fixed partially submerged cube is studied with experiments and theory. The temporal evolution of the water surface profile upstream of the front face of the cube in its center plane is measured with a cinematic laser-induced fluorescence technique using frame rates up to 4,500~Hz. For a small range of cube positions, the surface profiles are found to form a nearly circular arc with upward curvature between the front face of the cube and a point just downstream of the wave crest. As the crest approaches the cube, the effective radius of this portion of the profile decreases rapidly. At the same time, the portion of the profile that is upstream of the crest approaches a straight line with a downward slope of about 15$^{\circ}$. As the wave impact continues, the circular arc shrinks to zero radius with very high acceleration and a sudden transition to a high-speed vertical jet occurs. This flow singularity is modeled with a power-law scaling in time, which is used to create a time-independent system of equations of motion. The scaled governing equations are solved numerically and the similarly scaled measured free surface shapes, are favorably compared with the solutions. [Preview Abstract] |
Monday, November 24, 2014 4:40PM - 4:53PM |
L16.00006: Surface tension effects in wave breaking Luc Deike, W.K. Melville, Stephane Popinet We present a numerical study of wave breaking by solving the full Navier-Stokes equations for two-phase air-water flows using the solver Gerris [1]. We describe a parametric study of the influence of capillary effects on wave breaking using two-dimensional simulations. The onset of wave breaking as a function of the Bond number, Bo, and the initial wave steepness S is determined and a phase diagram in terms of (S,Bo) is presented that distinguishes between non-breaking gravity waves, parasitic capillaries on a gravity wave, spilling breakers and plunging breakers. The wave energy dissipation is computed for each wave regime and is found to be in good agreement with experimental results for breaking waves. Moreover, the enhanced dissipation just by parasitic capillaries is comparable to the dissipation due to breaking [2]. Extending the simulations to three dimensions permits studies of the generation and statistics of bubbles and spray during breaking. \\[4pt] [1] Popinet, S. 2003. Journal of Computational Physics 190, 572--600. Popinet, S. 2009. Journal of Computational Physics 228, 5838--5866.\\[0pt] [2] Deike, L., Popinet, S., and Melville, W.K. Submitted to Journal of Fluid Mechanics (June 2014). [Preview Abstract] |
Monday, November 24, 2014 4:53PM - 5:06PM |
L16.00007: The virial theorem for water waves and its application to deep-water wave breaking Nicholas Pizzo, W. Ken Melville The connection between the geometry, kinematics and dynamics of steep and breaking waves is crucial for an improved understanding of air-sea interaction processes. In this study, we present a virial theorem for deep-water surface gravity waves, related to a conserved integral quantity originally derived by Benjamin and Olver (1982), and we apply this theorem to the study of properties of steep and breaking waves. Specifically, we relate the geometry and dynamics of these wave scenarios in an attempt to better understand the breakdown of equipartition between the kinetic and potential energy. The virial theorem will be studied both analytically and numerically, where in the latter case we make use of a variational description of water waves in a conformally mapped reference frame (Balk 1996) that we have developed for use in a numerical model. Particular attention will be given to the application of these findings to recent theoretical and laboratory studies in which it has been shown that the potential energy available to breaking waves plays a crucial role in setting the scales of post-breaking phenomena; for example, the breaking induced energy dissipation rate (Drazen et al. 2008) and the circulation generated by breaking (Pizzo and Melville 2013). [Preview Abstract] |
Monday, November 24, 2014 5:06PM - 5:19PM |
L16.00008: Experimental study of breaking and energy dissipation in surface waves Gerardo Ruiz Chavarria, Patrice Le Gal, Michael Le Bars We present an experimental study of the evolution of monochromatic waves produced by a parabolic wave maker. Because of the parabolic shape of the wave front, the waves exhibit spatial focusing and their amplitude dramatically increases over distances of a few wavelengths. Unlike linear waves, the amplitude of the free surface deformation cannot exceed a certain threshold and when this happens the waves break. In order to give a criterion for the appearance of breaking, we calculate the steepness defined as $\varepsilon =$H/$\lambda $ (where H is the wave height and $\lambda $ their wavelength) for waves of frequencies in the range 4-10 Hz. We found that wave breaking develops when $\varepsilon $ attains approximately a value of 0.10. We also evaluate the lost of energy carried by the waves during their breaking by a detailed and accurate measurement of their amplitude using an optical Fourier transform profilometry. [Preview Abstract] |
Monday, November 24, 2014 5:19PM - 5:32PM |
L16.00009: Subharmonic waves produced by oscillating submerged solids Jose M. Perez-Gracia, Fernando Varas, Jose M. Vega Parametric excitation of subharmonic waves in a container due to the vertical oscillation of a (deeply) submerged solid is considered in this presentation. In general, two parametric forcing mechanisms will appear in this configuration, namely forcing from (directly excited) surface waves and forcing from an oscillatory flow in the bulk. Nevertheless, if the (oscillating) obstacle is submerged deeply enough (as it will be assumed) the second mechanism will dominate. This problem can then be seen as a generalization of the (classical) Faraday waves problem with a non-homogeneous forcing (associated to the oscillating flow generated near the cylinder). In fact, this problem corresponds (in the case of a cylinder with a proper symmetry) to the simplest case of symmetric non-homogeneous forcing of subharmonic waves, and it can be considered as the counterpart of horizontal vibration of containers (where an antisymmetric non-homogeneous parametric forcing is found). The analysis recently developed by the authors in the case of a horizontally vibrated container (Journal of Fluid Mechanics, vol. 739 pp. 196-228, 2014) is adapted here in order to obtain predictions of threshold vibration amplitudes, pattern orientation and periodic or quasi-periodic nature of subharmonic waves. [Preview Abstract] |
Monday, November 24, 2014 5:32PM - 5:45PM |
L16.00010: Pressure Stagnation Line on a Planing Hull in Calm Water Christine Ikeda, Carolyn Judge High-speed planing boats are subjected to repeat impacts due to slamming, which can cause structural damage and discomfort or injury to passengers. An experimental study aimed at understanding and predicting the physics of a planing craft re-entering the water after becoming partially airborne was conducted. A subset of this experiment includes calm water analysis to gain an understanding of the pressure stagnation line and its correlation with the wetted surface on the planning craft in calm water conditions. A planing hull model was towed in a 116-m long, 8-m wide tow-tank with a water depth of 5 m. Hull models at 1/10 and 1/4 of full-scale were examined. These models, only free to move in heave and pitch, were instrumented to measure dynamic pressures with point-pressure sensors at 12 locations near the LCG (longitudinal center of gravity) and transom as well as a highly spatially resolved pressure mapping system. These pressure measurements were sampled at rates up to 20kHz. Using these pressure measurements along with underwater photos of the wetted surface allowed for the v-shaped wetted line and stagnation line to be measured. Preliminary results show that the peak pressures occur before the wetted line and that atmospheric pressure is reached at the transom. [Preview Abstract] |
Monday, November 24, 2014 5:45PM - 5:58PM |
L16.00011: Kelvin ship waves: the effect of nonlinearity on the apparent wake angle Scott McCue, Ravindra Pethiyagoda, Timothy Moroney We learn as undergraduates that the half-angle which encloses a Kelvin ship wave pattern is simply $\arcsin(1/3)\approx 19.47^\circ$, provided the fluid is deep and the disturbance is small. But observations and calculations for sufficiently fast-moving ships suggest that the {\em apparent} wake angle decreases with ship speed. One explanation of this phenomenon is that the wave pattern that is observed in practice is defined by the location of the highest peaks; for wakes created by sufficiently fast-moving objects, these highest peaks no longer lie on the outermost divergent waves, resulting in a smaller apparent angle. We explore these ideas by analysing the linearised problems of flow past a submerged point source (semi-infinite Rankine body) or past a submerged source doublet (sphere). Then we consider the nonlinear versions of these problems. One result is that nonlinearity has the effect of increasing the apparent wake angle so that some highly nonlinear solutions have apparent wake angles that are greater than Kelvin's angle. [Preview Abstract] |
Monday, November 24, 2014 5:58PM - 6:11PM |
L16.00012: Reconstruction of a energy wave spectrum using a non-intrusive technique Diana Vargas, Adolfo Lugo, Edgar Mendoza, Rodolfo Silva For studies taken in a wave flume, it is frequent to use wave gauges to measure directly the free surface fluctuations. Sometimes these gauges can interfere the measures because this probes act as obstacles to water. Therefore we designed a non intrusive technique using a bubble curtain. In this work we pretend to reconstruct the energy wave spectrum of regular and irregular waves, generated in a wave flume, assuming linear and non linear wave theory by analyzing the time series of the bubbles velocity field given with the aid of PIV. [Preview Abstract] |
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