Bulletin of the American Physical Society
71st Annual Meeting of the APS Division of Fluid Dynamics
Volume 63, Number 13
Sunday–Tuesday, November 18–20, 2018; Atlanta, Georgia
Session F05: Surface Waves III |
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Chair: Nick Moore, Florida State University Room: Georgia World Congress Center B207 |
Monday, November 19, 2018 8:00AM - 8:13AM |
F05.00001: Scale effects for air entrainment in quasi-steady breaking waves Kelli Hendrickson, Dick K P Yue Quasi-steady breaking waves are prominent and highly observable features in civil, environmental, ocean and naval engineering applications with direct impact on turbulent dissipation and air-sea interaction. We use high-resolution 3D direct numerical simulation and implicit large eddy simulation of quasi-steady breaking waves to study the air entrainment characteristics as a function of resolvable features within the wave. The numerical method utilizes conservative Volume of Fluid (cVOF) to capture the interface on a Cartesian grid. A submerged lifting body generates the quasi-steady breaking wave. For low Reynolds number waves, we observe periodic wave breaking and entrainment and show that the bubble-size distribution (above the Hinze scale) for each entrainment period achieves an expected slope of r^{-β}, β=10/3. For high Reynolds number waves, we observe widespread wave breaking and entrainment. The slope of the bubble-size distribution β>10/3 reflects entrainment with continued breakup of the entrained cavities by turbulence. Our particular interest lies in developing parameterizations and models that relate the entrainment due to quasi-steady wave breaking to underlying flow characteristics. |
Monday, November 19, 2018 8:13AM - 8:26AM |
F05.00002: Energy dissipation in shallow water breaking waves Wouter D Mostert, Luc Deike We present numerical results of energy dissipation in two-dimensional shallow water breaking waves. Using a two-phase DNS approach, we seek a fundamental energy dissipation model and classification scheme for breaking type and mechanism. A solitary wave of amplitude a_{0} is initialized over a region of uniform depth h and propagated onto a beach with a uniformly sloping bathymetry of gradient α. We discuss the various types of resulting breakers as a function of these parameters, including plunging, spilling, and surging types. The breaker dissipates kinetic and gravitational potential energy in the wave before it runs up onto the beach. We discuss the energy dissipation and wave run-up in terms of the control parameters and propose a model for energy dissipation adapted from the inertial scaling model for deep water breakers. |
Monday, November 19, 2018 8:26AM - 8:39AM |
F05.00003: Inferring Wave Breaking Dissipation Using Cooling Whitecap Foam: A Proof of Concept Naeem Masnadi, Chris Chickadel, Andrew Jessup we present a novel approach for inferring energy dissipation using infrared imagery of the cooling residual foam left behind by a breaking wave. Previous studies have suggested that the visible decay time for the bubble plume of a breaker is correlated with the energy dissipation. In clean water, the plume decay time also correlates with the visible foam decay time; therefore, it is possible to quantify the energy dissipation by measuring the decay time of visible foam for individual breaking waves. But, the relationship between plume and foam decay times in the presence of surfactants is more complex. It has been observed that after a breaking event, the residual foam rapidly cools due to the enhanced evaporative cooling of the upper layer of the foam bubbles. Preliminary experiments suggest that the onset of cooling is not affected by surfactants and the foam starts to cool only after the bubble plume has decayed and no more foam is generated. Here, we present preliminary results from laboratory experiments on the effect of surfactant on the onset of cooling of the residual foam and the relationship between the time from the start of breaking to the onset of cooling, and the bubble plume decay time. |
Monday, November 19, 2018 8:39AM - 8:52AM |
F05.00004: An analytical approach to the statistical moments associated with large ocean waves. Legena A Henry, Jacqueline Bridge The non-Gaussian statistical behavior of ocean surface gravity waves is usually studied via computationally expensive direct Monte Carlo simulations of the ocean surface. We, however, directly solve the Zakharov ocean surface equations, analytically arriving at ocean surface statistical moments via Wiener Chaos Expansions (WCE). We thus apply our ocean surface kurtosis time evolution result to deduce the time evolution of ocean surface rogue wave probability. Additionally, we also demonstrate a probabilistic approach to the time evolution of ocean wave energy deterministically via the Wiener Chaos Expansion method, demonstrating the possibility of the use of the Wiener Chaos Expansion method in understanding the probabilistic behavior of the time-evolution of ocean wave energy for wave power applications. |
Monday, November 19, 2018 8:52AM - 9:05AM |
F05.00005: A framework for ocean surface waves atop a background flow of depth dependence in varying water depth Yan Li, Simen Å Ellingsen We present a theoretical and numerical framework for simple, efficient and accurate evaluation of surface wave models allowing presence of a shear current of arbitrary depth dependence, and a slowly varying bathymetry. The framework, which is named Direct Integration Method (DIM), furthermore yields the full-linearized flow field solution throughout the water column. The DIM is of wide applicability in an oceanography setting. We demonstrate this in four different aspects. The DIM is applied to strong and turning shear profiles and slowly varying bathymetry, for which existing approaches either cannot handle or show unsatisfactory performance. Compared to existing approaches in terms of applicability and computational cost, the DIM is, in our opinion, favorable for a wide range of practical applications. The DIM is moreover employed to obtain the full flow field beneath a 2D ring wave upon a near-surface wind-driven exponential shear current, revealing striking qualitative differences compared to no shear, of potential importance to thermal mixing and transport in the upper ocean. |
Monday, November 19, 2018 9:05AM - 9:18AM |
F05.00006: Transient total absorption for water waves Léo-Paul Euvé, Philippe Petitjeans, Agnès Maurel, Vincent Pagneux Wave absorption has been studied, theoretically and experimentally, in different domains of wave, like in optics, in acoustics or in water waves. In those examples, the absorption is obtained with dissipation processes in an harmonic regime (real frequencies). Baranov et al. introduced recently, in optics, the concept of coherent virtual absorption in a lossless case, involving scattering zeros at complex frequencies (sine wave with an exponential envelop). This leads to the capacity to store energy in a cavity and release it. We explore the same scenario in water waves, using a waveguide with a plunger-type wavemaker at one end, and a cavity at the other end, playing the role of a resonator. The waves are measured with the Fourier Transform Profilometry (FTP) technique. Studying the reflection, we show that it is possible to excite a complex frequency in the upper half-plane of the complex frequency map (corresponding to a exponential divergence in time), to obtain a transient total absorption with zero reflexion. In water waves, it is impossible to have a lossless system due to inevitable linear losses, but the transient total absorption is still robust in such lossy systems. The type of device described can be applied to the control of wave energy (absorption, storage). |
Monday, November 19, 2018 9:18AM - 9:31AM |
F05.00007: Anomalous wave statistics induced by abrupt topographical variations Nicholas Moore, Tyler Bolles, Kevin Speer Laboratory experiments reveal that an abrupt depth change can significantly alter the distribution of randomized surface waves. A normally-distributed, unidirectional wave field becomes strongly skewed upon encountering a step in bottom topography. A short distance downstream of the step, the wave-field conforms closely to a gamma distribution. Importantly, the exponential decay of the gamma distribution is much slower than Gaussian, signifying that extreme events occur more frequently. Under the conditions considered here, the probability of a rogue wave can increase by a factor of 50 or more. |
Monday, November 19, 2018 9:31AM - 9:44AM |
F05.00008: Evaluation of time step in the retardation function considering a statistical approach for offshore platforms. Abhishek Acharya, Ashoke Bhar In irregular wave excitation, correct evaluation of time step is extremely important for the accurate prediction of motions of the semi-submersible platform namely surge, heave and pitch which are predominant. The retardation function in the Cummins equation plays a major role in the evaluation of system damping. In the coupled equation of motion, the convolution integral involving the retardation function is very important for correct prediction of the responses. In this study, the probable time step for the calculation of retardation function has been found out using statistical outlier approach. The wave spectrum used was a JONSWAP spectra with a significant wave height 6.0 m and spectral peak period of 11.2 sec. The wave forces based on diffraction theory were calculated using the boundary element method. In the time domain simulation, numerical integration for the damping has been carried out using trapezoidal rule and to calculate the platform motions predictor-corrector rule has been applied. At last, comparing frequency domain analysis, the motion time history has been verified with power spectral density. |
Monday, November 19, 2018 9:44AM - 9:57AM |
F05.00009: Array resonances in periodic wave energy converter arrays Grgur Tokic, Dick K P Yue We study the hydrodynamics of ocean wave energy converter (WEC) arrays consisting of periodically repeated sub-arrays of heaving buoys. In particular, we focus on lattice-like array configurations and study the effects of periodicity and row spacing on array gain. We discuss two types of general array-configuration-related resonances that have not been discovered in WEC array context before. We first discuss the effects of Laue resonances -- a wave scattering phenomenon occurring when the phase difference between an incident wave and a scattered mode is the same for every body in the array. We present the analytic condition for the occurrence of Laue resonances (involving the incident wavenumber and the array configuration parameters) and match it to prominent decreases in array gain. Second, we discuss the presence of motion-trapped Rayleigh-Bloch (RB) waves -- homogeneous wave solutions to the governing equation that do not radiate to the far field, but stay trapped around a periodic array of oscillating bodies. Based on our numerical simulations, we present evidence that these RB waves exist for a special category of periodic arrays and that they can be excited by an incident wave. These resonances lead to large, narrow-banded increases in the array gain. |
Monday, November 19, 2018 9:57AM - 10:10AM |
F05.00010: Gravity–capillary jet-like surface waves generated by an underwater bubble Youn J. Kang, Yeunwoo Cho Jet-like surface waves generated by an electric-spark-generated underwater bubble are experimentally studied. Three different motions of jet-like surface waves are observed depending on the inception position of the bubble (d: 0.28~7mm) below the free surface and the maximum radius of the bubble (R_{m}: 1.4~3.6mm). When d/R_{m}>1.3, the surface wave shows a simple smooth hump (case 1). When 1<d/R_{m}<1.3, a single droplet or multiple droplets are pinched off sequentially or simultaneously at the tip or from some points of the jet-like surface wave (case 2). Finally, when d/R_{m}<1, a series of squirting & jetting phenomena are observed at the top of the jet-like surface wave (case 3). For the case 1, a proportional relationship is found between ρgh/Δp_{ }and (d/R_{m})^{-4}, where ρ is the density of the fluid, g is the gravitational acceleration, and Δp is the difference between the reference atmospheric pressure and the pressure inside a bubble. This proportional relationship is proved semi-analytically using a scaling argument, conservation of mass, momentum, and energy with the help of the Kelvin impulse theory. |
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