Bulletin of the American Physical Society
68th Annual Meeting of the APS Division of Fluid Dynamics
Volume 60, Number 21
Sunday–Tuesday, November 22–24, 2015; Boston, Massachusetts
Session L31: Waves: Nonlinear Waves and Turbulence |
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Chair: Eric Falcon, CNRS, Paris, France Room: 312 |
Monday, November 23, 2015 4:05PM - 4:18PM |
L31.00001: Observation of resonant interactions among gravity surface waves Eric Falcon, Felicien Bonnefoy, Florence Haudin, Guillaume Michel, Benoit Semin, Thomas Humbert, Sebastien Aumaitre, Michael Berhanu We experimentally study resonant interactions of gravity surface waves in a large basin. We generate two oblique sinusoidal swells of tunable angle, steepness and frequency ratio. These waves interact each other and give birth to a resonant wave whose properties (growth rate and resonant response curve) are fully characterized. A phase locking between waves is also evidenced. All our experimental results are found in good quantitative agreement with 4-wave interaction theory of gravity waves with no fitting parameter. Slightly off-resonance experiments are also reported. For stronger wave steepness, departures from the weakly nonlinear theory are observed. Our results thus strongly extend previous experimental results performed more than 50 years ago. [Preview Abstract] |
Monday, November 23, 2015 4:18PM - 4:31PM |
L31.00002: Role of the basin boundary conditions in gravity wave turbulence Michael Berhanu, Luc Deike, Benjamin Miquel, Pablo Gutierrez, Timothee Jamin, Benoit Semin, Eric Falcon, Felicien Bonnefoy Gravity wave turbulence is studied in a large wave basin where irregular waves are generated unidirectionally. The role of the basin boundary conditions (absorbing or reflecting) are investigated. To that purpose, an absorbing sloping beach opposite to the wavemaker can be replaced by a reflecting vertical wall. The wave field properties depend strongly on these boundary conditions. Unidirectional waves propagate before to be damped by the beach whereas a more multidirectional wave field is observed with the wall. In both cases, the wave spectrum scales as a frequency-power law with an exponent that increases continuously with the forcing amplitude up to a value close to -4. We have also studied freely decaying gravity wave turbulence in the closed basin. No self-similar decay of the spectrum is observed, whereas its Fourier modes decay first as a time power law due to nonlinear mechanisms, and then exponentially due to linear viscous damping. We estimate the linear, nonlinear and dissipative time scales to test the time scale separation. Using the mean energy flux from the initial decay of wave energy, the Kolmogorov-Zakharov constant of the weak turbulence theory is evaluated experimentally for the first time. [Preview Abstract] |
Monday, November 23, 2015 4:31PM - 4:44PM |
L31.00003: Experiments on linear waves propagating over a turbulent background Pablo Gutierrez, Sebastien Aumaitre, Claudio Falcon We are interested in what happens to a linear wave propagating on the surface of a turbulent flow. This problem is studied with two experimental procedures. First, we excite surface-resonant-modes by means of the periodic motion of a container with water. When we impose turbulent motion in the bulk of water, we observe a clear reduction in the resonance peaks. This represent a simple way to identify turbulent fluid motion as a source of dissipation for surface waves. The second procedure is to locally excite a wave at a given frequency, and to study its propagation along the container. Here again, when there is an underlying turbulent flow, we observe the enhancement of wave dissipation. Also, we observe a shift in the wavenumber through larger values, which can be understand as a random scattering of the wave on the turbulent structures. [Preview Abstract] |
Monday, November 23, 2015 4:44PM - 4:57PM |
L31.00004: Non local resonances in weak turbulence of gravity-capillary water waves Nicolas Mordant, Quentin Aubourg We investigate experimentally the statistical properties of wave turbulence of surface waves on water. In the limit of weak non linearity an energy cascade in scale is predicted by the Weak Turbulence Theory. Energy transfers are predicted to occur among resonant waves. We use a Fourier Transform Profilometry technique that provides a 2D measurement of the water surface deformation that is resolved in time and scale. The principle is to project a pattern on the surface of water which diffuses light thanks to the addition of a Titanium oxyde powder. The pattern can then be inverted to provide the elevation of the water surface. Our wave tank is 70 cm long and we investigate waves that lie is the vicinity of the capillary-gravity crossover with frequencies between 1Hz and 100 Hz. We compute 3-wave correlations so that to study the non linear coupling and the energy transfers among resonant waves. We observe a 3-wave non linear coupling which is dominantly unidirectional and non local in scale: a low frequency gravity wave can be coupled to 2 high frequency capillary waves. We will also discuss the importance of approximate resonances in the wave coupling. [Preview Abstract] |
Monday, November 23, 2015 4:57PM - 5:10PM |
L31.00005: Faraday waves on time-dependent domains Mahdi Ghadiri, Rouslan Krechetnikov Faraday wave patterns -- standing waves which form on the free fluid surface due to its vertical vibration -- have been frequently used as a testbed for new theories and ideas. As part of the recent effort to understand dynamics and evolution on time-dependent spatial domains, in this talk we will present experimental investigation on how Faraday wave patterns respond to the domain deformation. In our experimental setup of a vibrating water container with controlled moving walls, the characteristics of the free surface patterns are measured using the Fourier transform profilometry technique, which allows us to get accurate time history of patterns’ three-dimensional landscape. Our study reveals, at the experimental level, how patterns transform in response to the domain dynamics on various length- and time-scales. [Preview Abstract] |
Monday, November 23, 2015 5:10PM - 5:23PM |
L31.00006: Propagation of nonlinear waves over submerged step: wave separation and subharmonic generation Eduardo Monsalve, Agnes Maurel, Vincent Pagneux, Philippe Petitjeans Water waves can be described in simplified cases by the Helmholtz equation. However, even in these cases, they present a high complexity, among which their dispersive character and their nonlinearities are the subject of the present study. Using Fourier Transform Profilometry, we study experimentally the propagation of waves passing over a submerged step. Because of the small water depth after the step, the wave enters in a nonlinear regime. In the shallow water region, the second harmonic leads to two types of waves: bound waves which are slaves of the fundamental frequency with wavenumber $2k(\omega)$, and free waves which propagate according to the usual dispersion relation with wavenumber $k(2\omega)$. Because of the presence of these two waves, beats are produced at the second harmonic with characteristic beat length. In this work, for the first time we extended this analysis to the third and higher harmonics. Next, the region after the step is limited to a finite size L with a reflecting wall. For certain frequencies and L- values, the spectral component becomes involved, with the appearance of sub harmonics. This regime is analyzed in more details, suggesting a transition to a chaotic and quasi-periodic wave behavior. [Preview Abstract] |
Monday, November 23, 2015 5:23PM - 5:36PM |
L31.00007: Vortex kinematics and dynamics in deep-water breaking waves Ken Melville, Nicholas Pizzo, Luc Deike Surface wave breaking can be modeled as a transitional process from irrotational to turbulent flow. Thus the introduction of vorticity across the range of inertial to dissipative scales is of great significance for the kinematics and dynamics of breaking. In this presentation, we review laboratory experimental data showing the introduction of coherent vortices at breaking and present an impulsive force model (just half of the smoke ring problem) that predicts the coherent circulation in terms of the wave energy dissipated by breaking. We then use this model, supported by DNS of breaking, to predict the distribution of the energy lost from the wave field between turbulence and the coherent vorticity. The models and available experimental and numerical data are consistent with inertial scaling of the wave energy dissipated by breaking. [Preview Abstract] |
Monday, November 23, 2015 5:36PM - 5:49PM |
L31.00008: Experimental observation of steady inertial wave turbulence in deep rotating flows Ehud Yarom, Eran Sharon We present experimental evidence of inertial wave turbulence in deep rotating fluid. Experiments were performed in a rotating cylindrical water tank, where previous work showed statistics similar to 2D turbulence (specifically an inverse energy cascade). Using Fourier analysis of high resolution data in both space (3D) and time we show that most of the energy of a steady state flow is contained around the inertial wave dispersion relation. The nonlinear interaction between the waves is manifested by the widening of the time spectrum around the dispersion relation. We show that as the Rossby number increases so does the spectrum width, with a strong dependence on wave number. Our results suggest that in some parameters range, rotating turbulence velocity field can be represented as a field of interacting waves (wave turbulence). Such formalism may provide a better understanding of the flow statistics. [Preview Abstract] |
Monday, November 23, 2015 5:49PM - 6:02PM |
L31.00009: On the structure of turbulence dissipation rate under unsteady breaking waves Morteza Derakhti, James Kirby During the last decade, extensive laboratory and field measurements have been conducted for the estimation and parameterization of the turbulence dissipation rate under unsteady breaking waves, showing a large amount of scatter depending on the selected estimation, type and scale of the considered breaking waves. To further elucidate the physical processes involved in turbulence generation and dissipation mechanisms, Derakhti \& Kirby, JFM, (2014) examined shear- and bubble-induced dissipation. They used a 3D VOF-based Navier-Stokes solver extended to incorporate entrained bubble populations using an Eulerian-Eulerian formulation for a poly-disperse bubble phase, and found that the total bubble-induced dissipation accounts for more than 50\% of the total dissipation in the breaking region (the results were presented at DFD13, Abstract 001799). In this presentation, we will examine the 3D distribution of breaking-induced turbulent kinetic energy and dissipation rate during the active breaking period. The role of breaking-induced vortical structures in the transport of turbulent motions will be addressed as well. Finally, the accuracy of the available analytic scaling relations of the intensity and depth dependence of wave breaking turbulence dissipation rate will be discussed. [Preview Abstract] |
Monday, November 23, 2015 6:02PM - 6:15PM |
L31.00010: Interactions of steep and breaking waves with winds and solid bodies Zixuan Yang, Lian Shen The interactions of steep and breaking waves with winds and solid bodies at sea surface is important to many problems in ocean science and engineering. In this study, we perform large-eddy simulations using a finite-difference code with high-performance parallel computing. The air-water interface is captured using a coupled level set and volume of fluid method. A sharp interface immersed boundary method is applied to capture the effect due to the presence of solid bodies. A wall layer model is employed to address high Reynolds numbers. A numerical wave generator is utilized to accurately produce waves with specified parameters. The results are validated for a number of canonical problems, and the performances of different wall-layer model schemes are evaluated using a priori and a posteriori tests. Based on the simulation data, the flow details and interaction mechanisms are analyzed. [Preview Abstract] |
Monday, November 23, 2015 6:15PM - 6:28PM |
L31.00011: Effect of progressive surface waves on near-surface transport of scalars by turbulent wind Lian Shen, Di Yang The presence of progressive water surface waves plays a vital role in the air-sea exchange of scalar quantities, such as water vapor and heat. The periodic surface curvature and motions of the waves impose considerable disturbance to the turbulence boundary layer flow over the wave surface, affecting the transport of both momentum and scalars. In this study, the effect of surface waves on scalar transport is investigated using direct numerical simulation (DNS). The DNS solver uses pseudo-spectral and finite-difference schemes for the flow and scalar fields, with spatial discretization carried out on a moving wave-fitted computational grid to capture the surface wave effect. The results show considerable variations in the statistics of the scalar transport for different phase speeds of the waves that correspond to different development stages of wind-generated ocean waves. Based on the DNS data, several turbulent closure models for RANS modeling of scalar transport are evaluated using \textit{a priori} test. [Preview Abstract] |
Monday, November 23, 2015 6:28PM - 6:41PM |
L31.00012: Rogue waves for a system of coupled derivative nonlinear Schr\"{o}dinger equations Hiu Ning Chan, Boris Malomed, Kwok Wing Chow Previous works in the literature on water waves have demonstrated that the fourth-order evolution of gravity waves in deep water will be governed by a higher order nonlinear Schr\"{o}dinger equation. In the presence of two wave trains, the system is described by a higher order coupled nonlinear Schr\"{o}dinger system. Through a gauge transformation, these evolution equations are reduced to a coupled derivative nonlinear Schr\"{o}dinger system. The goal here is to study rogue waves, unexpectedly large displacements from an equilibrium position, through the Hirota bilinear transformation theoretically. The connections between the onset of rogue waves and modulation instability are investigated. The range of cubic nonlinearity allowing rogue wave formation is elucidated. Under a finite group velocity mismatch between the two components, the existence regime for rogue waves is extended as compared to the case with a single wave train. The amplification ratio of the amplitude can be higher than that of the single component nonlinear Schr\"{o}dinger equation. [Preview Abstract] |
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