Bulletin of the American Physical Society
70th Annual Meeting of the APS Division of Fluid Dynamics
Volume 62, Number 14
Sunday–Tuesday, November 19–21, 2017; Denver, Colorado
Session D19: Surface Waves IFree Surface

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Chair: Paul Fontana, Seattle University Room: 702 
Sunday, November 19, 2017 2:15PM  2:28PM 
D19.00001: Lagrangian particle drift and surface deformation in a rotating wave on a free liquid surface. Paul W. Fontana, Nicolas Francois, Hua Xia, Horst Punzmann, Michael Shats A nonlinear model of a rotating wave on the free surface of a liquid is presented. The flow is assumed to be inviscid and irrotational. The wave is constructed as a superposition of two perpendicular, monochromatic standing Stokes waves and is standingwavelike, but with ``antinodes" or cells consisting of rotating surface gradients of alternating polarity. Lagrangian fluid particle trajectories show a rotational drift about each cell in the direction of wave rotation, corresponding to a rotating Stokes drift. Each cell therefore has a circulating flow and localized angular momentum even though the Eulerian flow is irrotational. Meanwhile, the wave sets up a static displacement of the free surface, making a trough in each cell. This static surface gradient provides a centripetal force that may account for additional rotation seen in experiments. [Francois \em et al., Nat. Commun.\em\, 8:14325 (2017).] [Preview Abstract] 
Sunday, November 19, 2017 2:28PM  2:41PM 
D19.00002: Manipulating Effective Gravity and Trapping Shallow Water Waves Ahmad Zareei, MohammadReza Alam A perfect manipulation of water waves in shallow water using transformation media methods usually requires changes in both water depth and gravitational acceleration as medium properties; however gravitational acceleration is always a physical constant. Reduced models and conformal transformations are used to keep the gravitational acceleration as a constant at the cost of performance and restriction of use. Here we present a novel method of changing effective gravitational acceleration using a viscoelastic bottom topography. This method of manipulating effective gravitational acceleration, beside changes in bottom topography, opens new applications toward controlling surface waves and enables perfect manipulation of water waves in a broad range of frequencies. Using the viscoelastic bottom topography, we present a GRINlens based waveguide that traps water waves in a region along the axis of the lens. The presented method of manipulating effective gravitational acceleration can as well be applied to perfectly focus and rotate the waves for energy harvesting applications. [Preview Abstract] 
Sunday, November 19, 2017 2:41PM  2:54PM 
D19.00003: Determining the nearsurface current profile from measurements of the wave dispersion relation Benjamin Smeltzer, Peter Maxwell, Eirik Æsøy, Simen Ellingsen The currentinduced Doppler shifts of waves can yield information about the background mean flow, providing an attractive method of inferring the current profile in the upper layer of the ocean. We present measurements of waves propagating on shear currents in a laboratory water channel, as well as theoretical investigations of inversion techniques for determining the vertical current structure. Spatial and temporal measurements of the free surface profile obtained using a synthetic Schlieren method are analyzed to determine the wave dispersion relation and Doppler shifts as a function of wavelength. The vertical current profile can then be inferred from the Doppler shifts using an inversion algorithm. Most existing algorithms rely on a priori assumptions of the shape of the current profile, and developing a method that uses less stringent assumptions is a focus of this study, allowing for measurement of more general current profiles. The accuracy of current inversion algorithms are evaluated by comparison to measurements of the mean flow profile from particle image velocimetry (PIV), and a discussion of the sensitivity to errors in the Doppler shifts is presented. [Preview Abstract] 
Sunday, November 19, 2017 2:54PM  3:07PM 
D19.00004: Ship wakes and spectrograms: mathematical modelling and experimental data for finitedepth flows Scott McCue, Ravindra Pethiyagoda, Timothy Moroney, Gregor Macfarlane, Jonathan Binns We are concerned with how properties of a ship wake can be extracted from surface height data collected at a single point as the ship travels past. The tool we use is a spectrogram, which is a heat map that visualises the timedependent frequency spectrum of the surface height signal. In this talk, the focus will be on presenting the theoretical framework which involves an idealised mathematical model with a pressure distribution applied to the surface. A geometric argument based on linear water wave theory provides encouraging results for both subcritical and supercritical flow regimes. We then summarise some recent findings obtained by comparing our analysis to experimental data collected at the Australian Maritime College for various sailing speeds and hull shapes$^*$. Our work has the potential to inform ship design, the detection of irregular vessels, and how coastal damage is attributed to specific vessels in shipping channels.\\ $^*$R Pethiyagoda, TJ Moroney, GJ MacFarlane, JR Binns \& SW McCue (2017) Timefrequency analysis of ship wave patterns in shallow water: modelling and experiments, arXiv:1702.06275 [Preview Abstract] 
Sunday, November 19, 2017 3:07PM  3:20PM 
D19.00005: Highresolution reconstruction and prediction of irregular wave field using adjointbased data assimilation Jie Wu, Xuanting Hao, Lian Shen Wave surface elevation and/or velocity data observed from measurements such as marine radar and wave buoys are inevitably of limited resolution in time and space. In order to overcome this limitation, we developed an adjointbased data assimilation intended for wave reconstruction and prediction with high precision. In this model, we define a cost function for the error between computed surface elevation and measurement, where the initial surface elevation and surface pressure are treated as control variables. The cost function, namely the error, is reduced in an optimization process with the gradient information provided by the adjoint equations. The result is satisfactory when a highly nonlinear irregular wave field is reconstructed from marine radar data, and the reconstructed wave field recovers the kinematic and dynamic details missing from the original measured data. [Preview Abstract] 
Sunday, November 19, 2017 3:20PM  3:33PM 
D19.00006: Reducedorder prediction of rogue waves in twodimensional deepwater waves Themistoklis Sapsis, Mohammad Farazmand We consider the problem of large wave prediction in twodimensional water waves. Such waves form due to the synergistic effect of dispersive mixing of smaller wave groups and the action of localized nonlinear wave interactions that leads to focusing. Instead of a direct simulation approach, we rely on the decomposition of the wave field into a discrete set of localized wave groups with optimal length scales and amplitudes. Due to the shortterm character of the prediction, these wave groups do not interact and therefore their dynamics can be characterized individually. Using direct numerical simulations of the governing envelope equations we precompute the expected maximum elevation for each of those wave groups. The combination of the wave field decomposition algorithm, which provides information about the statistics of the system, and the precomputed map for the expected wave group elevation, which encodes dynamical information, allows (i) for understanding of how the probability of occurrence of rogue waves changes as the spectrum parameters vary, (ii) the computation of a critical length scale characterizing wave groups with high probability of evolving to rogue waves, and (iii) the formulation of a robust and parsimonious reducedorder prediction scheme for large waves. [Preview Abstract] 
Sunday, November 19, 2017 3:33PM  3:46PM 
D19.00007: Dispersion free control of hydroelastic waves down to subwavelength scale Lucie Domino, Marc Fermigier, Emmanuel Fort, Antonin Eddi Hydroelastic surface waves propagate at the surface of water covered by a thin elastic sheet and can be directly measured with accurate space and time resolution. We present an experimental approach using hydroelastic waves that allows us to control waves down to the subwavelength scale. We tune the wave dispersion relation by varying locally the properties of the elastic cover and we introduce a local index contrast. This index contrast is independent of the frequency leading to a dispersionfree SnellDescartes law for hydroelastic waves. We then show experimental evidence of broadband focusing, reflection and refraction of the waves. We also investigate the limits of diffraction through the example of a macroscopic analog to optical nanojets, revealing that any subwavelength configuration gives access to new features for surface waves. [Preview Abstract] 
Sunday, November 19, 2017 3:46PM  3:59PM 
D19.00008: Numerical study of windwave generation at the initial stage Tianyi Li, Lian Shen We present direct numerical simulation (DNS) results of windwave generation process at the initial stage. In the simulation, air and water are coupled by an efficient iteration scheme using dynamicallyevolving wavesurfacefitted grid. Due to the high waterair density ratio, the air sees the water surface as a moving deformable boundary and the water is driven by the shear stress and normal stress at the airwater interface. We use algebraic mapping to transform the irregular physical domain to the rectangular computational domain in the air phase and water phase. At the interface, the air phase provides stress information to the water phase and the water phase transfers geometry and velocity information to the air phase. The continuity of velocity and balance of stress at the interface are enforced via iteration. Fullynonlinear kinematic and dynamic boundary conditions are implemented. The results show that the mean square of wave amplitudes grow linearly at the initial stage and exponentially at the later stage. Effects of different physical parameters on the wave growth rate at the initial stage are investigated. [Preview Abstract] 
Sunday, November 19, 2017 3:59PM  4:12PM 
D19.00009: WaveInduced Momentum Flux over Winddriven Surface Waves Kianoosh Yousefi, Fabrice Veron, Marc Buckley, Nyla Husain, Tetsu Hara In recent years, the exchange of momentum between the atmosphere and the ocean has been the subject of several investigations. Although the role of surface waves on the airsea momentum flux is now well established, detailed quantitative measurements of waveinduced momentum fluxes are lacking. In the current study, using a combined Particle Image Velocimetry (PIV) and Laser Induced Fluorescence (LIF) system, we obtained laboratory measurements of the airflow velocity above surface waves for wind speeds ranging from 0.86 to 16.63 m s1. The mean, turbulent, and wavecoherent velocity fields are then extracted from instantaneous measurements. Waveinduced stress can, therefore, be estimated. In strongly forced cases in high wind speeds, the waveinduced stress near the surface is a significant fraction of the total stress. At lower wind speeds and larger wave ages, the waveinduced stress is positive very close to the surface, below the critical height and decreases to a negative value further above the critical height. This indicates a shift in the direction of the wavecoherent momentum flux across the critical layer. [Preview Abstract] 
Sunday, November 19, 2017 4:12PM  4:25PM 
D19.00010: Windwaves interactions in the Gulf of Eilat Almog ShaniZerbib, Dan Liberzon The Gulf of Eilat, at the southern tip of Israel, with its elongated rectangular shape and unique diurnal wind pattern is an appealing location for windwaves interactions research. Results of experimental work will be reported analyzing a continuous, 50 hour long, data. Using a combined array of wind and waves sensing instruments, the wave field statistics and its response to variations of wind forcing were investigated. Correlations between diurnal fluctuations in wind magnitude and direction and the wave field response will be discussed. The directional spread of waves' energy, as estimated by the Wavelet Directional Method, showed a strong response to small variations in wind flow direction attributed to the unique topography of the gulf surroundings and its bathymetry. Influenced by relatively strong winds during the light hours, the wave field was dominated by a significant amount of breakings that are well pronounced in the saturation range of waves spectra. Temporal growth and decay behavior of the waves during the morning and evening wind transition periods was examined. Sea state induced roughness, as experienced by the wind flow turbulent boundary layer, is examined in view of the critical layer theory. [Preview Abstract] 
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