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 H31: Waves: General |
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Chair: Lyubov Chumakova, University of Edinburgh Room: 312 |
Monday, November 23, 2015 10:35AM - 10:48AM |
H31.00001: Extending dispersive waves theory to use in semi-open systems Lyubov Chumakova, Ruben Rosales, Andrew Rzeznik, Esteban Tabak In the classical linear dispersive wave theory the sinusoidal waves $e^{i(k x -\omega t)}$ carry energy with the group speed $c_g = d\omega/dk$. This concept is limited to the case where both the frequency $\omega(k)$ and the wavenumber $k$ are real. On the other hand, semi-open dispersive systems allow more than just sinusoidal solutions: they can have exponentially blowing up and/or decaying solutions as well. In this talk I will address the questions of what is direction and the speed of the energy propagation for these exponential waves, extend the classical concept of group velocity, and use this theory to construct radiation boundary conditions for semi-open dispersive systems. This approach will be demonstrated on an example of dry hydrostatic troposphere which experiences effective damping due to gravity waves propagating into the stratosphere. [Preview Abstract] |
Monday, November 23, 2015 10:48AM - 11:01AM |
H31.00002: Optimal Configuration of Large Arrays of Floating Bodies for Ocean Wave Energy Extraction Grgur Tokic, Dick K.P. Yue We study the performance of large ($O(100)$) wave energy converter (WEC) arrays that are used for ocean energy harvesting. We developed a fast computational algorithm based on the multiple scattering framework that is capable of handling large arrays of different configurations (general finite-size arrays, periodic arrays, periodic arrays of subarrays); for axisymmetric bodies the algorithm imposes no constraints on the body-size-to-wavelength ratio or on the inter-body spacings. Using this fast algorithm, we optimize the spatial configurations of arrays of different types and with increasing number of bodies (up to 400), with the goal of maximizing energy extraction. The results show that employing non-uniform spacings between the bodies in ordered and non-ordered arrays can increase the array gain several times. This holds for body resonant and near-resonant frequencies, as well as for the full spectrum cases. The optimal configurations are analyzed from a physical standpoint and compared to other structured arrays in physics. These results give a guideline on the possible future design of WEC arrays. [Preview Abstract] |
Monday, November 23, 2015 11:01AM - 11:14AM |
H31.00003: On the response of a water surface to a surface pressure source moving at trans-critical gravity-capillary wave speeds Naeem Masnadi, Yeunwoo Cho, James H. Duncan, Triantaphyllos Akylas The non-linear response of a water free surface to a pressure source moving at speeds near the minimum speed of linear gravity-capillary waves ($C_{min}\approx23$ cm/s) is investigated with experiments and theory. In the experiments, waves are generated by a vertically oriented air-jet that moves at a constant speed over the water surface in a long tank. The 3-D surface shape behind the air-jet is measured using a cinematic refraction-based technique combined with an LIF technique. At towing speeds just below $C_{min}$, an unsteady pattern is formed where localized depressions periodically appear in pairs and move away from the source along the arms of a downstream V-shaped pattern. This behavior is analogous to the periodic shedding of solitary waves upstream of a source moving at the maximum wave speed in shallow water. The gravity-capillary depressions are rapidly damped by viscosity and their speed-amplitude characteristics closely match those from inviscid calculations of gravity-capillary lumps. The shedding frequency of the lumps in the present experiments increases with both increasing towing speed and air-flow rate. Predictions of this behavior using a model equation that incorporates damping and a quadratic nonlinearity are in good agreement with the experiments. [Preview Abstract] |
Monday, November 23, 2015 11:14AM - 11:27AM |
H31.00004: Spatiotemporal measurement of surfactant distribution on gravity-capillary waves Stephen Strickland, Michael Shearer, Karen Daniels Materials adsorbed to the surface of a fluid - for instance, crude oil, biogenic slicks, or industrial/medical surfactants - will move in response to surface waves. Due to the difficulty of non-invasive measurement of the spatial distribution of a molecular monolayer, little is known about the dynamics that couple the surface waves and the evolving density field. We report measurements of the spatiotemporal dynamics of the density field of an insoluble surfactant driven by gravity-capillary waves in a shallow cylindrical container. Standing Faraday waves and traveling waves generated by the meniscus are superimposed to create a non-trivial surfactant density field. We measure both the height field of the surface using moire-imaging and the density field of the surfactant via the fluorescence of NBD-tagged phosphatidylcholine. Through phase-averaging stroboscopically-acquired images of the density field, we determine that the surfactant accumulates on the leading edge of the traveling meniscus waves and in the troughs of the standing Faraday waves. We fit the spatiotemporal variations in the two fields and report measurements of the wavenumbers as well as a temporal phase shift between the two fields. These measurements suggest that longitudinal waves contribute to the dynamics. [Preview Abstract] |
Monday, November 23, 2015 11:27AM - 11:40AM |
H31.00005: Observation of Wood's anomalies on surface gravity waves propagating on a channel Claudio Falc\'on, Andrea Schmessane We report experiments demonstrating the appearance of Wood's anomalies in surface gravity waves in a shallow water limit propagating along a channel with a submerged obstacles. Space-time measurements of surface gravity waves allows us to compute the stationary complex field of the wave and the amplitude growth of localized and propagative modes over all the channel including the scattering region. This allows us to access the near and far field dynamics, which constitute a new and complementary way of observation of mode resonances of the incoming wave displaying Wood's anomalies. Transmission coefficient, dispersion relations and normalized wave energy of the incoming wave and the excited mode are measured and found to be in good agreement with theoretical predictions [Preview Abstract] |
Monday, November 23, 2015 11:40AM - 11:53AM |
H31.00006: ABSTRACT WITHDRAWN |
Monday, November 23, 2015 11:53AM - 12:06PM |
H31.00007: Efficient method for the computation of wave propagation in the atmosphere: horizontal rays and vertical normal modes Noe Lahaye, Stefan Llewellyn Smith The development of efficient methods for computing the propagation of waves throughout the atmosphere is a longstanding issue. The widely-used WKBJ approximation is inaccurate when the typical scale of the fluid properties is of the order of the wave scale, or in particular regions such as turning points or critical levels. Homogeneity in the horizontal allows one to reduce the problem to an ODE (generally in the vertical) and solve this numerically with no further approximation. However, this may not be a valid approximation in applications; for example tsunami-generated acoustic-gravity waves have a large length scale and propagate over long distances up to the ionosphere. We propose a resolution method for 3D wave propagation that combines normal-modes and ray tracing, relying on scale separation between vertical and horizontal directions. This method has been widely used in the oceanic acoustic context and in waveguide theory, yet few applications in the atmospheric context seem to have been reported. First, we present some results in a simple framework (quiescent fluid, rigid boundary conditions), then show how the method may be adapted in the atmospheric context (including compressibility) to the propagation of waves emitted by a moving source and/or in a moving fluid. [Preview Abstract] |
Monday, November 23, 2015 12:06PM - 12:19PM |
H31.00008: Growth of gravity-capillary waves in countercurrent air/water turbulence Alfredo Soldati, Francesco Zonta, Miguel Onorato We use Direct Numerical Simulation (DNS) of the Navier Stokes equations to analyze the dynamics of the interface between air and water when both phases are driven by opposite pressure gradients (countercurrent configuration). The Reynolds number ($Re_{\tau}$), the Weber number ($We$) and the Froude number ($Fr$) fully describe the physical problem. We examine the problem of the transient growth of interface waves for different combinations of physical parameters. Keeping $Re_{\tau}$ constant and varying $We$ and $Fr$, we show that, in the initial stages of the wave generation process, the amplitude of the interface elevation $\eta$ grows in time as $\eta \propto t^{2/5}$. Wavenumber spectra, $E(k_x)$, of the surface elevation in the capillary range are in good agreement with the prediction of the Wave Turbulence Theory. Finally, the wave-induced modification of the average wind and current velocity profiles will be addressed. [Preview Abstract] |
Monday, November 23, 2015 12:19PM - 12:32PM |
H31.00009: Analysis of Nonlinear Internal Wave Systems Driven From a Flexible Boundary Tom Dobra, Andrew Lawrie, Stuart Dalziel We present experiments and analysis of internal wave systems generated from motion of a flexible boundary driven by an array of electrical actuators. These actuators are independently controllable using arbitrary displacement profiles, and here we choose to coordinate their motion to create boundary displacements with a prescribed spectrum of temporal frequency and spatial wavenumber. We present first the simple case of two steady periodic signals of different frequency emanating from the same spatial location, and demonstrate a novel decomposition technique we have recently developed that isolates wave beams from their surroundings. This new methodology enables us to quantify weak nonlinearities in their interaction that are spatially local and aperiodic. We then apply our methodology to the more complex case of convergent focussed wave-beams generated from a spatially distributed source. [Preview Abstract] |
Monday, November 23, 2015 12:32PM - 12:45PM |
H31.00010: Solitary waves on a ferrofluid jet Mark Blyth, Emilian Parau The propagation of axisymmetric solitary waves on the surface of an otherwise cylindrical ferrofluid jet subjected to a magnetic field is investigated. An azimuthal magnetic field is generated by an electric current flowing along a stationary metal rod which is mounted along the axis of the moving jet. A numerical method is used to compute fully-nonlinear travelling solitary waves and predictions of elevation waves and depression waves by Rannacher \& Engel (2006) using a weakly-nonlinear theory are confirmed in the appropriate ranges of the magnetic Bond number. New nonlinear branches of solitary wave solutions are identified. As the Bond number is varied, the solitary wave profiles may approach a limiting configuration with a trapped toroidal-shaped bubble, or they may approach a static wave (i.e. one with zero phase speed). For a sufficiently large axial rod, the limiting profile may exhibit a cusp. [Preview Abstract] |
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