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 D13: Free Surface Flows II: Waves 
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Chair: Gary Lapham, Maine Maritime Academy Room: 201 
Sunday, November 22, 2015 2:10PM  2:23PM 
D13.00001: Unbounded wall flow with free surface waves and horizontal shear Gary Lapham, John McHugh Free surface waves in the presence of a nonuniform shear flow are treated. The shear flow of interest varies with both the transverse and vertical coordinates, $U(y,z)$. Initial results treat a mean flow varying only with the transverse, $U(y)$. The domain is bounded on one side by a flat rigid vertical wall and is unbounded on the other side. The mean flows considered here are nonzero near the vertical wall and approach zero far from the wall, e.g. $U = e^{ \gamma y}$. The flowfield is treated as inviscid but rotational. Linear solutions are obtained using a nonuniform coordinate transformation that converts the free surface boundary condition into a modified Bessel equation. Velocity components are expanded in modified Bessel functions of the first kind of purely imaginary order. The dispersion relation for steady waves are found with wavespeeds outside the range of $U$, matching previous results for a flow bounded on both sides. Corresponding eigenvectors show a sequence of wave profiles of increasing complexity near the wall. The wave amplitude approaches zero far from the wall. [Preview Abstract] 
Sunday, November 22, 2015 2:23PM  2:36PM 
D13.00002: Extreme Wave Impact on a Flexible Plate Aliza Abraham, Alexandra Techet Digital image correlation (DIC) and particle image velocimetry (PIV) are combined to characterize the flowstructure interaction of a breaking wave impacting a flexible vertically mounted plate. DIC is used with the beam bending equation to determine the stresses on the plate and PIV is used to describe the flow of the wave. In this experiment, a simulated dam break in which water is rapidly released from a reservoir generates the wave, which impinges on a cantilevered stainless steel plate downstream. Pressure sensors mounted on the plate are used to gather further information about the forces acting on it. A series of waves of different heights and breaking locations are tested, controlled by the volume of water in the tank and the volume of water in the dam break reservoir. The deflection of the plate varies depending on the point of breaking and the height of the wave. These results shed light on the effect of breaking wave impacts on offshore structures and ship hulls. [Preview Abstract] 
Sunday, November 22, 2015 2:36PM  2:49PM 
D13.00003: Onset of windwave generation on a viscous liquid Anna Paquier, Marc Rabaud, Frederic Moisy In a new experimental setup, we investigate the onset of wave generation over a viscous liquid. We access the spatiotemporal structure of the surface deformations using Free Surface Synthetic Schlieren. Above a critical wind speed, surface deformations organize themselves into quasimonochromatic transverse waves, with amplitude increasing spatially in the downstream direction. This spatial growth is found to be exponential with the fetch (distance along the tank) at small fetch. The spatial growth rate increases linearly with wind speed, from which the onset for wind generation can be determined accurately. At higher wind velocity or fetch, nonlinear effects are observed, resulting in an increase of the wavelength and phase velocity, and to more disordered wave patterns. [Preview Abstract] 
Sunday, November 22, 2015 2:49PM  3:02PM 
D13.00004: Experimental demonstration of epsilonnearzero water waves focusing Tomasz Bobinski, Antonin Eddi, Philippe Petitjeans, Agnes Maurel, Vincent Pagneux We demonstrate experimentally the epsilonnearzero (ENZ) analogue for water waves in the nonlinear regime. In the context of electromagnetic waves, ENZ media are known to realize super lensing effect, because they are associated to very large wavelength. A lens made of such material with, say, circular edge shape, produces focused waves at the center of the circle (focal point of the lens). In the context of water waves, we demonstrate the analog of these media by tuning the bathymetry of the bottom sea owing the analogy between electromagnetic waves and water waves in the shallow water regime. Experimentally, we obtain uniform phase of the water wave at the edge of the semicircular lens, resulting in the expected lensing effect. By using time space resolved measurement of the twodimensional field of surface elevation, we are able to separate the linear component of the wave and the harmonics generated by nonlinearities. Interestingly, we observe a cascade of highly focused harmonics. These harmonic components are analyzed in term of freewaves and boundwaves. [Preview Abstract] 
Sunday, November 22, 2015 3:02PM  3:15PM 
D13.00005: A seabedmounted diode for unidirectional waterwave propagation LouisAlexandre Couston, MohammadReza Alam The effect of a series of seabed patches of smallamplitude bars with increasing obliquity on a monochromatic oceanic wavetrain is shown to be analogous to the effect of a diode on the current in an electronic circuit. The incoming water wavetrain is deflected at a 90degree angle in one direction, while barely changing its route in the other. In the reverse direction, i.e. in the direction where wave propagation is blocked, the incoming wavetrain (with bearing angle bi$=$0 degrees) satisfies a Bragg resonance condition over each one of the seabed patches, ceding its energy to a series of transmitted waves of increasing bearing angle (i.e. $btj>>bt1>bi$ with btj the angle of the jth transmitted wave). The resonances continue over the patches until btj$=$90 degrees. In the forward direction, i.e. in the direction where wave propagation is allowed, the incident wave satisfies a Bragg condition only with the last patch such that its deflection remains small. The minimum patch lengths leading to full deflection are obtained within potential flow theory using multiplescale analysis, and the analytical results are validated and extended with HighOrder Spectral simulations. Some of the difficulties expected with laboratory experiments are given. [Preview Abstract] 

D13.00006: ABSTRACT WITHDRAWN 
Sunday, November 22, 2015 3:28PM  3:41PM 
D13.00007: Reconstruction of arbitrary surface wave fields by refraction global method in a wave tank Heynert Garcia, Andrei Ludu We use a new photographic procedure and design to construct reliable system for measurement and analysis of various surface water waves in a wave tank, including rogue and tsunamilike waves. The image of a grid placed at the bottom of the tank (3 feet maximum depth) is deformed by the surface waves and recorded on one or two cameras placed above the water. The measurement of the height and slope of the surface waves is determined by inverse refraction calculations plus the calibration information at four grouped points from capacitive level gauges. [Preview Abstract] 
Sunday, November 22, 2015 3:41PM  3:54PM 
D13.00008: Numerical simulation of the resonantly excited capillarygravity waves Hideshi Hanazaki, Motonori Hirata, Shinya Okino Capillary gravity waves excited by an obstacle are investigated by a direct numerical simulation. In the flow without capillary effects, it is well known that largeamplitude upstream advancing solitary waves are generated periodically under the resonant condition, i.e., when the phase velocity of the long surface waves and the mean flow velocity agrees. With capillary effects, solutions of the Euler equations show the generation of very short waves further upstream of the solitary waves and also in the depression region downstream of the obstacle. The overall characteristics of these waves agree with the solutions of the forced fifthorder KdV equation, while the weakly nonlinear theory generally overestimates the wavelength of the short waves. [Preview Abstract] 
Sunday, November 22, 2015 3:54PM  4:07PM 
D13.00009: Variational modelling of nonlinear water waves Anna Kalogirou, Onno Bokhove Mathematical modelling of water waves is demonstrated by investigating variational methods. A potential flow water wave model is derived using variational techniques and extented to include explicit timedependence, leading to nonautonomous dynamics. As a first example, we consider the problem of a soliton splash in a long wave channel with a contraction at its end, resulting after a sluice gate is removed at a finite time. The removal of the sluice gate is included in the variational principle through a timedependent gravitational potential. A second example involving nonautonomous dynamics concerns the motion of a free surface in a vertical HeleShaw cell. Explicit timedependence now enters the model through a linear damping term due to the effect of wall friction and a term representing the motion of an artificially driven wave pump. In both cases, the model is solved numerically using a Galerkin FEM and the numerical results are compared to wave structures observed in experiments. The water wave model is also adapted to accommodate nonlinear ship dynamics. The novelty is this case is the coupling between the water wave dynamics, the ship dynamics and water line dynamics on the ship. For simplicity, we consider a simple ship structure consisting of Vshaped crosssections. [Preview Abstract] 
Sunday, November 22, 2015 4:07PM  4:20PM 
D13.00010: Instability of propagating axial symmetric waves generated by a vertically oscillating sphere Meng Shen, Yuming Liu We study the instability of propagating axial symmetric waves in a basin that are generated by a vertically oscillating sphere. Laboratory experiments indicate that when the oscillation amplitude exceeds a threshold value, the axial symmetric propagating waves abruptly transfigure into nonaxial symmetric waves. Fullynonlinear timedomain numerical simulation of wavebody interaction is applied to describe the nonlinear temporal and spatial evolution dynamics of the propagating waves. Transition matrix method is employed to analyze the stability of the nonlinear time periodic wavebody interaction system. We identify the fundamental mechanism leading to the instability of the wavebody system and investigate the critical condition for the occurrence of the instability. We quantify the growth rate and dominant modes of unstable disturbances and study their dependence on physical parameters including body motion frequency and amplitude, body geometry, surface tension and basin size. Moreover, the longtime evolution dynamics of the unstable wavebod y system including wave patterns and responsive body forces are also investigated. [Preview Abstract] 
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