Bulletin of the American Physical Society
64th Annual Meeting of the APS Division of Fluid Dynamics
Volume 56, Number 18
Sunday–Tuesday, November 20–22, 2011; Baltimore, Maryland
Session G17: Waves II |
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Chair: James Duncan, University of Maryland Room: 320 |
Monday, November 21, 2011 8:00AM - 8:13AM |
G17.00001: The Non-Linear Response of a Water Free Surface to a Pressure Distribution Moving at Constant Speed N. Masnadi, J.H. Duncan, T.R. Akylas The non-linear response of a water free surface to a localized pressure distribution moving at constant speed just below the minimum phase speed ($C_{min}$) of gravity-capillary waves is studied experimentally. The experiments are performed in a tank that is 6~m long and 0.25~m wide with water depths ranging from 15 to 40~mm. The pressure distribution is generated by blowing air on the water surface via a vertically oriented 2-mm-ID tube that is mounted on an instrument carriage. The bottom of the tank is made of clear plastic and covered with translucent paper. A checkerboard pattern is printed on the paper and this pattern is viewed from above the water surface with a high-speed digital movie camera. The images of the checkerboard pattern are distorted by refraction at the water free surface and yield qualitative observations and quantitative measurements of the temporal evolution of the wave pattern. At towing speeds close to but below $C_{min}$, a gravity-capillary lump appears behind the pressure source. For higher speeds, but still below $C_{min}$ an unsteady wave pattern consisting of a wide V is generated. At the boundary between the two response states, the pattern is asymmetric in the cross-stream direction. Above this boundary, lumps are shed from the tips of the V and the frequency of shedding increases with towing speed. [Preview Abstract] |
Monday, November 21, 2011 8:13AM - 8:26AM |
G17.00002: Numerical simulation of wind-wave evolution and breaking Yi Liu, Lian Shen, Robert Dalrymple The wind-wave evolution and breaking play an important role in air-sea interaction by affecting the mass, momentum, and energy exchange between the atmosphere and the oceans. We perform large-eddy simulation of wind-wave interaction using a coupled level set/volume-of-fluid (CLSVOF) method. The dynamic evolution of waves including the entire breaking process under the wind forcing is simulated. With CLSVOF method, surface overturning, pinching off, and merging associated with wave breaking are captured. Different wind speeds are considered and their effects on the wave growth and breaking are examined. Based on the simulation results, various wind-wave interaction stages including wave growth, evolution, and breaking are investigated. Spectral analysis and wavelet analysis are applied to the wave field. The wave spectrum evolution under wind forcing is quantified and frequency downshift is observed. Wave groups leading to breaking are identified. The influence of the airflow separation over breaking waves on wave growth is also examined. [Preview Abstract] |
Monday, November 21, 2011 8:26AM - 8:39AM |
G17.00003: Laboratory study of the wind structure over surface waves Marc Buckley, Fabrice Veron Airflow dynamics above waves strongly influence exchanges of heat, momentum and mass between the Ocean and the Atmosphere. We present experimental results on the detailed structure of the airflow above waves. The experiments took place at University of Delaware's large (42m long, 1m wide, and 1.25m high) wind-wave facility where a variety of winds, wave ages and steepnesses were generated by a wind-tunnel and a mechanical wave generator. Airflow properties within and above the viscous sublayer were obtained using PIV, while wave profiles and spectra were measured by laser-induced fluorescence. We intermittently observe a separation of the viscous sublayer past the wave crest in certain wind-wave conditions. Despite the intermittent aspect of this sheltering effect, when averaged over all wave phases, our results suggest that there is a substantial along-wave variability of the surface viscous tangential stress, which in turn may affect wave growth and the air-water momentum balance. [Preview Abstract] |
Monday, November 21, 2011 8:39AM - 8:52AM |
G17.00004: Nonlinear growth of wind-driven oblique surface waves by critical-layer interaction Sang Soo Lee Nonlinear interaction between two (primary and secondary) free- surface waves of the same streamwise phase velocity and wind is studied by extending the linear resonant theory of Miles (1957). A nonlinear interaction occurs when the normalized amplitude of the primary 3-D wave becomes of the order of the cube of the density ratio of air to water. If the secondary wave (of smaller amplitude) is also an oblique wave, the nonlinear coupling between them generates a difference mode. Its amplitude becomes as large as the secondary wave in air, but smaller than the latter in water. In addition, the nonlinear interaction between the primary and difference modes induces a parametric growth on the secondary wave if the primary frequency is higher than the secondary frequency. The primary wave remains linear. The secondary and difference mode amplitudes are governed by integro-differential/integral equations. Numerical results show that the nonlinear growth rates become much larger than the linear growth rates. This nonlinear coupling occurs when the waves are very small. The nonlinear interaction is entirely confined to a thin critical layer (in air), and the perturbations outside the critical layer is governed by linear dynamics. It is shown that the initial nonlinear growth of a free-surface wave is governed by the mode-mode interaction in air rather than in water. [Preview Abstract] |
Monday, November 21, 2011 8:52AM - 9:05AM |
G17.00005: Airflow over groups of water waves Shar Sajjadi, Julian Hunt An analytic in conjunction with a numerical model is developed for the turbulent shear flow of an airflow over steadily moving wave groups in which individual waves are unsteady. Firstly this shows, by linear theory, for the individual waves in the group the combined effects of the unsteady critical layer flow, and the viscous/turbulent sheltering on the lee sides of the wave. Secondly, by using weakly non-linear theory to analyze the disturbed air flow over the waves in groups, it is shown how the air speed over the downwind part of the group is lower over the upwind part. This asymmetry causes the critical layer height to be lower over the downwind part, which leads to critical-layer-effect producing a net horizontal force on the waves, in addition to the sheltering effect. This analysis, which is confirmed by numerical solutions, shows why the critical layer is present over monochromatic waves but does not produce a net force, despite earlier arguments to the contrary. The concepts based on this analysis indicate how the effects of wave dynamics also affect the wave growth. [Preview Abstract] |
Monday, November 21, 2011 9:05AM - 9:18AM |
G17.00006: Kinetic Energy Balance Perspective on the Structure and Dynamics of the Air Flow Over Surface Waves Tihomir Hristov The transition from current empirical to mechanistic understanding of the interaction between wind and the wavy water surface requires describing the spatio-temporal dynamics of the wave-induced fields in the wind. Studies have reported failure to detect dynamic or statistical signature of such fields in spectra, structure functions, kinetic energy balance, or in turbulent dissipation measurements. Here we analyze the wave-induced fields of velocity and pressure, their structure functions and higher order moments, e.g. energy and momentum fluxes. The existence of wave-induced fields is demonstrated. While velocity is predominantly turbulent, pressure is organized and coherent with the waves. The latter indicates that random force mechanism for wind-wave interaction proposed by C. Eckart (1953) and O.M. Phillips (1957) is inefficient and virtually inactive. The explicit form of the structure function obtained here and the partitioning of fluxes into turbulent and wave-induced, explain the failures to observationally detect a wave signature in the structure function and in the TKE budget. [Preview Abstract] |
Monday, November 21, 2011 9:18AM - 9:31AM |
G17.00007: Numerical study of interaction of turbulence with free surface and wave Xin Guo, Lian Shen Direct numerical simulation is performed for free-surface turbulent flows. The Navier-Stokes equations subject to fully nonlinear dynamic and kinematic free-surface boundary conditions are integrated in time using a fractional-step method. The kinematic boundary condition is advanced in time with a Runge-Kutta scheme to obtain the evolution of surface elevation. Pseudo-spectral and finite-difference methods are used respectively in the horizontal and vertical directions for spatial discretization. Computational grid is clustered towards the free surface to ensure that flow details near the free surface are captured adequately. Various Froude and Weber numbers are considered. Surface signatures, e.g. propagating waves and surface roughness, are illustrated. The effect of free surface and surface waves is found to be important to the underlying turbulence. The variations of turbulence statistics and characteristic vortical structures near the free surface are elucidated. The budgets of turbulence kinetic energy and enstrophy are also quantified and their dependence on the free-surface conditions is analyzed. [Preview Abstract] |
Monday, November 21, 2011 9:31AM - 9:44AM |
G17.00008: Spatial statistics of capillary wave turbulence Michael Berhanu, Eric Falcon Wave turbulence concerns the study of the statistical properties of a set of numerous nonlinear interacting waves. The archetype of this phenomenon are waves on the surface of a fluid [1]. One of the challenge of wave turbulence is to reach a simultaneous 2D-space and time measurement of the wave amplitude that goes further than usual spatially localized ones. Recently, Herbert et al. [2] performs this measurement for gravity wave turbulence using an optical method (Fourier Transform Profilometry). Here, we used another optical technique (Diffusing Light Photography [3]) with a fast camera, to reach a better spatial resolution that allows us to investigate spatiotemporal statistics of capillary wave turbulence. Linear and nonlinear dispersion relations of capillary waves are obtained as well as the full spectrum of wave amplitude both in the k and omega spaces. Statistical properties are extracted and analyzed in order to test the validity of Weak Turbulence Theory. Moreover, as this technique is not limited to small amplitudes of surface deformation, we can observe appearance of small capillary waves on steep gravity waves, and to check the impact of this gravity to capillary conversion on the wave turbulence. \\[0pt] [1] A. C. Newell and B. Rumpf, Annu. Rev. Fluid Mech. 43, 59 (2011) [2] E. Herbert, N. Mordant and E. Falcon, Phys. Rev. Lett. 105, 144502 (2010) [3] W. B. Wright, R. Budakian and S. J. Putterman, Phys. Rev. Lett. 76, 4528 (1996) [Preview Abstract] |
Monday, November 21, 2011 9:44AM - 9:57AM |
G17.00009: Rain-induced momentum exchange at the ocean surface under low wind speed conditions Emily Harrison, Fabrice Veron We present results from laboratory experiments on the generation of turbulence and the damping of wind-waves by rainfall. These experiments were conducted in a wind-wave flume that is 7.3 m long, 0.48 m wide, and 0.61 m tall, with the mean water level maintained at 0.4 m. A rain module, 0.86 m by 0.38 m, was suspended 4.98 m above the flume to allow droplets to reach approximately 91{\%} of terminal velocity at impact. Turbulence was measured using both particle image velocimetry and planar laser induced fluorescence. Rain effects on the wave field were investigated with an optical wave gauge directly beneath the rain. We have completed a series of 70 experiments encompassing 7 rain kinetic energy flux conditions, 5 wind speeds, and 2 salinities (0 and 37ppt). We find that rainfall generates intense turbulence and mixing. We show that the mixing occurs in bursts associated with vortex rings generated by single drops, which are then sheared by the background current. This shearing and loss of coherence in the vortices generated by the drop impacts prevents significant vortex pairing thereby limiting the depth of the mixing region to a few 10s of cm. The depth of this mixed region is further reduced when raining on salt water. [Preview Abstract] |
Monday, November 21, 2011 9:57AM - 10:10AM |
G17.00010: Experiments on Normal Modes in a Tank with Corrugated Bottom Andrzej Herczynski, Patrick Weidman, Louis Howard, Jie Yu We report an experimental investigation of standing waves in a rectangular container of corrugated bottom partially filled with water. The study was stimulated by the theory of Howard and Yu\footnote{\textit{J. Fluid. Mech.} (2007), \textit{vol.} 593, \textit{pp}. 209-234.}$^,$\footnote{\textit{J. Fluid. Mech.} (2010), \textit{vol.} 659, \textit{pp.} 484-504.} predicting the existence of resonant normal modes --- called Bragg resonance --- wherein the amplitude grows exponentially, either from one end of the channel to the other or from the center out in each direction, depending on the endwall phases of the corrugated bottom. The tank, with adjustable length between 450 and 490 cm, width 13 cm, and height 30 cm, is fitted with a sinusoidal bottom (made of high density polyurethane foam) of wavelength 52 cm and peak-to-peak amplitude 5 cm. Waves are excited by shaking the container in periodic horizontal motion using an electrical motor. The amplitude of the standing waves was recorded using two sensitive pressure probes and also observed and filmed through the transparent acrylic walls. Experimental results are in essential agreement with the theory. [Preview Abstract] |
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