Steep gravity–capillary waves within the internal resonance regime

Steep gravity–capillary waves are studied experimentally in a channel. The range of cyclic frequencies investigated is 6.94–9.80 Hz; namely, the high‐frequency portion of the regime of internal resonances according to the weakly nonlinear theory (Wilton’s ripples). These wave trains are stable according to the nonlinear Schrödinger equation. The experimental wave trains are generated by large, sinusoidal oscillations of the wavemaker. A comparison is made between the measured wave fields and the (symmetric) numerical solutions of Schwartz and Vanden‐Broeck [J. Fluid Mech. 95, 119 (1979)], Chen and Saffman [Stud. Appl. Math. 60, 183 (1979); 62, 95 (1980)], and Huh (Ph.D. dissertation, University of Michigan, 1991). The waves are shown to be of slightly varying asymmetry as they propagate downstream. Their symmetric parts, isolated by determining the phase which provides the smallest mean‐square antisymmetric part, compare favorably with the ‘‘gravity‐type’’ wave solutions determined by numerical computations. The antisymmetric part of the wave profile is always less than 30% of the peak‐to‐peak height of the symmetric part. As nonlinearity is increased, the amplitudes of the short‐wave undulations in the trough of the primary wave increase; however, there are no significant changes in these short‐wave frequencies. The lowest frequency primary‐wave experiments, which generate the highest frequency short‐wave undulations, exhibit more rapid viscous decay of these high‐frequency waves than do the higher‐frequency primary wave experiments.  Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/69701/2/PFADEB-4-11-2466-1.pd

On the Boundary Conditions at an Oscillating Contact Line: A Physical/Numerical Experimental Program

We will pursue an improved physical understanding and mathematical model for the boundary condition at an oscillating contact line at high Reynolds number. We expect that the body force is locally unimportant for earth-based systems, and that the local behavior may dominate the mechanics of partially-filled reservoirs in the microgravity environment. One important space-based application for this contact-line study is for Faraday-waves. Oscillations in the direction of gravity (or acceleration) can dominate the fluid motion during take-off and reentry with large steady-state accelerations and in orbit, where fluctuations on the order of 10(exp -4)g occur about a zero mean. Our experience with Faraday waves has shown them to be 'cleaner' than those produced by vertical or horizontal oscillation of walls. They are easier to model analytically or computationally, and they do not have strong vortex formation at the bottom of the plate. Hence many, if not most, of the experiments will be performed in this manner. The importance of contact lines in the microgravity environment is well established. We will compare high resolution measurements of the velocity field (lO micro-m resolution) using particle-tracking and particle-image velocimetry as the fluid/fluid interface is approached from the lower fluid. The spatial gradients in the deviation provide additional means to determine an improved boundary condition and a measure of the slip region. Dissipation, the size of the eddy near the contact line, and hysteresis will be measured and compare to linear and nonlinear models of viscous and irrotational but dissipative models

An experimental study of deep water plunging breakers

Plunging breaking waves are generated mechanically on the surface of essentially deep water in a two‐dimensional wave tank by superposition of progressive waves with slowly decreasing frequency. The time evolution of the transient wave and the flow properties are measured using several experimental techniques, including nonintrusive surface elevation measurement, particle image velocimetry, and particle tracking velocimetry. The wave generation technique is such that the wave steepness is approximately constant across the amplitude spectrum. Major results include the appearance of a discontinuity in slope at the intersection of the lower surface of the plunging jet and the forward face of the wave that generates parasitic capillary waves; transverse irregularities occur along the upper surface of the falling, plunging jet while the leeward side of the wave remains very smooth and two dimensional; the velocity field is shown to decay rapidly with depth, even in this strongly nonlinear regime, and is similar to that expected from linear theory—the fluid is undisturbed for depths greater than one‐half the wavelength; a focusing or convergence of particle velocities are shown to create the jet in the wave crest; vorticity levels determined from the measured, full‐field velocity vectors show that the waves are essentially irrotational until incipient breaking occurs; and the magnitude of the largest water particle velocity is about 30% greater than the phase speed of the (equivalent) linear wave. © 1996 American Institute of Physics.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/71298/2/PHFLE6-8-9-2365-1.pd

Contact-line dynamics and damping for oscillating free surface flows

New experimental data on the frequency and damping of Faraday water waves in glass tanks are presented to demonstrate the contact-line effect on free surface flows. We find a complicated nonlinear relationship between wave frequency and amplitude near contact lines: The amplitude dispersion for decaying standing waves directly progresses from a nonlinear regime due to large amplitude to a regime due to contact-line nonlinearity. The relative damping rate is also a function of the wave amplitude, increasing significantly at smaller wave amplitude. These results are discussed in relation to different formulations of contact-line conditions for oscillatory motions and free surface flows. A new model is proposed to explain the observed amplitude scaling in the frequency and damping rate, and to relate these behaviors to slip-length and other contact-line measurements by Ting and Perlin [J. Fluid Mech. 295, 263 (1995)]. © 2004 American Institute of Physics.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70946/2/PHFLE6-16-3-748-1.pd