Bulletin of the American Physical Society
2005 58th Annual Meeting of the Division of Fluid Dynamics
Sunday–Tuesday, November 20–22, 2005; Chicago, IL
Session HL: Waves II |
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Chair: Mary Silber, Northwestern University Room: Hilton Chicago Astoria |
Monday, November 21, 2005 1:20PM - 1:33PM |
HL.00001: The Effects of Surfactants on Wind Waves X. Liu, M. Tavakolinejad, J.H. Duncan The effects of surfactants on wind waves are studied experimentally in a tank that is 11.8 m long, 1.1 m wide and 1.8 m high. The water depth is 1.0 m and the top 0.8 meters of the tank contains air flowing with speeds up to 10 m/s. A mechanical wave maker, which resides at the upwind end of the tank, is used in some cases to superimpose a monochromatic wavetrain with frequencies of about 2 Hz on the wind wave system. Wave profiles are measured along the center plane of the tank with an LIF technique that utilizes a high-speed digital camera. The measurement system is mounted on an instrument carriage that can be set to move along the tank with various speeds. Measurements were performed with clean water and with water mixed with Triton X-100, a soluble surfactant. The results show that in clean water strong and active gravity-capillary wave phenomena are observed at the leeward side of wind wave crests. In the presence of Triton X-100, these capillary wave phenomena become weaker and eventually disappear as the surfactant concentration (Triton X-100) is increased. The detailed experiments to quantify these features are undergoing. [Preview Abstract] |
Monday, November 21, 2005 1:33PM - 1:46PM |
HL.00002: Interactions of breathers and solitons of the extended Korteweg de Vries equation C.M. Shek, R.H.J. Grimshaw, E. Ding, K.W. Chow A popular model for the evolution of weakly nonlinear, weakly dispersive waves in the ocean is the extended Korteweg -- de Vries equation (eKdV), which incorporates both quadratic and cubic nonlinearities. The case of positive cubic nonlinearity allows for both solitons of elevation and depression, as well as breathers (pulsating modes). Multi-soliton solutions are computed analytically, and will yield expressions for breather-soliton interactions. Both the soliton and breather will retain their identities after interactions, but suffer phase shifts. However, the details of the interaction process will depend on the polarity of the interacting soliton, and have been investigated by a computer algebra software. This highly time dependent motion during the interaction process is important in nonlinear science and physical oceanography. As the dynamics of the current and an evolving internal oceanic tide can be modeled by eKdV, this knowledge is relevant to the temporal and spatial variability observed in the oceanic internal soliton fields. [Preview Abstract] |
Monday, November 21, 2005 1:46PM - 1:59PM |
HL.00003: Transverse instability of gravity-capillary solitary waves Boguk Kim, Triantaphyllos R. Akylas Using perturbation methods, the stability to long-wave transverse perturbations is discussed of gravity--capillary solitary waves for B (Bond number) $<$ 1/3 on water of finite or infinite depth. Consistent with Bridges (2001), if the total energy happens to be a decreasing function of wave speed, transverse instability occurs. Solitary waves of depression, although stable to longitudinal perturbations, are thus unstable to transverse perturbations, and this in stability apparently results in the formation of gravity--capillary lumps of the type recently shown to exist for B$<$1/3 (Kim \& Akylas 2005). Generalization of the stability analysis to interfacial gravity--capillary solitary waves is also discussed. [Preview Abstract] |
Monday, November 21, 2005 1:59PM - 2:12PM |
HL.00004: How the form of the forcing function determines Faraday wave instabilities in shallow viscous fluids Cristian Huepe, Yu Ding, Paul Umbanhowar, Mary Silber We investigate the relationship between the linear surface wave instabilities of a shallow viscous fluid layer and the shape of the periodic, parametric-forcing function (describing the vertical acceleration of the fluid container) that excites them. We find numerically that the envelope of the Arnold resonance tongues only develops multiple minima when the forcing function has more than two local extrema per cycle. Using an analytic WKB approximation, we explore the origin of this relationship and show that, as in the usual sinusoidal case, the envelope has only one minimum for any case with square or triangular forcing. With this insight, we construct a forcing function that generates a non-trivial harmonic instability at onset, which is distinct from a subharmonic response to any of its forcing frequency components. We measure the corresponding surface patterns experimentally and verify that small changes in the forcing function causes a transition (through the calculated bicritical point) from the predicted harmonic short-wavelength pattern to the much larger, standard subharmonic pattern. [Preview Abstract] |
Monday, November 21, 2005 2:12PM - 2:25PM |
HL.00005: Modulated surface waves in horizontally vibrated containers J.M. Vega, F. Varas Faraday waves excited by horizontal vibrations of a container may show interesting spatio-temporal behaviors, including spatially modulated waves at large aspect ratios. When the vibrating lateral walls extend down to the bottom of the container, the system exhibits an oscillatory bulk flow in a region around these walls of size comparable to the depth of the liquid. This oscillating bulk flow produces subharmonic instabilities if the vibrating acceleration excess a threshold value. Two systems of amplitude equations are derived to describe the evolution of harmonic and subharmonic waves in the combined limit of small viscosity, small wave steepness, and large depth (compared with the wavelength of the surface waves). Further simplifications occur depending on the relative values of the modulation length, the viscous length, and the horizontal size of the container. The amplitude equations are used to analyze the linear stability of the simplest steady states and to elucidate the dominant behavior. Harmonic waves dominate when the viscous length is of the order of the size of the container, and subharmonic waves dominate when the size is much larger. [Preview Abstract] |
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