Enhanced dissipation of short gravity and gravity capillary waves due to parasitic capillaries

Xin Zhang
2002 Physics of Fluids  
The dissipation rate of short, mechanically generated, monochromatic surface waves was measured in order to determine the increased dissipation due to the generation of parasitic capillary waves. As the surface waves propagate freely, the decaying wave elevations were measured by an ultra-thin capacitance wire. Measurements indicate that the dissipation rate increases approximately with the square of the wave slope, AK, and the generation of parasitic capillaries depends on the wavelength of
more » ... he wavelength of the surface waves. The maximum generation of parasitic capillaries coincides with a surface wave wavelength near 7 cm. Measured data fits a simple parameterized model of the dissipation rate reasonably well. Viscous dissipation is generally negligible for gravity water surface waves. However, on the forward face of short gravity and gravity-capillary ͑SGGC͒ waves of a few centimeters to tens of centimeters in wavelength, there commonly resides a train of short capillaries. These capillaries are known as parasitic capillaries, and are carried forward quasisteadily with the SGGC waves. 1,2 As the parasitic capillaries move forward with the SGGC waves, wave energy is transferred from these SGGC waves to the associated parasitic capillaries. This transfer of energy is through action of both the radiation stresses and surface pressure pulses at the crests of the SGGC waves. The energy of the capillary waves is then dissipated strongly by viscosity. Since the viscous dissipation is proportional to the inverse square of the wavelength, the energy loss associated with the capillaries can be many times that of the dissipation by the SGGC waves. In certain circumstances, this increased dissipation of SGGC waves due to parasitic capillaries cannot be ignored. Quantitative experimental results, however, have yet to be determined. Interest in more accurate prediction of the parasiticcoupled short wave systems has arisen from applications such as microwave remote sensing of ocean surface and airsea exchanges. In order to study such short wave systems, both wind-generated and mechanically generated waves have been observed. An advantage of mechanically generated wave experiments is that the observations can be directly compared with theories and numerical models. A brief, upto-date review was given by Perlin and Schultz 3 together with an extensive list of references on this topic. The primary interest in observing short wind waves is to determine the wave spectrum ͑see Refs. 1, 4 -7 for wind tank experiments and Refs. 8 -10 for field measurements͒. It has been shown that, at the wavenumber, kϭO(10) rad/cm, the surface slope spectrum is peaked and the corresponding directional spreading narrowed. 6 This can be explained by the dominance of parasitic capillaries. 11 The spectrum of the short wind waves, in a range from 3 to 15 cm, are well below the Phillips' equilibrium spectral level even under conditions of a very long fetch of 90 m. 4,12 A possible inferential factor ͑among many others͒ causing this lower spectrum is the transfer of the wave energy to the parasitic capillaries. These effects, however, are not known quantitatively. In order to perform experiments from which quantitative results could be obtained a proper apparatus was needed. With consideration of both water and wave qualities in mind we built a water tank with thick acrylic plates and supported it with a metal frame. The size of our tank is about 4 m long, 1 m wide, and 0.5 m high. It is wide enough to eliminate side wall effects, deep enough to hold the deep water wave assumption, and long enough to observe the waves at least a few wavelengths away from our mechanical wave maker. A wedge-type wave maker capable of generating a few Hz monochromatic waves was used at one end of the tank to generate waves with wavelengths from 5 to 15 cm. This long wave paddle, with a right-angle triangular cross section of height 10 cm and top width 4.5 cm, is made of foam filled fiberglass sheets. The paddle is strengthened by an aluminum bar running across the top. It is designed to be strong and light so that a stepper motor can drive the wave generating paddle system. Driving the system with a stepper motor allows precise control of the paddle motion, with programming flexibility. Two vertical hollow-shafts are attached near the ends of the wedge inhibiting its lateral movement. The wedge is coupled with the motor through gears and a driving belt. By micro-stepping the motor and properly adjusting the tension of the driving belt, the paddle can be moved up and down evenly and smoothly. Such even and smooth movement is necessary due to the inherent instability of steep gravity waves. Any unwanted motion disturbance can be amplified by the wave nonlinearity destabilizing the waveform quickly. To reduce wave reflection at the other end of the tank, we built a 1:10 sloping beach 1.5 m long. The roughened beach surface is made of 2-cm acrylic grid bound to an acrylic plate. The wave reflection from the beach is effectively reduced to less than 5%. To keep the water free from surface film and rust pollution, a surface skimmer-filter system is used and no metal parts come into contact with the PHYSICS OF FLUIDS VOLUME
doi:10.1063/1.1519260 fatcat:4yscu45pdrextc45qznk2xez4m