Wave dissipation by breaking, or the energy transfer from the surface wave field to currents and turbulence, is one of the least understood components of air–sea interaction. It is important for a better understanding of the coupling between the surface wave field and the upper layers of the ocean and for improved surface-wave prediction schemes. Simple scaling arguments show that the wave dissipation per unit length of breaking crest, ϵl, should be proportional to ρwgc5, where ρw is the density of water, g is the acceleration due to gravity and c is the phase speed of the breaking wave. The proportionality factor, or ‘breaking parameter’ b, has been poorly constrained by experiments and field measurements, although our earlier work has suggested that it should be dependent on measures of the wave slope and spectral bandwidth. In this paper we describe inertial scaling arguments for the energy lost by plunging breakers which predict that the breaking parameter b = β(hk)5/2, where hk is a local breaking slope parameter, and β is a parameter of O(1). This prediction is tested with laboratory measurements of breaking due to dispersive focusing of wave packets in a wave channel. Good agreement is found within the scatter of the data. We also find that if an integral linear measure of the maximum slope of the wave packet, S, is used instead of hk, then b ∝ S2.77 gives better agreement with the data. During the final preparation of this paper we became aware of similar experiments by Banner & Peirson (2007) concentrating on the threshold for breaking at lower wave slopes, using a measure of the rate of focusing of wave energy to correlate measurements of b. We discuss the significance of these results in the context of recent measurements and modelling of surface wave processes.
Laboratory measurements of the post-breaking velocity field due to unsteady deep-water breaking are presented. Digital particle image velocimetry (DPIV) is used to measure the entire post-breaking turbulent cloud with high-resolution imagery permitting the measurement of scales fromO(1m) down toO(1mm). Ensemble-averaged quantities including mean velocity, turbulent kinetic energy (TKE) density and Reynolds stress are presented and compare favourably with the results of Melville, Veron & White (J. Fluid Mech., vol. 454, 2002, pp. 203–233; MVW). However, due to limited resolution, MVW's measurements were not spatially coherent across the turbulent cloud, and this restricted their ability to compute turbulent wavenumber spectra. Statistical spatial quantities including the integral length scaleL11, Taylor microscale λfand the Taylor microscale Reynolds numberReλare presented. Estimation of an eddy viscosity for the breaking event is also given based on analysis of the image data. Turbulent wavenumber spectra are computed and within 12 wave periods after breaking exhibit what have been termed ‘spectral bumps’ in the turbulence literature. These local maxima in the spectra are thought to be caused by an imbalance between the transport of energy from large scales and the dissipation at small scales. Estimates of the dissipation rate per unit mass are computed using both direct and indirect methods. Horizontally averaged terms in the TKE budget are also presented up to 27 wave periods after breaking and are discussed with regard to the dynamics of the post-breaking flow. Comparisons of the TKE density in the streamwise and cross-stream planes with the three-dimensional full TKE density are given in an appendix.
Optically based measurements in high Reynolds number fluid flows often require high-speed imaging techniques. These cameras typically record data internally and thus are limited by the amount of onboard memory available. A novel camera technology for use in particle tracking velocimetry is presented in this paper. This technology consists of a dynamic vision sensor in which pixels operate in parallel, transmitting asynchronous events only when relative changes in intensity of approximately 10% are encountered with a temporal resolution of 1 mu s. This results in a recording system whose data storage and bandwidth requirements are about 100 times smaller than a typical high-speed image sensor. Post-processing times of data collected from this sensor also increase to about 10 times faster than real time. We present a proof-of-concept study comparing this novel sensor with a high-speed CMOS camera capable of recording up to 2,000 fps at 1,024 x 1,024 pixels. Comparisons are made in the ability of each system to track dense (rho >1 g/cm(3)) particles in a solid-liquid two-phase pipe flow. Reynolds numbers based on the bulk velocity and pipe diameter up to 100,000 are investigated. Abstract Optically based measurements in high Reynolds number fluid flows often require high-speed imaging techniques. These cameras typically record data internally and thus are limited by the amount of onboard memory available. A novel camera technology for use in Particle Tracking Velocimetry (PTV) is presented in this paper. This technology consists of a dynamic vision sensor (DVS) in which pixels operate in parallel, transmitting asynchronous events only when relative changes in intensity of approximately 10% are encountered with a temporal resolution of 1µs. This results in a recording system whose data storage and bandwidth requirements are about 100 times smaller than a typical high speed image sensor. Post-processing times of data collected from this sensor also increase to about 10 times faster than real time. We present a proof-of-concept study comparing this novel sensor to a high-speed CMOS camera capable of recording up to 2000 fps at 1024x1024 pixels. Comparisons are made in the ability of each system to track dense (ρ > 1 g/cm 3 ) particles in a solid-liquid two-phase pipe flow. Reynolds numbers based on the bulk velocity and pipe diameter up to 100,000 are investigated.
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