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- Author or Editor: W. Kendall Melville x
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Abstract
Recent field measurements by Agrawal et al. have provided evidence of a shallow surface mixed layer in which the rate of dissipation due to turbulence is one to two orders of magnitude greater than that in a comparable turbulent boundary layer over a rigid wall. It is shown that predictions by Phillips of the energy lost by breaking surface waves in an equilibrium regime and laboratory measurements by Rapp and Melville of the mixing and turbulence due to breaking together lead to estimates of the enhanced dissipation rate and the thickness of the surface layer consistent with the field measurements. Wave-age-dependent scaling of the dissipation layer is proposed. Laboratory measurements of dissipation rates in both unsteady and quasi-steady breaking waves are examined. It is shown that an appropriately defined dimensionless rate of dissipation in unsteady breaking waves is not constant, but increases with a measure of the wave slope. Differences between dissipation rates in quasi-steady and unsteady breakers are discussed. It is found that measurements of the dissipation rate in unsteady breakers are consistent with independent estimates of the turbulent dissipation. The application of these results to models of dissipation due to breaking and air-sea fluxes is discussed.
Abstract
Recent field measurements by Agrawal et al. have provided evidence of a shallow surface mixed layer in which the rate of dissipation due to turbulence is one to two orders of magnitude greater than that in a comparable turbulent boundary layer over a rigid wall. It is shown that predictions by Phillips of the energy lost by breaking surface waves in an equilibrium regime and laboratory measurements by Rapp and Melville of the mixing and turbulence due to breaking together lead to estimates of the enhanced dissipation rate and the thickness of the surface layer consistent with the field measurements. Wave-age-dependent scaling of the dissipation layer is proposed. Laboratory measurements of dissipation rates in both unsteady and quasi-steady breaking waves are examined. It is shown that an appropriately defined dimensionless rate of dissipation in unsteady breaking waves is not constant, but increases with a measure of the wave slope. Differences between dissipation rates in quasi-steady and unsteady breakers are discussed. It is found that measurements of the dissipation rate in unsteady breakers are consistent with independent estimates of the turbulent dissipation. The application of these results to models of dissipation due to breaking and air-sea fluxes is discussed.
Abstract
The development of a broadband sound velocimeter that allows the simultaneous measurement of sound speed and attenuation over a wide range of frequencies is described. The velocimeter measures the attenuation and dispersion of a broadband acoustic pulse over frequencies ranging from 4 to 100 kHz across a fixed pathlength using a two-transducer system. The resulting data are inverted to arrive at bubble size distributions over bubble radii in the range 30–800 μm.
The instrument was tested in the large wave channel at the Hydraulics Laboratory of Scripps Institution of Oceanography. The channel can generate breaking waves of O(1 m) height using a hydraulically driven wave generator, giving bubble size distributions similar to those found in the field. The presence of the bubbles significantly changes the acoustical properties of the water. Internal consistency checks of the acoustic data and measurements of bubbles using an independent optical sizing technique support the accuracy of the acoustic system in measuring bubble size distributions.
A field test of the system was performed off Scripps Pier in water of approximately 6-m depth. Observations demonstrate that bubble transport events with significant temporal and spatial variability are associated with rip currents and introduce significant vertical gradients in the acoustical properties of the water. The performance of the system in the field was found to be comparable to that found in the laboratory.
Abstract
The development of a broadband sound velocimeter that allows the simultaneous measurement of sound speed and attenuation over a wide range of frequencies is described. The velocimeter measures the attenuation and dispersion of a broadband acoustic pulse over frequencies ranging from 4 to 100 kHz across a fixed pathlength using a two-transducer system. The resulting data are inverted to arrive at bubble size distributions over bubble radii in the range 30–800 μm.
The instrument was tested in the large wave channel at the Hydraulics Laboratory of Scripps Institution of Oceanography. The channel can generate breaking waves of O(1 m) height using a hydraulically driven wave generator, giving bubble size distributions similar to those found in the field. The presence of the bubbles significantly changes the acoustical properties of the water. Internal consistency checks of the acoustic data and measurements of bubbles using an independent optical sizing technique support the accuracy of the acoustic system in measuring bubble size distributions.
A field test of the system was performed off Scripps Pier in water of approximately 6-m depth. Observations demonstrate that bubble transport events with significant temporal and spatial variability are associated with rip currents and introduce significant vertical gradients in the acoustical properties of the water. The performance of the system in the field was found to be comparable to that found in the laboratory.
Abstract
Visible sea surface images are analyzed to determine the distribution of the average length of breaking crests per unit sea surface area per unit speed increment Λ(c). The Λ(c) distribution offers a scale-dependent description of wave breaking that is valuable for understanding wave energy dissipation, momentum flux from the wave field to the surface currents, and air–sea fluxes of gas and sea salt aerosols. Two independent processing techniques for determining Λ(c) from video images are implemented. In particular, the importance of the definition of the velocity of a breaking event is considered, as a single value, as a function of time, or as a function of space and time. The velocity can furthermore be defined as the full translational velocity or as the velocity normal to the breaking front. The Λ(c) distributions resulting from various definitions of velocity, sensitivity to thresholds, observational resolution, and the effect of surface currents and long wave orbital velocity are presented. The appropriateness and limitations of the comparison of the first moment of Λ(c) with the breaking rate are discussed. Two previous field observations of Λ(c) give qualitatively different results: Melville and Matusov found an exponential form for Λ(c), whereas Gemmrich et al. obtained a function that peaks at intermediate speeds and is up to an order of magnitude higher than that of Melville and Matusov. Both results can qualitatively be reproduced using the current dataset by employing the definitions of breaking velocity used in the previous studies. The authors argue that the current optimal interpretation of breaking speed resolves the breaking velocity as a function of both space and time and considers the velocity orthogonal to the breaking crest.
Abstract
Visible sea surface images are analyzed to determine the distribution of the average length of breaking crests per unit sea surface area per unit speed increment Λ(c). The Λ(c) distribution offers a scale-dependent description of wave breaking that is valuable for understanding wave energy dissipation, momentum flux from the wave field to the surface currents, and air–sea fluxes of gas and sea salt aerosols. Two independent processing techniques for determining Λ(c) from video images are implemented. In particular, the importance of the definition of the velocity of a breaking event is considered, as a single value, as a function of time, or as a function of space and time. The velocity can furthermore be defined as the full translational velocity or as the velocity normal to the breaking front. The Λ(c) distributions resulting from various definitions of velocity, sensitivity to thresholds, observational resolution, and the effect of surface currents and long wave orbital velocity are presented. The appropriateness and limitations of the comparison of the first moment of Λ(c) with the breaking rate are discussed. Two previous field observations of Λ(c) give qualitatively different results: Melville and Matusov found an exponential form for Λ(c), whereas Gemmrich et al. obtained a function that peaks at intermediate speeds and is up to an order of magnitude higher than that of Melville and Matusov. Both results can qualitatively be reproduced using the current dataset by employing the definitions of breaking velocity used in the previous studies. The authors argue that the current optimal interpretation of breaking speed resolves the breaking velocity as a function of both space and time and considers the velocity orthogonal to the breaking crest.
Abstract
On 31 December 2012, an instrumented autonomous surface vehicle (ASV; Wave Glider) transiting across the Pacific from Hawaii to Australia as part of the Pacific Crossing (PacX) project came very close (46 km) to the center of a category 3 Tropical Cyclone (TC), Freda, experiencing winds of up to 37 
Abstract
On 31 December 2012, an instrumented autonomous surface vehicle (ASV; Wave Glider) transiting across the Pacific from Hawaii to Australia as part of the Pacific Crossing (PacX) project came very close (46 km) to the center of a category 3 Tropical Cyclone (TC), Freda, experiencing winds of up to 37
Abstract
Wave breaking is thought to be the dominant mechanism for energy loss by the surface wave field. Breaking results in energetic and highly turbulent velocity fields, concentrated within approximately one wave height of the surface. To make meaningful estimates of wave energy dissipation in the upper ocean, it is then necessary to make accurate measurements of turbulent kinetic energy (TKE) dissipation very near the surface. However, the surface wave field makes measurements of turbulence at the air–sea interface challenging since the energy spectrum contains energy from both waves and turbulence over the same range of wavenumbers and frequencies. Furthermore, wave orbital velocities can advect the turbulent wake of instrumentation into the sampling volume of the instrument. In this work a new technique for measuring TKE dissipation at the sea surface that overcomes these difficulties is presented. Using a stereo pair of longwave infrared cameras, it is possible to reconstruct the surface displacement and velocity fields. The vorticity of that velocity field can then be considered to be representative of the rotational turbulence and not the irrotational wave orbital velocities. The turbulent kinetic energy dissipation rate can then be calculated by comparing the vorticity spectrum to a universal spectrum. Average surface TKE dissipation calculated in this manner was found to be consistent with near-surface values from the literature, and time-dependent dissipation was found to depend on breaking.
Abstract
Wave breaking is thought to be the dominant mechanism for energy loss by the surface wave field. Breaking results in energetic and highly turbulent velocity fields, concentrated within approximately one wave height of the surface. To make meaningful estimates of wave energy dissipation in the upper ocean, it is then necessary to make accurate measurements of turbulent kinetic energy (TKE) dissipation very near the surface. However, the surface wave field makes measurements of turbulence at the air–sea interface challenging since the energy spectrum contains energy from both waves and turbulence over the same range of wavenumbers and frequencies. Furthermore, wave orbital velocities can advect the turbulent wake of instrumentation into the sampling volume of the instrument. In this work a new technique for measuring TKE dissipation at the sea surface that overcomes these difficulties is presented. Using a stereo pair of longwave infrared cameras, it is possible to reconstruct the surface displacement and velocity fields. The vorticity of that velocity field can then be considered to be representative of the rotational turbulence and not the irrotational wave orbital velocities. The turbulent kinetic energy dissipation rate can then be calculated by comparing the vorticity spectrum to a universal spectrum. Average surface TKE dissipation calculated in this manner was found to be consistent with near-surface values from the literature, and time-dependent dissipation was found to depend on breaking.
Abstract
This paper presents laboratory and field testing of a pulse-to-pulse coherent acoustic Doppler profiler for the measurement of turbulence in the ocean. In the laboratory, velocities and wavenumber spectra collected from Doppler and digital particle image velocimeter measurements compare very well. Turbulent velocities are obtained by identifying and filtering out deep water gravity waves in Fourier space and inverting the result. Spectra of the velocity profiles then reveal the presence of an inertial subrange in the turbulence generated by unsteady breaking waves. In the field, comparison of the profiler velocity records with a single-point current measurement is satisfactory. Again wavenumber spectra are directly measured and exhibit an approximate −5/3 slope. It is concluded that the instrument is capable of directly resolving the wavenumber spectral levels in the inertial subrange under breaking waves, and therefore is capable of measuring dissipation and other turbulence parameters in the upper mixed layer or surface-wave zone.
Abstract
This paper presents laboratory and field testing of a pulse-to-pulse coherent acoustic Doppler profiler for the measurement of turbulence in the ocean. In the laboratory, velocities and wavenumber spectra collected from Doppler and digital particle image velocimeter measurements compare very well. Turbulent velocities are obtained by identifying and filtering out deep water gravity waves in Fourier space and inverting the result. Spectra of the velocity profiles then reveal the presence of an inertial subrange in the turbulence generated by unsteady breaking waves. In the field, comparison of the profiler velocity records with a single-point current measurement is satisfactory. Again wavenumber spectra are directly measured and exhibit an approximate −5/3 slope. It is concluded that the instrument is capable of directly resolving the wavenumber spectral levels in the inertial subrange under breaking waves, and therefore is capable of measuring dissipation and other turbulence parameters in the upper mixed layer or surface-wave zone.
Abstract
Properties of internal wave fronts or Kelvin fronts travelling eastward in the equatorial waveguide are studied, motivated by recent studies on coastal Kelvin waves and jumps and new data on equatorial Kelvin waves. It has been recognized for some time that nonlinear equatorial Kelvin waves can steepen and break, forming a broken wave of depression, or front, propagating eastward. The three-dimensional structure of the wave field associated with such a front is considered. As for linear Kelvin waves, the front is symmetrical with respect to the equator. Sufficiently far away from the front, the wave profile is Gaussian in the meridional direction, with the equatorial Rossby radius of deformation being its decay scale. Due to nonlinearity, the phase speed of the front is greater than that of linear Kelvin waves, resulting in a supercritical flow. This leads to the resonant generation of equatorially trapped gravity–inertial (or Poincaré) waves, analogous in principle to the resonant mechanism for nonlinear coastal Kelvin waves. First-mode symmetrical Poincaré waves are generated, with their wavelength determined by the amplitude of the front. Finally, the propagation of a Kelvin front gives rise to a nonzero poleward mass transport above the thermocline, in consequence of which there is a poleward heat flux.
Abstract
Properties of internal wave fronts or Kelvin fronts travelling eastward in the equatorial waveguide are studied, motivated by recent studies on coastal Kelvin waves and jumps and new data on equatorial Kelvin waves. It has been recognized for some time that nonlinear equatorial Kelvin waves can steepen and break, forming a broken wave of depression, or front, propagating eastward. The three-dimensional structure of the wave field associated with such a front is considered. As for linear Kelvin waves, the front is symmetrical with respect to the equator. Sufficiently far away from the front, the wave profile is Gaussian in the meridional direction, with the equatorial Rossby radius of deformation being its decay scale. Due to nonlinearity, the phase speed of the front is greater than that of linear Kelvin waves, resulting in a supercritical flow. This leads to the resonant generation of equatorially trapped gravity–inertial (or Poincaré) waves, analogous in principle to the resonant mechanism for nonlinear coastal Kelvin waves. First-mode symmetrical Poincaré waves are generated, with their wavelength determined by the amplitude of the front. Finally, the propagation of a Kelvin front gives rise to a nonzero poleward mass transport above the thermocline, in consequence of which there is a poleward heat flux.
Abstract
The evolution of nonlinear Kelvin waves is studied using analytical and numerical methods. In the absence of dispersive (nonhydrostatic) effects, such waves may evolve to braking. The authors find that one of the effects of rotation is to delay the onset of breaking in time by up to 60%, with respect to a comparable wave in de absence of rotation. This delay is consistent with qualitative conclusions based on transverse averaging of the evolution equations. Further, the onset of breaking occurs almost simultaneously over a zone of uniform phase that is normal to the boundary and extends over a distance comparable to the Rossby radius of deformation. In other words, the process of breaking embraces the most energetic area of the wave. In contrast to the linear Kelvin wave, the nonlinear wave develops a dipole structure in the cross-shelf velocity, with a zero net offshore flow. With increasing nonlinearity the flow develops a stronger offshore jet ahead of the wave crest. The Kelvin wave amplitude at the coast delays slightly with time. This and other major features of the wave are accounted for by an analytical model based on slowly varying averaged variables. As part of the analysis it is demonstrated that the evolution of the wave phase may be described by an inhomogeneous Klein-Gordon equation.
Abstract
The evolution of nonlinear Kelvin waves is studied using analytical and numerical methods. In the absence of dispersive (nonhydrostatic) effects, such waves may evolve to braking. The authors find that one of the effects of rotation is to delay the onset of breaking in time by up to 60%, with respect to a comparable wave in de absence of rotation. This delay is consistent with qualitative conclusions based on transverse averaging of the evolution equations. Further, the onset of breaking occurs almost simultaneously over a zone of uniform phase that is normal to the boundary and extends over a distance comparable to the Rossby radius of deformation. In other words, the process of breaking embraces the most energetic area of the wave. In contrast to the linear Kelvin wave, the nonlinear wave develops a dipole structure in the cross-shelf velocity, with a zero net offshore flow. With increasing nonlinearity the flow develops a stronger offshore jet ahead of the wave crest. The Kelvin wave amplitude at the coast delays slightly with time. This and other major features of the wave are accounted for by an analytical model based on slowly varying averaged variables. As part of the analysis it is demonstrated that the evolution of the wave phase may be described by an inhomogeneous Klein-Gordon equation.
Abstract
Measurements of the ambient noise spectrum level N with simultaneous, coincident wind and wave measurements were made from RP FLIP in fall 1991. The measurements were designed to investigate the correlation between the ambient noise and relevant surface wave parameters. The results suggest that wave parameters related to the incidence of wave breaking correlated well with the ambient noise level. The correlation between N and the rms wave amplitude a was found to he poor but that between N and the rms amplitude of the local wind sea a w was comparable to that between wind speed U and N. Similar good correlations were found between the rms wave slope s and N, and the higher frequency surface wave spectral levels and N.
Correlations between the surface wave dissipation estimates D based on the Hasselmann and Phillips models and the ambient noise were comparable to those between the wind speed and the ambient noise. The mean square acoustic pressure was found to be proportional to D n with n in the range 0.5–0.8. The implications of these results for monitoring surface waves and air–sea fluxes are discussed.
Abstract
Measurements of the ambient noise spectrum level N with simultaneous, coincident wind and wave measurements were made from RP FLIP in fall 1991. The measurements were designed to investigate the correlation between the ambient noise and relevant surface wave parameters. The results suggest that wave parameters related to the incidence of wave breaking correlated well with the ambient noise level. The correlation between N and the rms wave amplitude a was found to he poor but that between N and the rms amplitude of the local wind sea a w was comparable to that between wind speed U and N. Similar good correlations were found between the rms wave slope s and N, and the higher frequency surface wave spectral levels and N.
Correlations between the surface wave dissipation estimates D based on the Hasselmann and Phillips models and the ambient noise were comparable to those between the wind speed and the ambient noise. The mean square acoustic pressure was found to be proportional to D n with n in the range 0.5–0.8. The implications of these results for monitoring surface waves and air–sea fluxes are discussed.
Abstract
Sea spray aerosols represent a large fraction of the aerosols present in the maritime environment. Despite evidence of the importance of surface wave– and wave breaking–related processes in coupling the ocean with the atmosphere, sea spray source generation functions are traditionally parameterized by the 10-m wind speed U 10 alone. It is clear that unless the wind and wave field are fully developed, the source function will be a function of both wind and wave parameters. This study reports primarily on the aerosol component of an air–sea interaction experiment, the phased-resolved High-Resolution Air–Sea Interaction Experiment (HIRES), conducted off the coast of northern California in June 2010. Detailed measurements of aerosol number concentration in the marine atmospheric boundary layer (MABL) at altitudes ranging from as low as 30 m up to 800 m above mean sea level (MSL) over a broad range of environmental conditions (significant wave height H s of 2 to 4.5 m and U 10 from 10 to 18 m s−1) collected from an instrumented research aircraft are presented. Aerosol number densities and volume are computed over a range of particle diameters from 0.1 to 200 μm, while the sea surface conditions, including H s , moments of the breaker length distribution Λ(c), and wave breaking dissipation, were measured by a suite of electro-optical sensors that included the NASA Airborne Topographic Mapper (ATM). The sea-state dependence of the aerosol concentration in the MABL is evident, stressing the need to incorporate wave parameters in the spray source generation functions that are traditionally parameterized by surface winds alone.
Abstract
Sea spray aerosols represent a large fraction of the aerosols present in the maritime environment. Despite evidence of the importance of surface wave– and wave breaking–related processes in coupling the ocean with the atmosphere, sea spray source generation functions are traditionally parameterized by the 10-m wind speed U 10 alone. It is clear that unless the wind and wave field are fully developed, the source function will be a function of both wind and wave parameters. This study reports primarily on the aerosol component of an air–sea interaction experiment, the phased-resolved High-Resolution Air–Sea Interaction Experiment (HIRES), conducted off the coast of northern California in June 2010. Detailed measurements of aerosol number concentration in the marine atmospheric boundary layer (MABL) at altitudes ranging from as low as 30 m up to 800 m above mean sea level (MSL) over a broad range of environmental conditions (significant wave height H s of 2 to 4.5 m and U 10 from 10 to 18 m s−1) collected from an instrumented research aircraft are presented. Aerosol number densities and volume are computed over a range of particle diameters from 0.1 to 200 μm, while the sea surface conditions, including H s , moments of the breaker length distribution Λ(c), and wave breaking dissipation, were measured by a suite of electro-optical sensors that included the NASA Airborne Topographic Mapper (ATM). The sea-state dependence of the aerosol concentration in the MABL is evident, stressing the need to incorporate wave parameters in the spray source generation functions that are traditionally parameterized by surface winds alone.
