On Phillips' Theory of Equilibrium Range in the Spectra of Wind-Generated Gravity Waves

Kitaigordskii, S. A.; Krasitskii, V. P.; Zaslavskii, M. M.

doi:10.1175/1520-0485(1975)005<0410:optoer>2.0.co;2

Cited by 173 publications

(74 citation statements)

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“…The direct estimation of the surface directional spectrum based on the measurement of the frequency spectrum cannot be obtained when the flow velocity is of a similar order of magnitude as the group and phase velocity of the waves on the surface. 21 For the streamwise wavenumber spectrum of waves generated by grid turbulence in a flow, Savelsberg and Van De Water 22 proposed a power-function spectrum with a very steep decay, proportional to k À8 . In shallow turbulent flows over a rough bed, Horoshenkov et al 17 suggested a Gaussian quasi-harmonic shape of the correlation function, which indicates a rapidly decaying Gaussian spectrum of the elevation.…”

Section: B Surface Modelmentioning

confidence: 99%

Doppler spectra of airborne sound backscattered by the free surface of a shallow turbulent water flow

Dolcetti

Krynkin

Horoshenkov

2017

The Journal of the Acoustical Society of America

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Measurements of the Doppler spectra of airborne ultrasound backscattered by the rough dynamic surface of a shallow turbulent flow are presented in this paper. The interpretation of the observed acoustic signal behavior is provided by means of a Monte Carlo simulation based on the Kirchhoff approximation and on a linear random-phase model of the water surface elevation. Results suggest that the main scattering mechanism is from capillary waves with small amplitude. Waves that travel at the same velocity of the flow, as well as dispersive waves that travel at a range of velocities, are detected, studied, and used in the acoustic Doppler analysis. The dispersive surface waves are not observed when the flow velocity is slow compared to their characteristic velocity. Relatively wide peaks in the experimental spectra also suggest the existence of nonlinear modulations of the short capillary waves, or their propagation in a wide range of directions. The variability of the Doppler spectra with the conditions of the flow can affect the accuracy of the flow velocity estimations based on backscattering Doppler. A set of different methods to estimate this velocity accurately and remotely at different ranges of flow conditions is suggested.

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Section: B Surface Modelmentioning

confidence: 99%

Doppler spectra of airborne sound backscattered by the free surface of a shallow turbulent water flow

Dolcetti

Krynkin

Horoshenkov

2017

The Journal of the Acoustical Society of America

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“…This spectrum cannot be inferred from the measurement of the surface frequency spectrum, especially when the flow mean surface velocity is of similar order of magnitude of the phase and group velocities of gravitycapillary waves. 26 For waves propagating in open channel flows where turbulence is generated by active or passive grids, Savelsberg and van de Water 27 measured a powerfunction spectrum with the formŴðkÞ / k Àa , and with the exponent a % 8. Power-function spectra of the surface elevation have been predicted also theoretically based on the rapid distortion theory for the waves generated by turbulence in a vertically sheared flow.…”

Section: )mentioning

confidence: 99%

Doppler spectra of airborne ultrasound forward scattered by the rough surface of open channel turbulent water flows

Dolcetti

Krynkin

2017

The Journal of the Acoustical Society of America

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Experimental data are presented on the Doppler spectra of airborne ultrasound forward scattered by the rough dynamic surface of an open channel turbulent flow. The data are numerically interpreted based on a Kirchhoff approximation for a stationary random water surface roughness. The results show a clear link between the Doppler spectra and the characteristic spatial and temporal scales of the water surface. The decay of the Doppler spectra is proportional to the velocity of the flow near the surface. At higher Doppler frequencies the measurements show a less steep decrease of the Doppler spectra with the frequency compared to the numerical simulations. A semi-empirical equation for the spectrum of the surface elevation in open channel turbulent flows over a rough bed is provided. The results of this study suggest that the dynamic surface of open channel turbulent flows can be characterized remotely based on the Doppler spectra of forward scattered airborne ultrasound. The method does not require any equipment to be submerged in the flow and works remotely with a very high signal to noise ratio.

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“…The wave spectra at high frequency can also be Doppler shifted due to orbital displacements (Kitaigordskii et al 1975). At any instantaneous time, the three lasers sample the same surface waves at three intersections between the lasers and the sea surface.…”

Section: ͑8͒mentioning

confidence: 99%

Measurement of Directional Wave Spectra Using Aircraft Laser Altimeters

Sun

Burns

Vandemark

et al. 2005

Journal of Atmospheric and Oceanic Technology

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A remote sensing method to measure directional oceanic surface waves by three laser altimeters on the NOAA LongEZ aircraft is investigated. To examine feasibility and sensitivity of the wavelet analysis method to various waves, aircraft motions, and aircraft flight directions relative to wave propagation directions, idealized surface waves are simulated from various idealized aircraft flights. In addition, the wavelet analysis method is also applied to two cases from field measurements, and the results are compared with traditional wave spectra from buoys. Since the wavelet analysis method relies on the "wave slopes" measured through phase differences between the time series of the laser distances between the aircraft and sea surface at spatially separated locations, the resolved directional wavenumber and wave propagation direction are not affected by aircraft motions if the resolved frequencies of the aircraft motion and the wave are not the same. However, the encounter wave frequency, which is directly resolved using the laser measurement from the moving aircraft, is affected by the Doppler shift due to aircraft motion relative to wave propagations. The wavelet analysis method could fail if the aircraft flies in the direction such that the aircraft speed along the wave propagation direction is the same as the wave phase speed (i.e., the aircraft flies along wave crests or troughs) or if two waves with different wavelengths and phase speed have the same encountered wavelength from the aircraft. In addition, the data noise due to laser measurement uncertainty or natural isotropic surface elevation perturbations can also affect the relative phase difference between the laser distance measurements, which in turn affects the accuracy of the resolved wavenumber and wave propagation direction. The smallest waves measured by the lasers depend on laser sampling rate and horizontal distances between the lasers (for the LongEZ this is 2 m). The resolved wave direction and wavenumber at the peak wave from the two field experiments compared well with on-site buoy observations. Overall, the study demonstrates that three spatially separated laser altimeters on moving platforms can be utilized to resolve two-dimensional wave spectra.

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On Phillips' Theory of Equilibrium Range in the Spectra of Wind-Generated Gravity Waves

Cited by 173 publications

References 0 publications

Doppler spectra of airborne sound backscattered by the free surface of a shallow turbulent water flow

Doppler spectra of airborne sound backscattered by the free surface of a shallow turbulent water flow

Doppler spectra of airborne ultrasound forward scattered by the rough surface of open channel turbulent water flows

Measurement of Directional Wave Spectra Using Aircraft Laser Altimeters

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