Analysis of SWADE Discus N Wind Speed and Wave Height Time Series. Part II: Quantitative Growth Rates during a Storm

Jorge F. Willemsen Rosenstiel School of Marine and Atmospheric Science, University of Miami, Miami, Florida

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Abstract

In Part I, wind speed and wave height time series obtained from the Discus N buoy during two storm events recorded in the SWADE experiment were analyzed using discrete wavelet packet transforms. One result of the analysis is that distinct tightly bunched wave frequency bands exist that evolve differently from one another in response to the wind. In this paper, that result is confirmed using a more traditional windowed Fourier transform approach. Additionally, the bands in which most of the wave energy is concentrated will be shown to grow in a manner consistent with the Plant formulation during the intervals of most intense growth. That formulation is parsimoniously extended to include the presence of a growing wind, under the hypothesis that wind fluctuations are too rapid for long waves to respond. The model of Al-Zanaidi and Hui will also be considered. Neither one of the formulations is predictive above approximately 0.22 Hz. Finally, the onset and offset times of very rapid wave growth are discussed in terms of associated winds.

Corresponding author address: Dr. Jorge F. Willemsen, RSMAS, University of Miami, 4600 Rickenbacker Causeway, Miami, FL 33149-4160.

Email: Jorge@maya.rsmas.miami.edu

Abstract

In Part I, wind speed and wave height time series obtained from the Discus N buoy during two storm events recorded in the SWADE experiment were analyzed using discrete wavelet packet transforms. One result of the analysis is that distinct tightly bunched wave frequency bands exist that evolve differently from one another in response to the wind. In this paper, that result is confirmed using a more traditional windowed Fourier transform approach. Additionally, the bands in which most of the wave energy is concentrated will be shown to grow in a manner consistent with the Plant formulation during the intervals of most intense growth. That formulation is parsimoniously extended to include the presence of a growing wind, under the hypothesis that wind fluctuations are too rapid for long waves to respond. The model of Al-Zanaidi and Hui will also be considered. Neither one of the formulations is predictive above approximately 0.22 Hz. Finally, the onset and offset times of very rapid wave growth are discussed in terms of associated winds.

Corresponding author address: Dr. Jorge F. Willemsen, RSMAS, University of Miami, 4600 Rickenbacker Causeway, Miami, FL 33149-4160.

Email: Jorge@maya.rsmas.miami.edu

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  • Al-Zanaidi, M. A., and W. H. Hui, 1984: Linear dynamics of wind waves in coupled turbulent air–water flow. Part 1. Theory. J. Fluid Mech.,148, 225–246.

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  • Pierson, W. J., 1990: Dependence of radar backscatter onenvironmental parameters. Vol. 2, Surface Waves and Fluxes, G. L. Geernaert and W. L. Plant, Eds., Kluwer Academic, 173–220.

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  • Plant, W. L., 1982: Mechanics of ocean surface waves. J. Geophys. Res.,87C, 1961–1967.

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  • Willemsen, J. F., 1995: Analysis of SWADE Discus N wind speed and wave height time series. Part I: Discrete wavelet packet representations. J. Atmos. Oceanic Technol.,12, 1248–1270.

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