Wind Wave Growth Research Articles

Analytically derived wind-wave directional spectrum part 1. Derivation of the spectrum

In contrast with the usual method to obtain the wind-wave directional spectrum by multiplying the frequency spectrum with an empirical directional function, the authors attempt to derive analytically the directional spectrum by adopting proper spectral form and using effective parameters, namely, the zero order momentm0 of the wind-wave frequency spectrumS(ω), its peak frequency ω0 and the so-called peakness factorP=ω0S(ω0)/m0, where ω is angular frequency. The directional spectrum is given in a form of frequency spectrum for each direction. The spectral directionality depends on, in addition to frequency, the wind-wave growth status, for the peakness factorP as introduced by the authors previously is a measure of the wave development stage. The salient features of the directional spectrum, comparison with existing formulas and the verification of the spectrum by observational data are to be given in the Part 2 of the paper.

Analytically derived wind-wave directional spectrum part 2. Characteristics, comparison and verification of spectrum

The dependence of the angular spreading on frequency and wind-wave growth status is discussed in great detail for the proposed spectrum. The calculated angular spreading agrees with the measurements of Donelanet al. but is slightly broader. Explanation is given to the appearance of the narrowest spreading at a frequency slightly smaller than that of the wind-wave frequency spectrum peak as found by these authors. There is also basic agreement between the calculated spreading and the formulas of Mitsuyasuet al. and Hasselmannet al. for the specific wind-wave status on which these empirical formulas are based, though the former is narrower. The wind-wave frequency spectrum obtained by integrating the proposed directional spectrum with respect to direction agrees with the JONSWAP spectrum and that derived by the authors previously. The proposed spectrum is preliminarily verified with field data obtained by optical method.

Surface films and wind wave growth

The generation and growth of surface water waves by the wind and including modified boundary conditions appropriate for the presence of surfactants at the surface are reconsidered using linear instability theory to describe the process. The new features of our work are the inclusion of both surfactants and a wind drift layer. We allow a coupled mean flow in both the air and water; the depth‐dependent mean flow is considered to be wind‐induced. The complex wave frequencies are determined numerically. Uncontrolled numerical errors associated with a direct numerical solution of the Orr‐Sommerfeld equation for the coupled mean flow are avoided by solving an associated equation obtained by a Riccati transformation of the original equation, allowing a straightforward and efficient determination of the eigenvalues of the linear stability problem. A different aspect of our analysis is the change of surface boundary conditions due to contamination of the surface, notably, the change of tangential stress at the surface due to surface tension gradients induced by the film (known as the Marangoni effect). Comparisons are made with previous work on both film‐free and contaminated surfaces. The dominant effect of introducing film boundary conditions is a large change in the wave number of the most unstable wave with an attendant reduction in the growth rate. Implications for wind wave growth on the ocean are discussed.

Growth of wind waves with fetch observed by the Geosat altimeter in the Japan Sea under winter monsoon

The wind speeds and the significant wave heights derived from the Geosat altimeter are validated by comparing with the data obtained at Japanese ocean data buoy stations. A systematic error is found in the altimeter wind speeds at high winds. An experimental equation is derived in order to correct this error for the present study. By using the corrected wind speeds and the wave heights, growth of wind waves with fetch in the Japan Sea under winter monsoon is investigated. The altimeter‐derived nondimensional significant wave height and nondimensional fetch show good agreement with the empirical fetch graph formulas. Fetch variation of the wind speeds is also discussed in relation to the evolution of the turbulent boundary layer over wind waves by using the altimeter data.

Laboratory measurements of modulation of short-wave slopes by long surface waves

Hydrodynamic modulation of wind waves by long surface waves in a wave tank is investigated, at wind speeds ranging from 1.5 to 10 m s−1. The results are compared with the linear, non-dissipative, theory of Longuet-Higgins & Stewart (1960), which describes the modulation of a group of short gravity waves due to straining of the surface by currents produced by the orbital motions of the long wave, and work done against the radiation stresses of the short waves. In most cases the theory is in good agreement with the experimental results when the short waves are not too steep, and the rate of growth due to the wind is relatively small. At the higher wind speeds, the effects of wind-wave growth, dissipation and wave-wave interactions are dominant.

On the local equilibrium of winds and wind-waves in relation to surface drag

Local equilibrium of winds and wind-waves is discussed as a basis for research of the drag coefficient of the water surface as well as for the spectral growth of wind-waves. This hypothesis assumes, in a narrow sense, that statistical properties are determined from four physical quantities, which represent winds and wind-waves: the friction velocityu *, the gravitational accelerationg, the powerE of the surface displacement, and the peak frequencyω p of a wind-wave spectrum. Then one has only one nondimensionalcontrol parameter, which may be either the wave age or wave nonlinearity (slope) of dominant waves. In a wide-sense, one can take into account viscosity and surface tension in terms of one more additional parameter by virtue of the virtual invariance of those material constants; that parameter describes the scale ratio between dominant waves and the short waves for which viscosity or surface tension is important. A unified expression for the roughness height according to this hypothesis turns out to include Charnock's and Toba's formulas as special cases. On the basis of a preliminary analysis of the experimental data, a new empirical formula is proposed.

Wind Wave Growth in Shallow Water

New developments in the area of shallow water wave spectra have aided in the derivation of an equation for the limiting wave height in the case of fully saturated wind seas in shallow water. The result is very similar to the empirically derived expression obtained by Bretschneider in 1958. Starting with an equation for the depth controlled zero moment wave height in terms of depth, Phillip's coefficient, and the wave period associated with the peak spectral frequency, the result is obtained using a recently developed empirical experssion for the Phillip's coefficient and a method for specifying the peak spectral frequency at full development in shallow water. The good comparison to Bretschneider's result is satisfying in that further validity is added to the basic equation used in the derivation and to the newer developments in shallow water spectral representations.

Growth and equilibrium of wind waves in a laboratory channel : Leykin, I.A., K.V. Pokazeev and A.D. Rozenberg, 1984. Fiz. Atmosf. Okeana, 20(4): 297–304. (In Russian, English abstract.)

Growth and equilibrium of wind waves in a laboratory channel : Leykin, I.A., K.V. Pokazeev and A.D. Rozenberg, 1984. Fiz. Atmosf. Okeana, 20(4): 297–304. (In Russian, English abstract.)

Comment on ‘A Monte Carlo Approach to the computation of refraction of water waves’ by Evert Bouws and Jurjen A. Battjes

Journal of Geophysical Research: OceansVolume 88, Issue C10 p. 6082-6082 CommentariesFree Access Comment on ‘A Monte Carlo Approach to the computation of refraction of water waves’ by Evert Bouws and Jurjen A. Battjes Sasithorn Aranuvachapun, Sasithorn AranuvachapunSearch for more papers by this author Sasithorn Aranuvachapun, Sasithorn AranuvachapunSearch for more papers by this author First published: 20 July 1983 https://doi.org/10.1029/JC088iC10p06082Citations: 1AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL No abstract is available for this article. References Bouws, E., J. A. Battjes, A Monte Carlo approach to the computation of refraction of water waves, J. Geophys. Res., 87, 5718– 5722, 1982. Hasselmann, K., T. P. Barnett, E. Bouws, H. Carlson, D. E. Cartwright, K. Enke, J. A. Ewing, H. Gienapp, D. E. Hasselmann, P. Kruseman, A. Meerburg, P. Müller, D. J. Olbers, K. Richter, W. Sell, H. Walden, Measurements of wind-wave growth and swell decay during the Joint North Sea Wave Project (JONSWAP), Dtsch. Hydrogr. Z., Ser. A, 8, 95, 1973. Ripley, B. D., Spatial Statistics, 16, John Wiley, New York, 1981. Citing Literature Volume88, IssueC1020 July 1983Pages 6082-6082 ReferencesRelatedInformation

Wind‐Wave Growth with High Friction

An approximate method is presented for estimating wind-wave growth over flooded areas where there is a major effect from bottom friction because of dense vegetation. The method estimates wave growth using an adjusted fetch length which is shorter than the actual fetch length. The adjusted fetch length is determined by comparing decay factors for the case of low bottom friction and the case of high bottom friction.

Prediction of ocean waves based on the single-parameter growth equation of wind waves (II) introduction of grid method

The present study is a modification of the wave prediction model presented in the first paper of this title (Kawaiet al., 1979) based on the Toba's (1978) single parameter equation of the wind wave growth. The introduction of a grid method reduces the two defects pointed out inKawaiet al., i.e., the absence of the prediction of certain instants at fixed points, and the concentration of wave energy at certain points in the wind direction, arising from the lack of treatment of the lateral spreading of wave energy around the wind direction. The new model is applied to the same set of data. The results shows overall improvements, such as the elimination of certain overestimate in the first study and the coincidence of the predicted maximum with the measured one. The swells are separately hindcasted and a very good agreement with measurement is obtained.

Stochastic Form of the Growth of Wind Waves in a Single-Parameter Representation with Physical Implications

Abstract It is shown that a simple relation, E* = 5.1 × 10−2 σm*−3 for describing the conditions of growing wind waves, is supported by various available data, where E* = g2E/u*4 is dimensionless energy. σm* = u*σm/g the dimensionless angular frequency at the maximum of the energy spectrum, g the acceleration of gravity and u* the friction velocity of the air. This expression is an alternative form of the relation between dimensionless wave height and period, H* ∝ T*3/2, which was previously proposed by the author (Toba, 1972) for energy-containing waves, and is extended to individual waves in the wind-wave field in a statistical sense. It is also shown, supported by various data, that the essential part of the one-dimensional energy spectra of growing wind waves should have the form g*u*σ−4 for the high-frequency tail of the frequency spectrum, where g* is g expanded to include the surface tension. This is the form previously proposed by the author (Toba, 1973b) as the one-dimensional spectral form consi...

The growth of duration-limited wind waves

Laboratory measurements have been made of the one-dimensional spectra of the duration-limited wind waves which are generated when a wind abruptly begins to blow over a water surface, maintaining a constant speed during the succeeding period of time. The duration dependences of the wave energy E and the spectral peak frequency fm determined from the measured spectra are slightly different from those inferred from the fetch dependences of these quantities. The normalized spectra of the duration-limited wind waves are also slightly different from those of fetch-limited wind waves: the concentration of the normalized spectral energy near the spectral peak frequency is smaller, in many cases, for the duration-limited wind waves than for fetch-limited wind waves. The exponential growth rates β of the duration-limited wind-wave spectra are generally larger than those of fetch-limited wind-wave spectra. Furthermore, both for the duration-limited wind waves and for fetch-limited wind waves the exponential growth rate has a behaviour which is different from the empirical formula of Snyder & Cox (1966). A new empirical formula for the growth rate of the wave spectrum is proposed, from which the empirical formula of Snyder & Cox (1966) can be derived as a special case. Agreement between the new empirical formula and the experimental results is satisfactory for fetch-limited wave spectra, but is confined to the qualitative features for the duration-limited wave spectra.

The growth of gravity-capillary waves in a coupled shear flow

The growth rates and phase speeds of gravity-capillary wind waves are investigated through numerical solution of a linear, viscous, coupled, shear-flow perturbation model. Numerical results are obtained by transforming the boundary-value problem of a perturbed mean laminar shear flow into a matrix-eigenvalue problem using standard finite-difference methods.Detailed calculations are performed for a basic state composed of a logarithmic-linear mean flow profile in the air and a linear-logarithmic mean flow profile in the water. We exclude turbulent Reynolds stresses. Calculated growth rates show excellent agreement with corresponding experimental growth rates. This implies that the initial growth of gravity-capillary wind waves is almost certainly due to the instability of the coupled laminar shear flow in the air and water.The investigation also demonstrates that the shear flow in the water cannot be ignored in wave growth studies, since the usual 3-4%, highly sheared, wind-induced surface drift produces a significant increase in the growth of wind-generated gravity-capillary waves.

Studies on wind waves by wind flume experiments. (II) On the generation and growth of wind waves : Kunishi H., 1962. (In Japanese; English summary). J. Oceanogr. Soc., Jap., 20th Ann. Vol.: 470–486

Studies on wind waves by wind flume experiments. (II) On the generation and growth of wind waves : Kunishi H., 1962. (In Japanese; English summary). J. Oceanogr. Soc., Jap., 20th Ann. Vol.: 470–486

Laboratory Study of Wind Waves in Shallow Water

Very little quantitative information exists on growth of wind waves in waters where relatively shallow depth could influence wave growth; results of laboratory investigation of growth of waves in shallow water is presented, showing experimental relationships between wind velocity, fetch, and wave parameters for two different water depths.