Spectrum Of Wind-generated Waves Research Articles

In Memoriam: Sergei A. Kitaigorodskii, 1934—2014

Professor Sergei A. Kitaigorodskii, one of the pioneers of air-sea interaction studies, passed away on 4 December 2014 in Helsinki, at the age of 80. He had a clear vision of the fundamental problems of marine boundary layer physics. His bold ideas opened new paths more than a half century ago, and they continue to stimulate active research. In particular, he made significant progress on the difficult problem of estimating gas transfer rates through gas-liquid interfaces and contributed to many of the Gas Transfer at Water Surfaces conferences.Kitaigorodskii was born in Moscow on 13 September 1934. His father, Professor Alexander Kitaigorodskii, was a well-known physicist. Sergei Kitaigorodskii completed his undergraduate studies at Moscow State University in 1956, and he continued his postgraduate studies on the theory of turbulent mixing at the Academy of Sciences, Moscow, where he was awarded his Ph.D. from the Institute of Physics of the Atmosphere in 1960.As a post-doctoral fellow at the Institute of Oceanology of the Academy of Sciences, he formulated the Kitaigorodskii similarity hypothesis for the wind-generated wave spectrum in 1961. He later recounted how, as a young student, he had been impressed by the simple and at the same time fundamental results of O. M. Phillips, and he had wanted to follow that path by combining it with the Russian tradition, the Kolmogorov similarity hypothesis of turbulence. The Kitaigorodskii hypothesis immediately showed its value when W. J. Pierson Jr. and L. Moskowitz were able in 1964 to collapse their empirical data into a single dimensionless curve, and to formulate the Pierson-Moskowitz spectrum for fully developed seas. At the same time Kitaigorodskii continued his studies of the atmospheric side and showed how swell could influence the marine boundary layer, a topic upon which his ideas remain important.In 1962 Kitaigorodskii became a Senior Scientist at the institute and turned his main interest back to turbulence of the oceanic mixed layer. Here he again made fundamental contributions. These, combined with his earlier studies of waves and the air-sea boundary layer, were summarized in his thesis for the Russian degree of Doctor of Science in 1968. This work was the basis of a monograph, Physics of Air- Sea Interaction, published in 1970 and translated into English in 1973; it was used widely as a textbook. In the same year, 1973, he received the Rosenstiel gold medal, and in 1978 the Liege University Award.Between 1968 and 1977 Kitaigorodskii was head of the Laboratory of the Physics of Ocean- Atmosphere Interaction in the Institute of Oceanology.During the 1970s Kitaigorodskii established contacts with the Finnish geophysics community. His Finnish wife had completed her term as a press correspondent in Moscow, and she returned to Helsinki with their twin daughters. The Soviet system allowed Kitaigorodskii to visit his family every other year, and he used this opportunity to lecture and conduct research at several Finnish institutes.

Energy dissipation through wind-generated breaking waves

Wave breaking is an important process that controls turbulence properties and fluxes of heat and mass in the upper oceanic layer. A model is described for energy dissipation per unit area at the ocean surface attributed to wind-generated breaking waves, in terms of ratio of energy dissipation to energy input, wind-generated wave spectrum, and wave growth rate. Also advanced is a vertical distribution model of turbulent kinetic energy, based on an exponential distribution method. The result shows that energy dissipation rate depends heavily on wind speed and sea state. Our results agree well with predictions of previous works.

Owen Martin Phillips

Owen Martin Phillips

Field Investigation of Transformation of the Wind Wave Frequency Spectrum with Fetch and the Stage of Development

Abstract The variability of frequency spectra of waves is considered; for example, the dependencies of integral and spectral parameters of waves on wave-development factors and the interrelationships of the parameters are examined. Also studied is the transformation of the frequency spectrum shape in the course of its development, as well as the transition from the spectrum of developing waves to the spectrum of fully developed waves. Data were obtained in situ with common methods during a long-term program in the Black Sea. The variability of the spectrum of developing waves, as a function of the stage of wave development, is described on the basis of field data using estimates of parameters for the spectrum form of the JONSWAP type. A novel approximation of the equilibrium interval level dependence on the dimensionless peak frequency fm is obtained, which includes periods of stable and changeable behavior of the spectrum level. Transformation of the spectrum of wind-generated waves related to the devel...

Variability of directional spectra of wind-generated waves, studied by means of wave staff arrays

Parameterization of the directional distribution of the wave energy obtained by means of arrays of wave probes is suggested. The parameterization encompasses a wide frequency band both above and below the peak frequency as well as a broad range of wave ages. The parameterization is developed for the integral width of the directional spectrum, which does not depend on a specific form of the approximating function. The width of the directional distribution depends on the stage of wave development and relative frequency. The narrowest directional spectra are observable, on average, 5% below the peak frequency. Above that frequency, the width of the directional spectrum increases as the frequency rises, and the rate of widening does not depend on the wave age. On the forward face of the spectrum, the rate of widening of the directional distributions towards low frequencies depends strongly on the stage of wave development and, at early stages, the directional spectra in this range are unchangeable. In general, the directional distributions of wave energy become narrower as the waves develop.

Comment on “Velocity observations above a rippled bed using laser Doppler velocimetry” by Y. C. Agrawal and D. G. Aubrey

Journal of Geophysical Research: OceansVolume 98, Issue C11 p. 20331-20333 CommentariesFree Access Comment on “Velocity observations above a rippled bed using laser Doppler velocimetry” by Y. C. Agrawal and D. G. Aubrey T. H. C. Herbers, T. H. C. HerbersSearch for more papers by this authorR. T. Guza, R. T. GuzaSearch for more papers by this author T. H. C. Herbers, T. H. C. HerbersSearch for more papers by this authorR. T. Guza, R. T. GuzaSearch for more papers by this author First published: 15 November 1993 https://doi.org/10.1029/93JC01757Citations: 6AboutPDF 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 Share a linkShare onFacebookTwitterLinkedInRedditWechat No abstract is available for this article. References Agrawal, Y. C., D. G. Aubrey, Velocity observations above a rippled bed using laser Doppler velocimetry, J. Geophys. Res., 97, 20249– 20259, 1992. Bowden, K. F., R. A. White, Measurements of the orbital velocities of sea waves and their use in determining the directional spectrum, Geophys. J.R. Astron. Soc., 12, 33– 54, 1966. Donelan, M. A., J. Hamilton, W. H. Hui, Directional spectra of wind-generated waves, Philos. Trans. R. Soc. London, Ser. A, 315, 509– 562, 1985. Hasselmann, D. E., M. Dunckel, J. A. Ewing, Directional wave spectra observed during JONSWAP 1973, J. Phys. Oceanogr., 10, 1264– 1280, 1980. Hasselmann, K., On the non-linear energy transfer in a gravity-wave spectrum, 1, General theory, J. Fluid Mech., 12, 481– 500, 1962. Hasselmann, K., T. P. Barnett, E. Bouws, H. Carlsson, D. E. Cartwright, K. Enke, J. A. Ewing, H. Gienapp, D. E. Hasselmann, P. Kruseman, A. Meerburg, P. Muller, 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, 8(12), suppl. A, 95, 1973. Kitaigorodskii, S. A., M. A. Donelan, J. L. Lumley, E. A. Terray, Wave-turbulence interactions in the upper ocean, II, Statistical characteristics of wave and turbulent components of the random velocity field in the marine surface layer, J. Phys. Oceanogr., 13, 1988– 1999, 1983. Kuik, A. J., G. P. vanVledder, L. H. Holthuijsen, A method for routine analysis of pitch-and-roll buoy data, J. Phys. Oceanogr., 18, 1020– 1034, 1988. Longuet-Higgins, M. S., D. E. Cartwright, N. D. Smith, Observations of the directional spectrum of sea waves using the motions of a floating buoy, Ocean Wave Spectra, 111– 136, Prentice Hall, Englewood Cliffs, N.J., 1963. Mitsuyasu, H., F. Tasai, T. Suhara, S. Mizuno, M. Ohkusu, T. Honda, K. Rikiishi, Observations of the directional spectrum of ocean waves using a cloverleaf buoy, J. Phys. Oceanogr., 5, 750– 760, 1975. Nagata, Y., The statistical properties of orbital wave motions and their application for the measurement of directional wave spectra, J. Oceanogr. Soc. Jpn., 19, 169– 181, 1964. Phillips, O. M., On the dynamics of unsteady gravity waves of finite amplitude, 1, The elementary interactions, J. Fluid Mech., 9, 193– 217, 1960. Regier, L. A., R. E. Davis, Observations of the power and directional spectrum of ocean surface waves, J. Mar. Res., 353, 433– 451, 1977. Simpson, J. H., Observations of the directional characteristics of sea waves, Geophys. J. R. Astron. Soc., 17, 93– 120, 1969. Tyler, G. L., C. C. Teague, R. H. Stewart, A. M. Peterson, W. H. Munk, J. W. Joy, Wave directional spectra from synthetic aperture observations of radio scatter, Deep Sea Res., 21, 989– 1016, 1974. Citing Literature Volume98, IssueC1115 November 1993Pages 20331-20333 ReferencesRelatedInformation

Wave spectrum filtration by current and wave height calculation

Theoretical models for the interaction between wind-generated wave spectra and currents are worked out on the basis of wave dispersion equations with nonuniform currents. The relationships obtained for critical velocity of surface adverse current are compared with experimental data from a laboratory wave channel. As a result of wave-current interaction, the filtration of the wave frequency spectrum by current causes the mean wave height to diminish. The results of the study of wave frequency spectrum filtration by an adverse current and by a following current when the waves approach the current at some angle, are compared with experimental field and laboratory results. The available field data (Hayes, 1980) verify the effect of partial spectrum filtration due to a caustic. The calculation of the wave spectrum frequency filtration by an adverse current correlates satisfactorily with the experimental investigations of the pneumatic barriers.

風波を中心とする海面の力学過程の研究

It is indeed a great honor for me to be awarded the Oceanographic Society of Japan Prize (1993), and to be given this opportunity to reflect on my past activities in oceanographical research. For this award, I owe a debt of gratitude to many people, including my former colleagues at the Research Institute for Applied Mechanics of Kyushu University and many friends in Japan and abroad, who supported and encouraged me during the long period of my reseach on ocean waves. I am very grateful to all of them. Taking this opportunity, I would like to talk on my representative works on wind waves and related dynamical processes at the air-sea boundary by selecting the following ten topics ; 1) Interaction between water waves and wind, 2) Nonlinear energy transfer in the spectrum of wind-generated waves, 3) The growth of the spectrum of wind-generated waves, 4) Directional spectrum of ocean waves, 5) High frequency spectrum of wind-generated waves, 6) The dispersion relation of random waves, 7) Wind-induced growth of water waves, 8) The momentum transfer from winds to waves, 9) The effect of swell on certain air-sea interaction phenomena, and 10) The microwave back-scattering from wind wave surface. For each topic, I would like to talk mainly on the motivation and background of the studies, the processes which led to the conclusions, and some significant results. Finally, several important problems for future studies are briefly discussed.

Characteristics of acoustic scattering from a wind-created water surface covered with monomolecular organic films

Abstract A spectrum of amplitude fluctuations of the acoustic signal scattered from a wind-driven water surface coated with a monomolecular film of well-defined viscoelastic surface properties was studied under laboratory conditions. The presence of an oil film causes a shift of the peak frequency to higher frequencies and increases the fall-off in the high-frequency band of the spectrum compared with clean surface scattering. The effect turned out to be unequivocally related to rheological parameters of the surface film. Similar features of the scattered signal and wind-generated wave spectra observed for film-covered surfaces can be treated by the Marangoni theory of damping of water surface waves by viscoelastic films.

Fetch Relations for Wind-Generated Waves as a Function of Wind-Stress Scaling

Abstract We present the variation that results when fetch relations for wind-generated wave spectra are sealed by the friction velocity component in the dominant wave direction rather than the magnitude of the friction velocity, using the data collected during the Canadian Atlantic Storms Program (CASP). The effects of three possible drag coefficients are considered. the usual constant drag coefficient, the open-ocean long fetch drag coefficient, and finally, the wave age dependent drag coefficient for growing waves recently measured by Smith and Anderson in HEXOS. Contributions to the correlation coefficients for dimensionless variables due to both scaling variables and dimensional variables are computed. We find that the friction velocity component in the dominant wave direction rather than the friction velocity magnitude should be used as the scaling variable. The self-correlation introduced to the correlation coefficients is then less than that resulting from the friction velocity magnitude. Balance r...

Directional spectra of wind-generated ocean waves

From observations of wind and of water surface elevation at 14 wave staffs in an array in Lake Ontario and in a large laboratory tank, the directional spectrum of wind-generated waves on deep water is determined by using a modification of Barber’s (1963) method. Systematic investigations reveal the following: ( a ) the frequency spectrum in the rear face is inversely proportional to the fourth power of the frequency w, with the equilibrium range parameter and the peak enhancement factor clearly dependent on the ratio of wind speed to peak wave speed; ( b ) the angular spreading 0 of the wave energy is of the form sech 2 (fid), where /? is a function of frequency relative to the peak; ( c ) depending on the gradient of the fetch, the direction of the waves at the spectral peak may differ from the mean wind direction by up to 50°, but this observed difference is predictable by a similarity analysis; ( d ) under conditions of strong wind forcing, significant effects on the phase velocity caused by amplitude dispersion and the presence of bound harmonics are clearly observed and are in accordance with the Stokes theory, whereas ( e ) the waves under natural wind conditions show amplitude dispersion, but bound harmonics are too weak to be detected among the background of free waves.

On the Theory of the Equilibrium Range in the Spectrum of Wind-Generated Gravity Waves

It is shown that an exact analog of Kolmogoroff's spectrum in a random field of weekly nonlinear surface gravity waves gives a spectral form for frequency spectra S(ω) ∼ ω−4 in close agreement with the results of recent observational studies. The proposed theory also indicates the existence of a “transitional” range of wavenumbers (frequencies) where the deviation from Kolmogoroff's equilibrium is due to gravitational instability (wave breaking). Because of this it is suggested dot the equilibrium form for the spectrum of wind-generated waves has two asymptotic regimes: Kolmogoroff's and Philips' type of equilibrium with a relatively rapid transition from the first to the second. The experiments data favor such an interpretation.

A representation for the frequency spectrum of wind-generated waves

Abstract This paper proposes the following generalized representation for a wind-wave frequency spectrum: where E = ∫S(f) d f is the variance of the surface displacement; f m is the frequency of the spectral peak; and C i ' s , i = 1,2,3 , are dimensionless parameters that can be determined from the internal spectral parameters of a given spectrum. When applied to 234 sets of wave spectra recorded in the Great Lakes, this representation has been realistic, accurate, and capable of representing widely varied wave processes. The C i ' s are clearly related to wave growth processes; they are large during early growth, decrease as waves grow, and reach approximate equilibrium when waves are fully developed.

On the Steady-State Energy Balance of Short Gravity Wave Systems

Steady-state energy balances of short gravity wave systems generated in a wave tank with and without airflow have been measured and compared with the predictions of perturbation theory. Wind-wave spectra were found to fit a JONSWAP form to a good approximation if a wind-dependent equilibrium range coefficient was used. Mechanically generated waves were produced which had frequency spectra similar to wind-generated wave spectra and which exhibited nonlinear effects through a decrease in the spectral peak frequency with fetch. In the wind-wave case, perturbation theory well predicted the difference between the net source function and energy input from the wind for a wide range of fetch and wind speed conditions provided that surface tension was properly taken into account. In the case of waves generated without airflow, perturbation theory predicted energy transfer rates much smaller than the measured values.

Rederivation of the Saturation Range in the Frequency Spectrum of Wind-Generated Gravity Waves

Abstract The saturation range in the frequency spectrum of wind-generated waves is rederived. Laboratory and theoretical work show that wave breaking is the result of kinematic instability, suggesting that wave celerity is the governing parameter in the saturation range. Using similarity arguments, a general formulation is rederived giving the wave profile spectrum Sη(ω) ∝ ω−5 in deep water as derived by Phillips and Sη(ω) ∝ ω−3 in shallow water. The velocity spectrum in the saturation range is derived using linear wave theory as a spectral transfer function. In both deep and shallow water the horizontal velocity spectrum Su(ω) ∝ ω−3. Wave and velocity measurements made in deep and shallow water are presented showing agreement with theory.

The high frequency spectrum of wind-generated waves

The high frequency part (10 Hz∼50 Hz) of the one-dimensional wave spectrum was measured in a wind-wave channel under accurately controlled conditions. The results are compared with the spectral forms for the capillary range that have been proposed recently byPierson andStacy (1973) andToba (1973). In a general sense, fairly good agreement is found between the present results and those ofPierson andStacy (1973) and ofToba (1973). The spectrum in the capillary range is clearly wind speed dependent, and the spectral density in that range increases with increasing wind speed.

THE ONE-DIMENSIONAL WAVE SPECTRA AT LIMITED FETCH

The data for the spectra of wind-generated waves measured in a laboratory tank and in a bay are analyzed using the similarity theory of Kitaigorodski, and the one-dimensional spectra of fetch-limited wind waves are determined from the data. The combined field and laboratory data cover such a wide range of dimensionless fetch F (= gF/u2 ) as F : 102 ~ 10 . The fetch relations for the growthes of spectral peak frequency u)m and of total energy E of the spectrum are derived from the proposed spectra, which are consistent with those derived directly from the measured spectra.

On the Form of Fetch-Limited Wave Spectrum

The results of the author's recent studies on the growth of the spectrum of wind-generated waves have been used for determining a simple form of fetch- limited wave spectrum which can be used for p...

On the Growth of the Spectrum of Wind-Generated Waves

This paper presents some recent experimental results concerning properties of fetch-limited wind waves, which have been measured in a laboratory tank and in a bay. The fetch relations which are ver...

On wave breaking and the equilibrium spectrum of wind-generated waves

A theoretical calculation is made of the loss of energy by wave breaking in a random sea state in terms of the spectral density function. In the special case of the equilibrium spectrum F(σ) = αg 2 σ -5 the proportion ɷ of energy lost per mean wave cycle is found to be given by ω ≑ e -1/8α irrespective of the low-frequency cut-off in the spectrum. Assuming that in the equilibrium state the loss of energy by breaking is comparable to that supplied by the wind, one can estimate the constant α in terms of the drag coefficient of the wind on the sea surface. It is found that α≑ -1/8/ln[1600C 3/2 ( ρ air/ ρ water)]. Taking a representative value of C one finds α ≑ 1.3 x 10 -2 , which falls within the range of observed values of α. The above equation for α is rather insensitive to the various assumptions made in the analysis. There is some evidence, derived from observation, that α may not in fact be quite constant, but may decrease slightly as the wave age ( gt/U ) or the non-dimensional fetch ( gx/U 2 ) is increased. It is suggested that the drag coefficient may behave similarly.