Abstract
A state of wind waves at a fetch is assumed to be transformed into another state of wind waves at a different fetch by the renormalization group transformation. The scaling laws for the covariance of water surface displacement and for the one-dimensional and two-dimensional spectrum and the power law for the growth relation are derived from the fact that the renormalization group transformation constitutes a semigroup. The scaling relation or the relation among the exponents of the power law is also derived, using the two assumptions that the renormalization group transformation is applicable to fetch-limited wind waves and that the saturated range exists, which implies that the directional distribution function of energy in the wave number region much larger than the peak wave number does not depend on wave number.
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Ueno, K. A derivation of the scaling law, the power law and the scaling relation for fetch-limited wind waves using the renormalization group theory. J Oceanogr 54, 641–649 (1998). https://doi.org/10.1007/BF02823284
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DOI: https://doi.org/10.1007/BF02823284