FRF spectrum: TMA with kitaigorodskii's f-4 scaling

Herman C. Miller, C. Linwood Vincent

Research output: Contribution to journalArticlepeer-review

20 Scopus citations


This paper describes the development of a mathematical function that represents the spectrum of wind-generated gravity waves in water of arbitrary depth. The derivation parallels that of the TMA spectrum. The primary difference is that Phillips' (1958) model for saturation at high frequencies is replaced by Kitaigorodskii's (1983) model. This spectrum incorporates wind speed directly into the formulation and is consistent with a f-4 power law scaling for deep water. In its raw form, the new model requires four internal constraints (gravity, depth, wind speed, and peak frequency) and has four model coefficients. Values for the coefficients are determined for 1,022 observations of wave spectra made at the Corps of Engineers Field Research Facility (FRF) in depths of 19, 8.5, and 6 m. The coefficients are then correlated with dimensionless combinations of the physical parameters associated with the spectrum to see if the number of coefficients can be reduced. If three of the coefficients are held constant at their mean values, a direct relationship to wave steepness is obtained for the fourth coefficient that is related to the peakedness of the spectrum.

Original languageEnglish (US)
Pages (from-to)57-78
Number of pages22
JournalJournal of Waterway, Port, Coastal and Ocean Engineering
Issue number1
StatePublished - Jan 1990
Externally publishedYes

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Water Science and Technology
  • Ocean Engineering


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