EM 1110-2-1100 (Part II)
(Change 1) 31 July 2003
(Sverdrup and Munk 1947, Bretschneider 1952), which suggested that a "fully developed" wave height would
evolve under the action of the wind. Available data indicated that this fully developed wave height could be
represented as
λ5 u 2
H4 '
(II-2-30)
g
where
H4 = fully developed wave height
λ5 =dimensionless coefficient (approximately equal to 0.27)
u = wind speed
Wave heights defined by Equation II-2-30 are usually taken as representing an upper limit to wave growth
for any wind speed.
(7) In the 1950's, researchers began to recognize that the wave generation process was best described
as a spectral phenomenon (e.g. Pierson, Neumann, and James (1955)). Theoreticians then began to reexamine
their ideas on the wave-generation process, with regard to how a turbulent wind field could interact with a
random sea surface. Following along these lines, Phillips (1958) and Miles (1957) advanced two theories
that formed the cornerstone of the understanding of wave generation physics for many years. Phillips'
concept involved the resonant interactions of turbulent pressure fluctuations with waves propagating at the
same speed. Miles' concept centered on the mean flux of momentum from a "matched layer" above the wave
field into waves travelling at the same speed. Phillips' theory predicted linear wave growth and was believed
to control the early stages of wave growth. Miles' theory predicted an exponential growth and was believed
to control the major portion of wave growth observed in nature. Direct measurements of the Phillips'
resonance mechanism indicated that the measured turbulent fluctuations were too small by about an order of
magnitude to explain the observed early growth in waves; however, it was still adopted as a plausible concept.
Subsequent field efforts by Snyder and Cox (1966) and Snyder et al. (1981) have supported at least the
functional form of Miles' theory for the transfer of energy into the wave field from winds.
(8) From basic concepts of energy conservation and the fact that waves do attain limiting fully
developed wave heights, it is obvious that wave generation physics cannot consist of only wind source terms.
There must be some physical mechanism or mechanisms that leads to a balance of wave growth and
dissipation for the case of fully developed conditions. Phillips (1958) postulated that one such mechanism
in waves would be wave breaking. Based on dimensional considerations and the knowledge that wave
breaking has a very strong local effect on waves, Phillips argued that energy densities within a spectrum
would always have a universal limiting value given by
α g 2 f &5
E(f) '
(II-2-31)
(2 π)4
where E(f) is the spectral energy density in units of length squared per hertz and α was understood to be a
universal (dimensionless) constant approximately equal to 0.0081. It should be noted here that energy
densities in this equation are proportional to f-5 (as can be deduced from dimensional arguments) and that they
are independent of wind speed. Phillips hypothesized that local wave breaking would be so strong that wind
effects could not affect this universal level. In this context, a saturated region of spectral energy densities is
assumed to exist in some region from near the spectral peak to frequencies sufficiently high that viscous
Meteorology and Wave Climate
II-2-39
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