Scale-Dependent Ocean Wave Turbulence

  • Roman E. Glazman
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 85)


Wave turbulence is a common feature of nonlinear wave motions observed when external forcing acts during a long period of time, resulting in developed spectral cascades of energy, momentum and, possibly, other conserved integrals. In the ocean, wave turbulence occurs on scales from capillary ripples and to those of baroclinic inertia-gravity and Rossby waves. In general, oceanic wave motions are characterized by rather complicated dispersion laws containing characteristic scales such as, for instance, the Rossby radius of deformation. The resulting absence of scale invariance makes many problems of wave turbulence intractable by standard, small-perturbation-based techniques. As a result, present theoretical understanding has been limited to short- and long-wave asymptotic regimes (Zakharov et al., 1992). Another, more fundamental limitation of the small perturbation theories is the assumption that the wave amplitude be small in relation to the wavelength. Thus, rare (and highly intermittent) events of appearance of the strongly nonlinear wavelets are disregarded at the outset. A number of laboratory and field measurements reveal rather peculiar wave spectra which cannot be explained by scale-invariant and/or weak-turbulence theories. The peculiarities include multiple breaks of power laws and saturation of the otherwise monotonous dependence of wave spectra on external forcing (Jähne and Riemer, 1990; Hwang et al, 1993; Hara et al., 1994; LeTraon et al., 1990).


Gravity Wave Rossby Wave Wave Spectrum Collision Integral Wave Turbulence 
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Copyright information

© Springer-Verlag New York, Inc. 1997

Authors and Affiliations

  • Roman E. Glazman
    • 1
  1. 1.Jet Propulsion LaboratoryCalifornia Institute of TechnologyPasadenaUSA

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