On wave interactions in a stratified fluid

Thorpe, S. A.

doi:10.1017/s002211206600096x

Cited by 77 publications

(57 citation statements)

References 19 publications

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“…fl.. p' g < 0) may be accurate (though it is difficult to prove it is either necessary or sufficient), but it should probably not be applied directly to test a type of motion that may provide only the first event of a sequence. Early work on the departure of internal waves from i inear propagation theory (Ball 1964, Thorpe 1966, Davis & Acrivos 1967, Hasselman 1967, Phillips 1968, Martin, Simmons & Wunsch 1972, McEwan 1971 had fo cused on the possibility of interaction of internal gravity waves within continuously stratified fluids or at an interface and interaction of surface waves with internal gravity waves. Two types of interactions were singled out.…”

Section: The Inherent Instability Of Long Internal Waves In a Continumentioning

confidence: 99%

Turbulence and Mixing in Stably Stratified Waters

Sherman¹,

Imberger²,

Corcos³

1978

Annu. Rev. Fluid Mech.

136

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Section: The Inherent Instability Of Long Internal Waves In a Continumentioning

confidence: 99%

Turbulence and Mixing in Stably Stratified Waters

Sherman¹,

Imberger²,

Corcos³

1978

Annu. Rev. Fluid Mech.

136

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“…The dominant interaction is given by the diagram in Figure 4. The quadratic interaction among Interactions between discrete surface waves and internal waves have been studied by Ball [1964] and Thorpe [1966]. The statistical case is being investigated by Kenyon [1966].…”

Section: Scattering In the Oceanic Wave Guidementioning

confidence: 99%

Feynman diagrams and interaction rules of wave‐wave scattering processes

Hasselmann¹

1966

Reviews of Geophysics

195

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The energy transfer due to weak nonlinear interactions in random wave fields is reinterpreted in terms of a hypothetical ensemble of interacting particles, antiparticles, and virtual particles. In the particle picture, the interactions can be conveniently described by Feynman diagrams, which may be regarded either as branch diagrams of the perturbation expansion or as collision diagrams. The derivation of the transfer expressions can then be reduced to a few general rules for the construction of the diagrams and the associated collision cross sections. The representation follows closely the standard treatment of nonlinear lattice vibrations, but the particle picture differs from the usual phonon interpretation of lattice waves. It has the unreMistie property that the energies and number densities of antiparticles are negative. This is offset by simpler interaction rules and a closer correspondence between the perturbation graphs and collision diagrams. The method is illustrated for scattering processes in the oceanic wave guide involving surface and internal gravity waves, horizontal currents (turbulence), seismic waves, and bottom irregularities. Nonlinear interactions between surface gravity waves have been studied byPhillips [1960], Hasselmann [1962; 1963a, b], Longuet-Higgins [1062], Benney [1962], Bretherton [1064], among others. Computations of the energy transfer for a random wave field were found to be in qualitative agreement with the observed decay of ocean swell [Snodgrass et al., 1965]. 2 K. HASSELMANN Scattering from gravity waves into elastic waves is one of the principal sources of microseisms. The conversion can occur either through direct nonlinear interactions between gravity waves [Longuet-Higgins, 1950] or through the interaction of gravity waves with an inhomogeneous ocean bottom [Wiechert, 1904]. Both processes have been quantitatively confirmed by measurements byHaubrich et al. [1963] [Hasselmann, 1963c]. The generation of long gravity waves with periods in •he minute range ('surf bea•' [Munk, 1949; Tucker, 1950]) may be a•tributed to a nonlinear gravity wave interaction plus a bottom interaction [Longuet-Higgins and Stewart, 1962; Hasselmann et al., 1963; Gallagher, 1965]. Sca•ering between surface and in•ernal gravity waves has been investigated by Ball [1964], Thorpe [1966], and Kenyon [1966]. Kenyon has computed •ransfer ra•es for both gravity wave and Rossby wave interactions. Nonlinear interactions between surface gravity waves and quasi-s•eady curren•s or •urbulence have been s•udied by Longuet-Higgins and Stewart [1961] and Phillips [1959]. Sca•ering processes very similar •o •hese geophysical examples have also been considered in o•her fields. In a fundamental paper on •he hea• conduction in solids, Peierls [1929] investigated •he •ransfer effects due •o secular interactions between random lattice vibrations. Nonlinear interactions between ligh• waves and lattice vibrations, firs• investigated in •he classic papers of Brillouin [1922] and Raman [1928], have la•ely received renewed ...

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“…Three peak frequency components of 1.0Hz, 1.8Hz and 2.8Hz are recognized at Γ, of single horseshoe vortex (24) . (29) . The fact must be noticed that the internal gravity waves are spontaneously induced in a wind tunnel without giving any finite disturbances.…”

Section: Spontaneous Generation Of An Internal Gravity Wavementioning

confidence: 99%

Forefront of Wind-Tunnel Experiment on Turbulence Structure

Makita

2007

JFST

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Many interesting and important basic problems still remain unsolved or ever untouched in the fields of experimental fluid dynamics. The present report explains a variety of newest results of wind tunnel experiments conducted chiefly in our laboratory with respect to the features of large scale quasi-isotropic turbulence, anisotropic turbulence, three-dimensional vortical structure in the wake of a sphere, the process of vortex pairing in a two-dimensional jet, the proposal for a new model on a boundary layer transition in a view point of hairpin or horse-shoe vortex and lastly the analysis on spontaneously generated internal gravity waves in a stably stratified mixing layer. These results, the author guesses, will promise the future possibility in the fields of experimental fluid dynamics.

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On wave interactions in a stratified fluid

Cited by 77 publications

References 19 publications

Turbulence and Mixing in Stably Stratified Waters

Turbulence and Mixing in Stably Stratified Waters

Feynman diagrams and interaction rules of wave‐wave scattering processes

Forefront of Wind-Tunnel Experiment on Turbulence Structure

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