Experimental measurement of three‐wave coupling and energy cascading

The nonlinear coupling coefficient and the energy transfer associated with three‐wave interactions are computed from measured data of the turbulent edge plasma of the Texas Experimental Tokamak(TEXT) [Nucl. Technol. Fusion 1, 479 (1981)]. The results show the presence of three‐wave interactions. The interactions cause energy to cascade away from the dominant waves of the spectrum primarily toward lower, but also toward higher frequencies. The results are obtained with a new digital spectral analysis technique based on the estimation of higher‐order cumulants. The method is discussed and tested on a simulation experiment. The same technique is useful for neutral fluids as well.

[1]  R. Kraichnan Inertial Ranges in Two‐Dimensional Turbulence , 1967 .

[2]  A. Hasegawa,et al.  Pseudo-three-dimensional turbulence in magnetized nonuniform plasma , 1978 .

[3]  J. R. Roth Experimental study of spectral index, mode coupling, and energy cascading in a turbulent, hot-ion plasma , 1971 .

[4]  R. W. Miksad,et al.  Application of digital cross-bispectral analysis techniques to model the non-linear response of a moored vessel system in random seas , 1985 .

[5]  P. Diamond,et al.  Role of impurity dynamics in resistivity-gradient-driven turbulence and tokamak edge plasma phenomena , 1987 .

[6]  A. Townsend The Structure of Turbulent Shear Flow , 1975 .

[7]  R. Waltz Numerical simulation of electromagnetic turbulence in tokamaks , 1985 .

[8]  P. Diamond,et al.  Reply to comments of J. A. Krommes on ''Theory of dissipative density-gradient driven turbulence in the tokamak edge'' , 1985 .

[9]  P. Liewer Measurements of microturbulence in tokamaks and comparisons with theories of turbulence and anomalous transport , 1985 .

[10]  E. Powers,et al.  On modeling the nonlinear relationship between fluctuations with nonlinear transfer functions , 1980, Proceedings of the IEEE.

[11]  Patrick H. Diamond,et al.  Theory of resistive pressure-gradient-driven turbulence , 1987 .

[12]  R. Slusher,et al.  Waves and Turbulence in a Tokamak Fusion Plasma , 1983, Science.

[13]  A. Hasegawa,et al.  A collisional drift wave description of plasma edge turbulence , 1984 .

[14]  E. Mazzucato Spectrum of small-scale density fluctuations in tokamaks , 1982 .

[15]  R. W. Miksad,et al.  Measurements of nonlinear interactions during natural transition of a symmetric wake , 1983 .

[16]  B. Harris Spectral Analysis Of Time Series , 1967 .

[17]  W. Horton,et al.  Drift wave turbulence in a low‐order k space , 1983 .

[18]  A. Hasegawa,et al.  Nonlinear behavior and turbulence spectra of drift waves and Rossby waves , 1979 .

[19]  Kenneth W Gentle,et al.  Texas Experimental Tokamak (TEXT) facility , 1981 .

[20]  E. Powers,et al.  Nonlinear spectral dynamics of a transitioning flow , 1988 .

[21]  R. Slusher,et al.  Study of density fluctuations in plasmas by small‐angle CO2 laser scattering , 1980 .

[22]  D. Brower,et al.  The spectrum, spatial distribution and scaling of microturbulence in the TEXT tokamak , 1987 .

[23]  P. Diamond,et al.  Effects of a radial electric field on tokamak edge turbulence , 1985 .

[24]  S. Zweben,et al.  Structure of edge-plasma turbulence in the Caltech tokamak , 1985 .

[25]  D. Brower,et al.  Characterization of tokamak edge turbulence by far-infrared laser scattering and Langmuir probes , 1987 .

[26]  Edward J. Powers,et al.  Space/time statistics of the turbulence in a tokamak edge plasma , 1984 .

[27]  R. Waltz Numerical study of drift wave turbulence with simple models for wave–wave nonlinear coupling , 1983 .

[28]  E. Powers,et al.  Turbulent structure in the edge plasma of the TEXT tokamak , 1984 .

[29]  Francis F. Chen,et al.  SPECTRUM OF LOW-$beta$ PLASMA TURBULENCE , 1965 .

[30]  D. B. Preston Spectral Analysis and Time Series , 1983 .

[31]  W. Horton,et al.  Kelvin-Helmholtz instability and vortices in magnetized plasma , 1987 .

[32]  E. Powers,et al.  Bispectrum and nonlinear wave coupling , 1980 .

[33]  E. Powers,et al.  Digital Bispectral Analysis and Its Applications to Nonlinear Wave Interactions , 1979, IEEE Transactions on Plasma Science.

[34]  Steve Elgar,et al.  Observations of bispectra of shoaling surface gravity waves , 1985, Journal of Fluid Mechanics.

[35]  E. J. Powers,et al.  Experimental determination of the spectral index of a turbulent plasma from digitally computed power spectra , 1973 .

[36]  R. W. Miksad,et al.  Modeling of the nonlinear drift oscillations of moored vessels subject to non-Gaussian random sea-wave excitation , 1987 .

[37]  Michael H. Freilich,et al.  Nonlinear effects on shoaling surface gravity waves , 1984, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[38]  F. L. Jones,et al.  Measurement of the local wavenumber and frequency spectrum in a plane wake , 1988 .