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Volumn 4, Issue 11, 1997, Pages 3895-3909

The realizable Markovian closure and realizable test-field model. II. Application to anisotropic drift-wave dynamics

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; COMPUTER SIMULATION; DAMPING; FOURIER TRANSFORMS; MARKOV PROCESSES; MATHEMATICAL MODELS; NAVIER STOKES EQUATIONS; STATISTICAL METHODS; WAVE PLASMA INTERACTIONS;

EID: 0031268489     PISSN: 1070664X     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.872510     Document Type: Article
Times cited : (45)

References (56)
  • 5
    • 0001466688 scopus 로고
    • edited by M. N. Rosenbluth and R. Z. Sagdeev North-Holland, Amsterdam
    • J. A. Krommes, in Handbook of Plasma Physics, edited by M. N. Rosenbluth and R. Z. Sagdeev (North-Holland, Amsterdam, 1984), Vol. 2;
    • (1984) Handbook of Plasma Physics , vol.2
    • Krommes, J.A.1
  • 8
    • 85033303620 scopus 로고    scopus 로고
    • note
    • A closure is said to be realizable if there exists an underlying probability density function for the statistics it predicts.
  • 9
    • 0002870182 scopus 로고
    • Theoretical Approaches to Turbulence, edited by D. L. Dwoyer, M. Y. Hussaini, and R. G. Voigt Springer, New York, Chap. V
    • R. H. Kraichnan, in Theoretical Approaches to Turbulence, Vol. 58 of Applied Mathematical Sciences Series, edited by D. L. Dwoyer, M. Y. Hussaini, and R. G. Voigt (Springer, New York, 1985), Chap. V, p. 91.
    • (1985) Applied Mathematical Sciences Series , vol.58 , pp. 91
    • Kraichnan, R.H.1
  • 26
    • 85033321334 scopus 로고
    • Ph.D. thesis, Princeton University, Princeton, NJ
    • J. C. Bowman, Ph.D. thesis, Princeton University, Princeton, NJ, 1992.
    • (1992)
    • Bowman, J.C.1
  • 32
    • 85033306707 scopus 로고    scopus 로고
    • note
    • This is apparent even from a heuristic renormalization (resonance broadening) of the δ function in the wave kinetic equation to a Lorentzian.
  • 33
    • 85033301275 scopus 로고    scopus 로고
    • note
    • The quasistationary formulation used in Ref. 30 does not ensure that the transient energies are non-negative since η can achieve negative values during the evolution.
  • 35
    • 85033290244 scopus 로고    scopus 로고
    • note
    • There is a typographical error in the triad assignments given in Ref. 33.
  • 37
    • 5944241397 scopus 로고    scopus 로고
    • EDQNM model of evolution of homogeneous anisotropic turbulence in a helicity representation
    • submitted
    • L. Turner, "EDQNM model of evolution of homogeneous anisotropic turbulence in a helicity representation," submitted to J. Fluid Mech. (1997).
    • (1997) J. Fluid Mech.
    • Turner, L.1
  • 39
    • 2842598973 scopus 로고
    • edited by L. J. S. Bradbury, F. Durst, B. E. Launder, F. W. Schmidt, and J. H. Whitelaw Springer, New York
    • M. Larcheveque, J. P. Chollet, J. R. Herring, M. Lesieur, G. R. Newman, and D. Schertzer, in Turbulent Shear Flows, edited by L. J. S. Bradbury, F. Durst, B. E. Launder, F. W. Schmidt, and J. H. Whitelaw (Springer, New York, 1980), Vol 2, pp. 50-65.
    • (1980) Turbulent Shear Flows , vol.2 , pp. 50-65
    • Larcheveque, M.1    Chollet, J.P.2    Herring, J.R.3    Lesieur, M.4    Newman, G.R.5    Schertzer, D.6
  • 44
    • 0021785265 scopus 로고
    • A more sophisticated technique for extending the computational power of the DIA, which partially accounts for the non-Gaussian statistics predicted during a previous evolution, has been developed in H. A. Rose, Physica D 14, 216 (1985).
    • (1985) Physica D , vol.14 , pp. 216
    • Rose, H.A.1
  • 45
    • 85033280867 scopus 로고    scopus 로고
    • note
    • The substantial memeory requirements, roughly 200 Megabytes, make it difficult to continue the evolution without a dramatic decrease in the speed of the calculation because of the need to swap data to disk.
  • 46
    • 85033315837 scopus 로고
    • private communication
    • W. P. Dannevik (private communication, 1990).
    • (1990)
    • Dannevik, W.P.1
  • 48
    • 85033284575 scopus 로고    scopus 로고
    • note
    • Waltz describes the equations he solves as the result of applying a "resonance approximation" to "the DIA weak coupling theory." He also sometimes refers to these equations as the DIA itself; however they are really just a quasistationary version of the EDQNM closure.
  • 50
    • 85033293325 scopus 로고    scopus 로고
    • note
    • 2 appears because the fundamental nonlinear interaction arises from the polarization drift.
  • 52
    • 85033284050 scopus 로고    scopus 로고
    • note
    • The value of Θ at the singular points (0,y) is arbitrary since this corresponds to points in the integration that precisely satisfy k=p cos r, which may be removed since the integrand is bounded.
  • 54
    • 85033278358 scopus 로고    scopus 로고
    • note
    • The difference between this algorithm and the one used for the energy equation appears only above second order.
  • 55
    • 85033319939 scopus 로고    scopus 로고
    • note
    • If the error was computed solely by the ratio of the predictor-corrector difference to the current value of a corrected variable that happened to be passing through zero, this relative error could become arbitrarily large. The error is therefore computed with respect to both current and previous values; our formula removes the artifact just described by calculating a combination of relative and absolute errors.
  • 56
    • 85033324373 scopus 로고    scopus 로고
    • note
    • These tolerance parameters are chosen to yield an efficient evolution that does not become unstable. Of course, even if the evolution is stable, it may still be inaccurate; in this case the maximum error tolerance should be decreased. In practice, our convergence tests indicate that whenever the numerical scheme is stable, the results are sufficiently accurate, bearing in mind the inherent inaccuracies of statistical closures.


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.