---

Prog. Theor. Phys. Vol. 41 No. 2 (1969) pp. 358-366

The Wiener-Hermite Expansion with Time-Dependent Ideal Random Function

Masaaki Doi and Tsutomu Imamura

Department of Physics, Kwansei Gakuin University, Nishinomiya

(Received July 17, 1968)

Abstract:

Extension of the Wiener-Hermite expansion to a new one with time-dependent ideal random function is proposed. Exact Gaussian solutions for an incompressible inviscid fluid, which are not expressed in terms of the truncated usual Wiener-Hermite expansion, are expressed by a single term of the new expansion. Application of this formulation to the shear flow turbulence is discussed and also the possibility of application to the nearly Gaussian phenomena is remarked.

URL : http://ptp.ipap.jp/link?PTP/41/358/
DOI : 10.1143/PTP.41.358

[ Full Text PDF : FREE ACCESS (526K) ] Citation: Plain Text BiBTeX EndNote(RIS) RSS

---

References:

1. G. K. Batchlor, Homogeneous Turbulence (Cambridge University Press, Combridge, England, 1956).
2. R. H. Cameron and W. T. Martin, Ann. Math. 48 (1947), 385.
3. N. Wiener, Nonlinear Problem in Random Theory (John Wiley & Sons, Inc., New York, 1958).
4. A. Siegel, T. Imamura and W. C. Meecham, Phys. Fluids 6 (1963), 1519[AIP Scitation].
5. T. Imamura, W. C. Meecham and A. Siegel, J. Math. Phys. 6 (1965), 695[CrossRef].
6. A. Siegel, T. Imamura and W. C. Meecham, J. Math. Phys. 6 (1965), 707[CrossRef].
7. W. C. Meecham and A. Siegel, Phys. Fluids 7 (1964), 1178[AIP Scitation].
8. T. Imamura and T. Taniuti, Phys. Fluids 9 (1966), 1603[AIP Scitation].
9. S. A. Orszag and L. R. Bissonnette, Phys. Fluids 10 (1967), 2603[AIP Scitation].
10. E. Hopf, J. Rat. Mech. Analysis 1 (1952), 87.
11. R. H. Kraichmann, Phys. Fluids 6 (1963), 1603[AIP Scitation].
12. T. Tatsumi, Ranryu (in Japanese) (Maki Press, Japan, 1962), p. 138.
13. D. Meksyn and J. T. Stuart, Proc. Roy. Soc. A 208 (1951), 517.

Citing Article(s) :

1. Progress of Theoretical Physics Vol. 45 No. 4 (1971) pp. 1098-1105 :

   The Wiener-Hermite Expansion with Time-Dependent Ideal Random Function. II

   Shūhei Tanaka and Tsutomu Imamura

2. Progress of Theoretical Physics Vol. 47 No. 2 (1972) pp. 732-733 :

   Exact Gaussian Solution of a Passive Scalar in an Isotropic and Gaussian Turbulent Flow

   Tsutomu Imamura

3. Progress of Theoretical Physics Vol. 48 No. 1 (1972) pp. 339-340 :

   Exact Gaussian Solution of a Turbulent Flow and a Temperature Distribution

   Tsutomu Imamura

---

[PTP HOME] [BROWSE] [SEARCH] [SUBSCRIPTION] [SUBMISSION] [REGISTRATION]

Copyright © Progress of Theoretical Physics 2013 All rights reserved.