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Statistics of nonlinear dispersive systems with small dissipation

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  • Matsuno, Y.

Abstract

We investigate the effect of a small dissipation on the turbulent motion in a nonlinear dispersive medium governed by the Korteweg de Vries (KdV) equation. A closed equation for the energy spectrum function is derived by making use of the derivative expansion method. From the solution of this equation we obtain the analytical expression for various statistical quantities such as the kinetic energy per unit mass, the energy spectrum function, the velocity correlation function and the 2nth order moment of the energy spectrum function. Asymptotic expressions of these quantities for large times are also given.

Suggested Citation

  • Matsuno, Y., 1978. "Statistics of nonlinear dispersive systems with small dissipation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 92(3), pages 410-422.
    • Handle: RePEc:eee:phsmap:v:92:y:1978:i:3:p:410-422
    DOI: 10.1016/0378-4371(78)90140-1
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    1. Newell, William H., 1973. "The Agricultural Revolution in Nineteenth-Century France," The Journal of Economic History, Cambridge University Press, vol. 33(4), pages 697-731, December.
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    Cited by:

    1. Fernández-Barbero, A. & Schmitt, A. & Cabrerizo-Vílchez, M. & Martínez-García, R., 1996. "Cluster-size distribution in colloidal aggregation monitored by single-cluster light scattering," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 230(1), pages 53-74.

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