Diffusion spreading of localized hydrodynamic disturbances under the action of random forces. (English. Russian original) Zbl 0691.76042
J. Appl. Math. Mech. 52, No. 2, 165-170 (1988); translation from Prikl. Mat. Mekh. 52, No. 2, 211-217 (1988).
Summary: The effect of a time-dependent random force on fluid flow may be found by changing to a non-inertial coordinate system. It is shown that, under the action of a Gaussian random force, initially localized disturbances undergo spreading of a diffusion type. Explicit analytic solutions are given for the interior wave soliton under the action of a random force. It is shown that, in the presence of a soliton, the growth of velocity pulsing may either increase or moderate.
MSC:
| 76M35 | Stochastic analysis applied to problems in fluid mechanics |
| 76D33 | Waves for incompressible viscous fluids |
Keywords:
time-dependent random force; non-inertial coordinate system; Gaussian random force; Explicit analytic solutionsReferences:
| [1] | Witham, J., Linear and Non-linear Waves (1977), Mir: Mir Moscow, /Russian translation/ |
| [2] | Ablovits, M.; Sigur, Kh., Solitons and the Inverse Problem Method (1987), Mir: Mir Moscow, /Russian translation/ |
| [3] | Wadati, M., Stochastic Korteweg — de Vries equation, J. Phys. Soc. Japan, 52, 8 (1983) |
| [4] | Wadati, M.; Akutsu, Y., Stochastic Korteweg — de Vries equation with and without damping, J. Phys. Soc. Japan, 53, 10 (1984) |
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