dorsal/arxiv
View SchemaThe decay of plane wave pulses with complex structure in a nonlinear dissipative medium
| Authors | Sergei N. Gurbatov, Bengt O. Enflo, Galina V. Pasmanik |
|---|---|
| Categories | |
| ArXiv ID | physics/0010034 |
| URL | https://arxiv.org/abs/physics/0010034 |
Abstract
Nonlinear plane acoustic waves propagating through a fluid are studied using Burgers' equation with finite viscosity. The evolution of a simple N-pulse with regular and random initial amplitude and of pulses with monochromatic and noise carrier is considered. In the latter case the initial pulses are characterized by two length scales. The length scale of the modulation function is much greater than the period or the length scale of the carrier. With increasing time the initial pulses are deformed and shocks appear. The finite viscosity leads to a finite shock width, which does not depend on the fine structure of the initial pulse and is fully determined by the shock position in the zero viscosity limit. The other effect of nonzero viscosity is the shift of the shock position from the position at zero viscosity. This shift, as well as the linear time, at which the nonlinear stage of evolution changes to the linear stage, depends on the fine structure of the initial pulse. It is also shown that the nonlinearity of the medium leads to generation of a nonzero mean field from an initial random field with zero mean value. The relative fluctuation of the field is investigated both at the nonlinear and the linear stage.
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"abstract": "Nonlinear plane acoustic waves propagating through a fluid are studied using\nBurgers\u0027 equation with finite viscosity. The evolution of a simple N-pulse with\nregular and random initial amplitude and of pulses with monochromatic and noise\ncarrier is considered. In the latter case the initial pulses are characterized\nby two length scales. The length scale of the modulation function is much\ngreater than the period or the length scale of the carrier. With increasing\ntime the initial pulses are deformed and shocks appear. The finite viscosity\nleads to a finite shock width, which does not depend on the fine structure of\nthe initial pulse and is fully determined by the shock position in the zero\nviscosity limit. The other effect of nonzero viscosity is the shift of the\nshock position from the position at zero viscosity. This shift, as well as the\nlinear time, at which the nonlinear stage of evolution changes to the linear\nstage, depends on the fine structure of the initial pulse. It is also shown\nthat the nonlinearity of the medium leads to generation of a nonzero mean field\nfrom an initial random field with zero mean value. The relative fluctuation of\nthe field is investigated both at the nonlinear and the linear stage.",
"arxiv_id": "physics/0010034",
"authors": [
"Sergei N. Gurbatov",
"Bengt O. Enflo",
"Galina V. Pasmanik"
],
"categories": [
"physics.flu-dyn"
],
"title": "The decay of plane wave pulses with complex structure in a nonlinear dissipative medium",
"url": "https://arxiv.org/abs/physics/0010034"
},
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