dorsal/arxiv
View SchemaThe hodograph method applicability in the problem of long-scale nonlinear dynamics of a thin vortex filament near a flat boundary
| Authors | V. P. Ruban |
|---|---|
| Categories | |
| ArXiv ID | physics/0302064 |
| URL | https://arxiv.org/abs/physics/0302064 |
| DOI | 10.1103/PhysRevE.67.066301 |
Abstract
Hamiltonian dynamics of a thin vortex filament in ideal incompressible fluid near a flat fixed boundary is considered at the conditions that at any point of the curve determining shape of the filament the angle between tangent vector and the boundary plane is small, also the distance from a point on the curve to the plane is small in comparison with the curvature radius. The dynamics is shown to be effectively described by a nonlinear system of two (1+1)-dimensional partial differential equations. The hodograph transformation reduces that system to a single linear differential equation of the second order with separable variables. Simple solutions of the linear equation are investigated at real values of spectral parameter $\lambda$ when the filament projection on the boundary plane has shape of a two-branch spiral or a smoothed angle, depending on the sign of $\lambda$.
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"abstract": "Hamiltonian dynamics of a thin vortex filament in ideal incompressible fluid\nnear a flat fixed boundary is considered at the conditions that at any point of\nthe curve determining shape of the filament the angle between tangent vector\nand the boundary plane is small, also the distance from a point on the curve to\nthe plane is small in comparison with the curvature radius. The dynamics is\nshown to be effectively described by a nonlinear system of two\n(1+1)-dimensional partial differential equations. The hodograph transformation\nreduces that system to a single linear differential equation of the second\norder with separable variables. Simple solutions of the linear equation are\ninvestigated at real values of spectral parameter $\\lambda$ when the filament\nprojection on the boundary plane has shape of a two-branch spiral or a smoothed\nangle, depending on the sign of $\\lambda$.",
"arxiv_id": "physics/0302064",
"authors": [
"V. P. Ruban"
],
"categories": [
"physics.flu-dyn"
],
"doi": "10.1103/PhysRevE.67.066301",
"title": "The hodograph method applicability in the problem of long-scale nonlinear dynamics of a thin vortex filament near a flat boundary",
"url": "https://arxiv.org/abs/physics/0302064"
},
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