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V P Ruban

Publications and source records attributed to V P Ruban.

13 recordsLinked to original sources
PubMed2006

Breathing rogue wave observed in numerical experiment.

Numerical simulations of the recently derived fully nonlinear equations of motion for long-crested water waves [V. P. Ruban, Phys. Rev. E 71, 055303(R) (2005)] with quasirandom initial conditions are reported, which show the spontaneous formation of a single extreme wave on deep water. This rogue wave behaves in an oscillating manner and exists for a relatively long time (many wave periods) without significant change of its maximal amplitude.

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PubMed2005

Quasiplanar steep water waves.

A unique description for highly nonlinear potential water waves is suggested, where weak three-dimensional effects are included as small corrections to exact two-dimensional equations written in conformal variables. Contrary to the traditional approach, a small parameter in this theory is not a surface slope, but it is the ratio of a typical wavelength to a large transversal scale along the second horizontal coordinate. A first-order correction for the Hamiltonian functional is calculated, and the corresponding equations of motion are derived for steep water waves over an arbitrary nonuniform quasi-one-dimensional bottom profile.

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PubMed2004

Water waves over a strongly undulating bottom.

Two-dimensional free-surface potential flows of an ideal fluid over a strongly inhomogeneous bottom are investigated with the help of conformal mappings. Weakly nonlinear and exact nonlinear equations of motion are derived by the variational method for an arbitrary seabed shape parametrized by an analytical function. As applications of this theory, the band structure of linear waves over periodic bottoms is calculated and the evolution of strong solitary waves running from a deep region to a shallow region is numerically simulated.

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PubMed2003

Toroidal bubbles with circulation in ideal hydrodynamics: a variational approach.

Incompressible, inviscid, irrotational, unsteady flows with circulation Gamma around a distorted toroidal bubble are considered. A general variational principle that determines the evolution of the bubble shape is formulated. For a two-dimensional (2D) cavity with a constant area A, exact pseudodifferential equations of motion are derived, based on variables that determine a conformal mapping of the unit circle exterior into the region occupied by the fluid. A closed expression for the Hamiltonian of the 2D system in terms of canonical variables is obtained. Stability of a stationary drifting 2D hollow vortex is demonstrated, when the gravity is small, gA(3/2)/Gamma(2)<<1. For a circulation-dominated regime of three-dimensional flows a simplified Lagrangian is suggested, inasmuch as the bubble shape is well described by the center line R(xi,t) and by an approximately circular cross section with relatively small area, A(xi,t)<<(contour integral operator |R'|dxi)(2). In particular, a finite-dimensional dynamical system is derived and approximately solved for a vertically moving axisymmetric vortex ring bubble with a compressed gas inside.

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PubMed2003

Variational principle for frozen-in vorticity interacting with sound waves.

General properties of conservative hydrodynamic-type models are treated from positions of the canonical formalism adopted for liquid continuous media. A variational formulation is found for motion and interaction of frozen-in localized vortex structures and acoustic waves in a special description where dynamical variables are, besides the Eulerian fields of the fluid density and the potential component of the canonical momentum, also the shapes of frozen-in lines of the generalized vorticity. This variational principle can serve as a basis for approximate dynamical models with reduced number of degrees of freedom.

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PubMed2003

Applicability of the hodograph method for the problem of long-scale nonlinear dynamics of a thin vortex filament near a flat boundary.

Hamiltonian dynamics of a thin vortex filament in an ideal incompressible fluid near a flat fixed boundary is considered under the conditions that at any point of the curve, determining the 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 this system to a single linear differential equation of the second order with separable variables. Simple solutions of the linear equation are investigated for 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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PubMed2002

Current-sheet formation in incompressible electron magnetohydrodynamics.

The nonlinear dynamics of axisymmetric, as well as helical, frozen-in vortex structures is investigated by the Hamiltonian method in the framework of ideal incompressible electron magnetohydrodynamics. For description of current-sheet formation from a smooth initial magnetic field, local and nonlocal nonlinear approximations are introduced and partially analyzed that are generalizations of the previously known exactly solvable local model neglecting electron inertia.

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PubMed2001

Slow inviscid flows of a compressible fluid in spatially inhomogeneous systems.

An ideal compressible fluid is considered, with an equilibrium density being a given function of coordinates due to presence of some static external forces. The slow flows in such system, which do not disturb the density, are investigated with the help of the Hamiltonian formalism. The equations of motion of the system are derived for an arbitrary given topology of the vorticity field. The general form of the Lagrangian for frozen-in vortex lines is established. The local induction approximation for motion of slender vortex filaments in several inhomogeneous physical models is studied.

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PubMed2001

Finite time singularities in a class of hydrodynamic models.

Models of inviscid incompressible fluid are considered, with the kinetic energy (i.e., the Lagrangian functional) taking the form L approximately integral k(alpha)/vk/2dk in 3D Fourier representation, where alpha is a constant, 0<alpha<1. Unlike the case alpha=0 (the usual Eulerian hydrodynamics), a finite value of alpha results in a finite energy for a singular, frozen-in vortex filament. This property allows us to study the dynamics of such filaments without the necessity of a regularization procedure for short length scales. The linear analysis of small symmetrical deviations from a stationary solution is performed for a pair of antiparallel vortex filaments and an analog of the Crow instability is found at small wave numbers. A local approximate Hamiltonian is obtained for the nonlinear long-scale dynamics of this system. Self-similar solutions of the corresponding equations are found analytically. They describe the formation of a finite time singularity, with all length scales decreasing like (t*-t)(1/(2-alpha)), where t* is the singularity time.

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