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V. P. Ruban

Publications and source records attributed to V. P. Ruban.

At least 19 recordsLinked to original sources
arXiv2017

Dynamics of quantum vortices in a quasi-two-dimensional Bose-Einstein condensate with two "holes"

The dynamics of interacting quantum vortices in a quasi-two-dimensional spatially inhomogeneous Bose-Einstein condensate, whose equilibrium density vanishes at two points of the plane with a possible presence of an immobile vortex with a few circulation quanta at each point, has been considered in a hydrodynamic approximation. A special class of density profiles has been chosen, so that it proves possible to calculate analytically the velocity field produced by point vortices. The equations of motion have been given in a noncanonical Hamiltonian form. The theory has been generalized to the case where the condensate forms a curved quasi-two-dimensional shell in the three-dimensional space.

cond-mat.quant-gas↗
arXiv2017

On the nonlinear Schrödinger equation for waves on a nonuniform current

A nonlinear Schrödinger equation with variable coefficients for surface waves on a large-scale steady nonuniform current has been derived without the assumption of a relative smallness of the velocity of the current. This equation can describe with good accuracy the loss of modulation stability of a wave coming to a counter current, leading to the formation of so called rogue waves. Some theoretical estimates are compared to the numerical simulation with the exact equations for a two-dimensional potential motion of an ideal fluid with a free boundary over a nonuniform bottom at a nonzero average horizontal velocity.

physics.flu-dyn↗
arXiv2017

The dynamics of straight vortex filaments in a Bose-Einstein condensate with a Gaussian density profile

The dynamics of interacting quantized vortex filaments in a rotating trapped Bose-Einstein condensate, which is in the Thomas-Fermi regime at zero temperature and described by the Gross-Pitaevskii equation, is considered in the hydrodynamic "anelastic" approximation. In the presence of a smoothly inhomogeneous array of filaments (vortex lattice), a non-canonical Hamiltonian equation of motion is derived for the macroscopically averaged vorticity, with taking into account the spatial non-uniformity of the equilibrium condensate density determined by the trap potential. A minimum of the corresponding Hamiltonian describes a static configuration of deformed vortex lattice against a given density background. The minimum condition is reduced to a vector nonlinear partial differential equation of the second order, for which some approximate and exact solutions are found. It is shown that if the condensate density has an anisotropic Gaussian profile then equation of motion for the averaged vorticity admits solutions in the form of a spatially uniform vector with a nontrivial time dependence. An integral representation is obtained for the matrix Green function determining the non-local Hamiltonian of a system of arbitrary shaped vortex filaments in a condensate with Gaussian density. ... A simple approximate expression for the two-dimensional Green function is suggested at rather arbitrary density profile, and its successful comparison to the exact result in the Gaussian case is done. Approximate equations of motion are derived which describe a long-wave dynamics of interacting vortex filaments in condensates with the density depending on the transverse coordinates only.

cond-mat.quant-gas↗
arXiv2016

Some exact solutions of the local induction equation for motion of a vortex in a Bose-Einstein condensate with Gaussian density profile

The dynamics of a vortex filament in a trapped Bose-Einstein condensate is considered when the equilibrium density of the condensate, in rotating with angular velocity ${\bfΩ}$ coordinate system, is Gaussian with a quadratic form ${\bf r}\cdot\hat D{\bf r}$. It is shown that equation of motion of the filament in the local induction approximation admits a class of exact solutions in the form of a straight moving vortex, ${\bf R}(β,t)=β{\bf M}(t) +{\bf N}(t)$, where $β$ is a longitudinal parameter, and $t$ is the time. The vortex is in touch with an ellipsoid, as it follows from the conservation laws ${\bf N}\cdot \hat D {\bf N}=C_1$ and ${\bf M}\cdot \hat D {\bf N}=C_0=0$. Equation of motion for the tangent vector ${\bf M}(t)$ turns out to be closed, and it has the integrals ${\bf M}\cdot \hat D {\bf M}=C_2$, $(|{\bf M}| -{\bf M}\cdot\hat G{\bf Ω})=C$, where the matrix $\hat G=2(\hat I \mbox{Tr\,} \hat D -\hat D)^{-1}$. Intersection of the corresponding level surfaces determines trajectories in the phase space.

cond-mat.quant-gas↗
arXiv2016

Hamilton's equations of motion of a vortex filament in the rotating Bose-Einstein condensate and their "soliton" solutions

The equation of motion of a quantized vortex filament in a trapped Bose-Einstein condensate [A. A. Svidzinsky and A. L. Fetter, Phys. Rev. A {\bf 62}, 063617 (2000)] has been generalized to the case of an arbitrary anharmonic anisotropic rotating trap and presented in a variational form. For condensate density profiles of the form $ρ=f(x^2+y^2+\mbox{Re\,}Ψ(x+iy))$ in the presence of the plane of symmetry $y=0$, the solutions $x(z)$ describing stationary vortices of U and S types coming to the surface and solitary waves have been found in quadratures. Analogous three-dimensional configurations of the vortex filament uniformly moving along the $z$ axis have also been found in strictly cylindrical geometry. The dependence of solutions on the form of the function $f(q)$ has been analyzed.

cond-mat.quant-gas↗
arXiv2016

Predictability of the Appearance of Anomalous Waves at Sufficiently Small Benjamin-Feir Indices

The numerical simulation of the nonlinear dynamics of random sea waves at moderately small Benjamin-Feir indices and its comparison with the linear dynamics (at the coincidence of spatial Fourier harmonics near a spectral peak at a certain time $t_p$) indicate that the appearance of a rogue wave can be predicted in advance. If the linear approximation shows the presence of a sufficiently extensive and/or high group of waves in the near future after $t_p$, an anomalous wave is almost necessarily formed in the nonlinear model. The interval of reliable forecasting covers several hundred wave periods, which can be quite sufficient in practice for, e.g., avoiding the meeting of a ship with a giant wave.

physics.flu-dyn↗
arXiv2016

Anomalous wave as a result of the collision of two wave groups on sea surface

The numerical simulation of the nonlinear dynamics of the sea surface has shown that the collision of two groups of relatively low waves with close but noncollinear wave vectors (two or three waves in each group with a steepness of about 0.2) can result in the appearance of an individual anomalous wave whose height is noticeably larger than that in the linear theory. Since such collisions quite often occur on the ocean surface, this scenario of the formation of rogue waves is apparently most typical under natural conditions.

physics.flu-dyn↗
arXiv2015

Gaussian variational ansatz in the problem of anomalous sea waves: Comparison with direct numerical simulations

The nonlinear dynamics of an obliquely oriented wave packet at sea surface is studied both analytically and numerically for various initial parameters of the packet, in connection with the problem of oceanic rogue waves. In the framework of Gaussian variational ansatz applied to the corresponding (1+2D) hyperbolic nonlinear Schrödinger equation, a simplified Lagrangian system of differential equations is derived, which determines the evolution of coefficients of the real and imaginary quadratic forms appearing in the Gaussian. This model provides a semi-quantitative description for the process of nonlinear spatio-temporal focusing, which is one of the most probable mechanisms of rogue wave formation in random wave fields. The system is integrated in quadratures, which fact allows us to understand qualitative differences between the linear and nonlinear regimes of the focusing of wave packet. Comparison of the Gaussian model predictions with results of direct numerical simulation of fully nonlinear long-crested water waves is carried out.

physics.flu-dyn↗
arXiv2015

Steady mirror structures in a plasma with pressure anisotropy

In the first part we present a review of our results concerning the weakly nonlinear regime of the mirror instability in the framework of an asymptotic model. This model belongs to the class of gradient type systems for which the free energy can only decrease in time. It reveals a behavior typical for subcritical bifurcations: below the mirror instability threshold, all localized stationary structures are unstable, while above threshold, the system displays a blow-up behavior. It is shown that taking the electrons into account (non-zero temperature) does not change the structure of the asymptotic model. For bi-Maxwellian distribution functions for both electrons and ions, the model predicts the formation of magnetic holes. The second part contains original results concerning two-dimensional steady mirror structures which can form in the saturated regime. Based on Grad-Shafranov-like equations, a gyrotropic plasma, where the pressures in the static regime are only functions of the amplitude of the local magnetic field, is shown to be amenable to a variational principle with a free energy density given by the parallel tension. This approach is used to demonstrate that small-amplitude static holes constructed slightly below the mirror instability threshold identify with lump solitons of KPII equation and turn out to be unstable. It is also shown that regularizing effects such as finite Larmor radius corrections cannot be ignored in the description of large-amplitude mirror structures. Using the gradient method, which is based on a variational principle for anisotropic MHD taking into account ion finite Larmor radius effects, we found both one-dimensional magnetic structures in the form of stripes and two-dimensional bubbles when the magnetic field component transverse to the plane is increased. These structures realize minimum of the free energy.

physics.plasm-ph↗
arXiv2014

Ideal hydrodynamics inside as well as outside non-rotating black hole: Hamiltonian description in the Painlev{é}-Gullstrand coordinates

It is demonstrated that with using Painlev{é}-Gullstrand coordinates in their quasi-Cartesian variant, the Hamiltonian functional for relativistic perfect fluid hydrodynamics near a non-rotating black hole differs from the corresponding flat-spacetime Hamiltonian just by a simple term. Moreover, the internal region of the black hole is then described uniformly together with the external region, because in Painlev{é}-Gullstrand coordinates there is no singularity at the event horizon. An exact solution is presented which describes stationary accretion of an ultra-hard matter ($\varepsilon\propto n^2$) onto a moving black hole until reaching the central singularity. Equation of motion for a thin vortex filament on such accretion background is derived in the local induction approximation. The Hamiltonian for a fluid having ultra-relativistic equation of state $\varepsilon\propto n^{4/3}$ is calculated in explicit form, and the problem of centrally-symmetric stationary flow of such matter is solved analytically.

gr-qc↗
arXiv2013

Subcritical mirror structures in an anisotropic plasma

Based on Grad-Shafranov-like equations, a gyrotropic plasma where the pressures in the static regime are only functions of the amplitude of the local magnetic field is shown to be amenable to a variational principle with a free energy density given by the parallel tension. This approach is used to demonstrate that small- amplitude static holes constructed slightly below the mirror instability threshold identify with lump solitons of KPII equation and turn out to be unstable. It is also shown that regularizing effects such as finite Larmor radius corrections cannot be ignored in the description of large-amplitude mirror structures.

physics.plasm-ph↗
arXiv2011

Comment on "Triggering Rogue Waves in Opposing Currents"

The authors of a recent Letter ([1] M. Onorato, D. Proment, and A. Toffoli, Phys. Rev. Lett. 107, 184502 (2011)) based their study of rogue waves in nonuniform currents on a modified nonlinear Schrödinger equation (NLSE; see Eq.(1) in [1]). However, I show here that equation is not correct. It gives wrong solutions even in the first order on the supposedly small parameter $U/c_{\rm g}$, where $U(x)$ is a current, and $c_{\rm g}=g/(2 ω)$ [here $ω$ is a mean frequency of a quasi-monochromatic wave train, and $g$ is the gravity acceleration]. I also suggest an accurate variant of NLSE, valid in the presence of a large-scale nonuniform current under condition $(1+4ωU/g) \gtrsim 0.2$.

physics.flu-dyn↗
arXiv2011

3D effects in the dynamics of oceanic rogue waves: A numerical study

Recent results of numerical simulations of fully nonlinear evolutionary equations for long-crested deep-water waves are discussed, where formation of extreme waves was observed. Several examples demonstrate that three-dimensionality of the fluid motion has an essential influence on the process of rogue wave formation. In particular, in the presence of elongate wave groups, the most tall extreme waves occur when in an initial state the wave fronts were oriented obliquely to the direction of the group. An "optimal" angle, resulting in the highest rogue waves, depends on initial wave amplitude and group width, and it is about 18-28 degrees in a practically important range of parameters. Besides that, the mechanism of spatial-temporal focusing on a random wave background has been simulated for several values of nonlinearity.

physics.ao-ph↗
arXiv2011

Enhanced rise of rogue waves in slant wave groups

Numerical simulations of fully nonlinear equations of motion for long-crested waves at deep water demonstrate that in elongate wave groups the formation of extreme waves occurs most intensively if in an initial state the wave fronts are oriented obliquely to the direction of the group. An "optimal" angle, resulting in the highest rogue waves, depends on initial wave amplitude and group width, and it is about 18-28 degrees in a practically important range of parameters.

physics.flu-dyn↗
arXiv2011

The Fermi-Pasta-Ulam recurrence and related phenomena for 1D shallow-water waves in a finite basin

In this work, different regimes of the Fermi-Pasta-Ulam (FPU) recurrence are simulated numerically for fully nonlinear "one-dimensional" potential water waves in a finite-depth flume between two vertical walls. In such systems, the FPU recurrence is closely related to the dynamics of coherent structures approximately corresponding to solitons of the integrable Boussinesq system. A simplest periodic solution of the Boussinesq model, describing a single soliton between the walls, is presented in an analytical form in terms of the elliptic Jacobi functions. In the numerical experiments, it is observed that depending on a number of solitons in the flume and their parameters, the FPU recurrence can occur in a simple or complicated manner, or be practically absent. For comparison, the nonlinear dynamics of potential water waves over nonuniform beds is simulated, with initial states taken in the form of several pairs of colliding solitons. With a mild-slope bed profile, a typical phenomenon in the course of evolution is appearance of relatively high (rogue) waves, while for random, relatively short-correlated bed profiles it is either appearance of tall waves, or formation of sharp crests at moderate-height waves.

physics.flu-dyn↗
arXiv2011

Numerical study of Fermi-Pasta-Ulam recurrence for water waves over finite depth

Highly accurate direct numerical simulations have been performed for two-dimensional free-surface potential flows of an ideal incompressible fluid over a constant depth $h$, in the gravity field $g$. In each numerical experiment, at $t=0$ the free surface profile was in the form $y=A_0\cos(2πx/L)$, and the velocity field ${\bf v}=0$. The computations demonstrate the phenomenon of Fermi-Pasta-Ulam (FPU) recurrence takes place in such systems for moderate initial wave amplitudes $A_0\lesssim 0.12 h$ and spatial periods at least $L\lesssim 120 h$. The time of recurrence $T_{\rm FPU}$ is well fitted by the formula $T_{\rm FPU}(g/h)^{1/2}\approx 0.16(L/h)^2(h/A_0)^{1/2}$.

physics.flu-dyn↗
arXiv2010

Nonlinear interfacial waves in a constant-vorticity planar flow over variable depth

Exact Lagrangian in compact form is derived for planar internal waves in a two-fluid system with a relatively small density jump (the Boussinesq limit taking place in real oceanic conditions), in the presence of a background shear current of constant vorticity, and over arbitrary bottom profile. Long-wave asymptotic approximations of higher orders are derived from the exact Hamiltonian functional in a remarkably simple way, for two different parametrizations of the interface shape.

physics.ao-ph↗