206 research outputs found
Incompressible viscous fluid flows in a thin spherical shell
Linearized stability of incompressible viscous fluid flows in a thin
spherical shell is studied by using the two-dimensional Navier--Stokes
equations on a sphere. The stationary flow on the sphere has two singularities
(a sink and a source) at the North and South poles of the sphere. We prove
analytically for the linearized Navier--Stokes equations that the stationary
flow is asymptotically stable. When the spherical layer is truncated between
two symmetrical rings, we study eigenvalues of the linearized equations
numerically by using power series solutions and show that the stationary flow
remains asymptotically stable for all Reynolds numbers.Comment: 28 pages, 10 figure
Slow solitary waves in multi-layered magnetic structures
The propagation of slow sausage surface waves in a multi-layered magnetic configuration is considered. The magnetic configuration consists of a central magnetic slab sandwiched between two identical magnetic slabs (with equilibrium quantities different from those in the central slab) which in turn are embedded between two identical semi-infinite regions. The dispersion equation is obtained in the linear approximation. The nonlinear governing equation describing waves with a characteristic wavelength along the central slab much larger than the slab thickness is derived. Solitary wave solutions to this equation are obtained in the case where these solutions deviate only slightly from the algebraic soliton of the Benjamin-Ono equation
Super rogue waves in simulations based on weakly nonlinear and fully nonlinear hydrodynamic equations
The rogue wave solutions (rational multi-breathers) of the nonlinear
Schrodinger equation (NLS) are tested in numerical simulations of weakly
nonlinear and fully nonlinear hydrodynamic equations. Only the lowest order
solutions from 1 to 5 are considered. A higher accuracy of wave propagation in
space is reached using the modified NLS equation (MNLS) also known as the
Dysthe equation. This numerical modelling allowed us to directly compare
simulations with recent results of laboratory measurements in
\cite{Chabchoub2012c}. In order to achieve even higher physical accuracy, we
employed fully nonlinear simulations of potential Euler equations. These
simulations provided us with basic characteristics of long time evolution of
rational solutions of the NLS equation in the case of near breaking conditions.
The analytic NLS solutions are found to describe the actual wave dynamics of
steep waves reasonably well.Comment: under revision in Physical Review
Long-range sound-mediated dark soliton interactions in trapped atomic condensates
A long-range soliton interaction is discussed whereby two or more dark
solitons interact in an inhomogeneous atomic condensate, modifying their
respective dynamics via the exchange of sound waves without ever coming into
direct contact. An idealized double well geometry is shown to yield perfect
energy transfer and complete periodic identity reversal of the two solitons.
Two experimentally relevant geometries are analyzed which should enable the
observation of this long-range interaction
Freak waves in 2005
International audienceInformation about freak wave events in the ocean reported by mass media and derived from personal observations in 2005 is collected and analysed. Nine cases are selected as true freak wave events from a total number of 27 mentioned. Besides rogue waves in the open sea, the problem of freak wave events on the shore is emphasized. These accidents are related to unexpected wave impact upon the coast and shore constructions or to sudden intensive flooding of the coast. Of the nine events considered reliable here, three events correspond to open-sea cases, while the six others occurred nearshore
A scalar nonlocal bifurcation of solitary waves for coupled nonlinear Schroedinger systems
An explanation is given for previous numerical results which suggest a
certain bifurcation of `vector solitons' from scalar (single-component)
solitary waves in coupled nonlinear Schroedinger (NLS) systems. The bifurcation
in question is nonlocal in the sense that the vector soliton does not have a
small-amplitude component, but instead approaches a solitary wave of one
component with two infinitely far-separated waves in the other component. Yet,
it is argued that this highly nonlocal event can be predicted from a purely
local analysis of the central solitary wave alone. Specifically the
linearisation around the central wave should contain asymptotics which grow at
precisely the speed of the other-component solitary waves on the two wings.
This approximate argument is supported by both a detailed analysis based on
matched asymptotic expansions, and numerical experiments on two example
systems. The first is the usual coupled NLS system involving an arbitrary ratio
between the self-phase and cross-phase modulation terms, and the second is a
coupled NLS system with saturable nonlinearity that has recently been
demonstrated to support stable multi-peaked solitary waves. The asymptotic
analysis further reveals that when the curves which define the proposed
criterion for scalar nonlocal bifurcations intersect with boundaries of certain
local bifurcations, the nonlocal bifurcation could turn from scalar to
non-scalar at the intersection. This phenomenon is observed in the first
example. Lastly, we have also selectively tested the linear stability of
several solitary waves just born out of scalar nonlocal bifurcations. We found
that they are linearly unstable. However, they can lead to stable solitary
waves through parameter continuation.Comment: To appear in Nonlinearit
Fast magnetoacoustic waves in a randomly structured solar corona
The propagation of fast magnetoacoustic waves in a randomly structured solar corona is considered in the linear and cold plasma limits. The random field is assumed to be static and associated with plasma density inhomogeneities only. A transcendental dispersion relation for the fast magnetoacoustic waves which propagate perpendicularly to the magnetic field is derived in the weak random field approximation. It is shown analytically that the fast magnetosonic waves experience acceleration, attenuation, and dispersion in comparison to the homogeneous case. These analytical findings are essentially confirmed by numerical simulations for a wide-spectrum pulse, except that the waves were found decelerated. It is concluded that the coronal Moreton waves can be applied to MHD seismology of the solar corona
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