1,333 research outputs found
Turbulence characteristics of the B\"{o}dewadt layer in a large enclosed rotor-stator system
A three-dimensional (3D) direct numerical simulation is combined with a
laboratory study to describe the turbulent flow in an enclosed annular
rotor-stator cavity characterized by a large aspect ratio G=(b-a)/h=18.32 and a
small radius ratio a/b=0.152, where a and b are the inner and outer radii of
the rotating disk and h is the interdisk spacing. The rotation rate Omega under
consideration is equivalent to the rotational Reynolds number Re=Omegab2/nu=9.5
x 104, where nu is the kinematic viscosity of the fluid. This corresponds to a
value at which an experiment carried out at the laboratory has shown that the
stator boundary layer is turbulent, whereas the rotor boundary layer is still
laminar. Comparisons of the 3D computed solution with velocity measurements
have given good agreement for the mean and turbulent fields. The results
enhance evidence of weak turbulence at this Reynolds number, by comparing the
turbulence properties with available data in the literature. An approximately
self-similar boundary layer behavior is observed along the stator side. The
reduction of the structural parameter a1 under the typical value 0.15 and the
variation in the wall-normal direction of the different characteristic angles
show that this boundary layer is three-dimensional. A quadrant analysis of
conditionally averaged velocities is performed to identify the contributions of
different events (ejections and sweeps) on the Reynolds shear stress producing
vortical structures. The asymmetries observed in the conditionally averaged
quadrant analysis are dominated by Reynolds stress-producing events in this
B\"{o}dewadt layer. Moreover, case 1 vortices (with a positive wall induced
velocity) are found to be the major source of generation of special strong
events, in agreement with the conclusions of Lygren and Andersson.Comment: 16 page
Two-dimensional matter-wave solitons and vortices in competing cubic-quintic nonlinear lattices
The nonlinear lattice---a new and nonlinear class of periodic
potentials---was recently introduced to generate various nonlinear localized
modes. Several attempts failed to stabilize two-dimensional (2D) solitons
against their intrinsic critical collapse in Kerr media. Here, we provide a
possibility for supporting 2D matter-wave solitons and vortices in an extended
setting---the cubic and quintic model---by introducing another nonlinear
lattice whose period is controllable and can be different from its cubic
counterpart, to its quintic nonlinearity, therefore making a fully `nonlinear
quasi-crystal'.
A variational approximation based on Gaussian ansatz is developed for the
fundamental solitons and in particular, their stability exactly follows the
inverted \textit{Vakhitov-Kolokolov} stability criterion, whereas the vortex
solitons are only studied by means of numerical methods. Stability regions for
two types of localized mode---the fundamental and vortex solitons---are
provided. A noteworthy feature of the localized solutions is that the vortex
solitons are stable only when the period of the quintic nonlinear lattice is
the same as the cubic one or when the quintic nonlinearity is constant, while
the stable fundamental solitons can be created under looser conditions. Our
physical setting (cubic-quintic model) is in the framework of the
Gross-Pitaevskii equation (GPE) or nonlinear Schr\"{o}dinger equation, the
predicted localized modes thus may be implemented in Bose-Einstein condensates
and nonlinear optical media with tunable cubic and quintic nonlinearities.Comment: 8 pages,7 figures, Frontiers of Physics (In Press
Two-dimensional discrete solitons in rotating lattices
We introduce a two-dimensional (2D) discrete nonlinear Schr\"{o}dinger (DNLS)
equation with self-attractive cubic nonlinearity in a rotating reference frame.
The model applies to a Bose-Einstein condensate stirred by a rotating strong
optical lattice, or light propagation in a twisted bundle of nonlinear fibers.
Two species of localized states are constructed: off-axis fundamental solitons
(FSs), placed at distance from the rotation pivot, and on-axis (R=0) vortex
solitons (VSs), with vorticities and 2. At a fixed value of rotation
frequency , a stability interval for the FSs is found in terms of the
lattice coupling constant , , with monotonically
decreasing . VSs with S=1 have a stability interval,
\tilde{C}_{\mathrm{cr}%}^{(S=1)}(\Omega),
which exists for below a certain critical value,
. This implies that the VSs with S=1 are
\emph{destabilized} in the weak-coupling limit by the rotation. On the
contrary, VSs with S=2, that are known to be unstable in the standard DNLS
equation, with , are \emph{stabilized} by the rotation in region
%, with growing as a
function of . Quadrupole and octupole on-axis solitons are considered
too, their stability regions being weakly affected by .Comment: To be published in Physical Review
Three-dimensional hybrid vortex solitons
We show, by means of numerical and analytical methods, that media with a
repulsive nonlinearity which grows from the center to the periphery support a
remarkable variety of previously unknown complex stationary and dynamical
three-dimensional solitary-wave states. Peanut-shaped modulation profiles give
rise to vertically symmetric and antisymmetric vortex states, and novel
stationary hybrid states, built of top and bottom vortices with opposite
topological charges, as well as robust dynamical hybrids, which feature stable
precession of a vortex on top of a zero-vorticity base. The analysis reveals
stability regions for symmetric, antisymmetric, and hybrid states. In addition,
bead-shaped modulation profiles give rise to the first example of exact
analytical solutions for stable three-dimensional vortex solitons. The
predicted states may be realized in media with a controllable cubic
nonlinearity, such as Bose-Einstein condensates.Comment: To appear in the New Journal of Physic
Unstaggered-staggered solitons on one- and two-dimensional two-component discrete nonlinear Schr\"{o}dinger lattices
We study coupled unstaggered-staggered soliton pairs emergent from a system
of two coupled discrete nonlinear Schr\"{o}dinger (DNLS) equations with the
self-attractive on-site self-phase-modulation nonlinearity, coupled by the
repulsive cross-phase-modulation interaction, on 1D and 2D lattice domains.
These mixed modes are of a "symbiotic" type, as each component in isolation may
only carry ordinary unstaggered solitons. While most work on DNLS systems
addressed symmetric on-site-centered fundamental solitons, these models give
rise to a variety of other excited states, which may also be stable. The
simplest among them are antisymmetric states in the form of discrete twisted
solitons, which have no counterparts in the continuum limit. In the extension
to 2D lattice domains, a natural counterpart of the twisted states are vortical
solitons. We first introduce a variational approximation (VA) for the solitons,
and then correct it numerically to construct exact stationary solutions, which
are then used as initial conditions for simulations to check if the stationary
states persist under time evolution. Two-component solutions obtained include
(i) 1D fundamental-twisted and twisted-twisted soliton pairs, (ii) 2D
fundamental-fundamental soliton pairs, and (iii) 2D vortical-vortical soliton
pairs. We also highlight a variety of other transient dynamical regimes, such
as breathers and amplitude death. The findings apply to modeling binary
Bose-Einstein condensates, loaded in a deep lattice potential, with identical
or different atomic masses of the two components, and arrays of bimodal optical
waveguides.Comment: to be published in Communications in Nonlinear Science and Numerical
Simulatio
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