9,502 research outputs found
Generating boundary conditions for a Boussinesq system
We present a new method for the numerical implementation of generating
boundary conditions for a one dimensional Boussinesq system. This method is
based on a reformulation of the equations and a resolution of the dispersive
boundary layer that is created at the boundary when the boundary conditions are
non homogeneous. This method is implemented for a simple first order finite
volume scheme and validated by several numerical simulations. Contrary to the
other techniques that can be found in the literature, our approach does not
cause any increase in computational time with respect to periodic boundary
conditions
Whirling Hexagons and Defect Chaos in Hexagonal Non-Boussinesq Convection
We study hexagon patterns in non-Boussinesq convection of a thin rotating
layer of water. For realistic parameters and boundary conditions we identify
various linear instabilities of the pattern. We focus on the dynamics arising
from an oscillatory side-band instability that leads to a spatially disordered
chaotic state characterized by oscillating (whirling) hexagons. Using
triangulation we obtain the distribution functions for the number of pentagonal
and heptagonal convection cells. In contrast to the results found for defect
chaos in the complex Ginzburg-Landau equation and in inclined-layer convection,
the distribution functions can show deviations from a squared Poisson
distribution that suggest non-trivial correlations between the defects.Comment: 4 mpg-movies are available at
http://www.esam.northwestern.edu/~riecke/lit/lit.html submitted to New J.
Physic
Extreme-value statistics from Lagrangian convex hull analysis for homogeneous turbulent Boussinesq convection and MHD convection
We investigate the utility of the convex hull of many Lagrangian tracers to
analyze transport properties of turbulent flows with different anisotropy. In
direct numerical simulations of statistically homogeneous and stationary
Navier-Stokes turbulence, neutral fluid Boussinesq convection, and MHD
Boussinesq convection a comparison with Lagrangian pair dispersion shows that
convex hull statistics capture the asymptotic dispersive behavior of a large
group of passive tracer particles. Moreover, convex hull analysis provides
additional information on the sub-ensemble of tracers that on average disperse
most efficiently in the form of extreme value statistics and flow anisotropy
via the geometric properties of the convex hulls. We use the convex hull
surface geometry to examine the anisotropy that occurs in turbulent convection.
Applying extreme value theory, we show that the maximal square extensions of
convex hull vertices are well described by a classic extreme value
distribution, the Gumbel distribution. During turbulent convection,
intermittent convective plumes grow and accelerate the dispersion of Lagrangian
tracers. Convex hull analysis yields information that supplements standard
Lagrangian analysis of coherent turbulent structures and their influence on the
global statistics of the flow.Comment: 18 pages, 10 figures, preprin
Universality of the Small-Scale Dynamo Mechanism
We quantify possible differences between turbulent dynamo action in the Sun
and the dynamo action studied in idealized simulations. For this purpose we
compare Fourier-space shell-to-shell energy transfer rates of three
incrementally more complex dynamo simulations: an incompressible, periodic
simulation driven by random flow, a simulation of Boussinesq convection, and a
simulation of fully compressible convection that includes physics relevant to
the near-surface layers of the Sun. For each of the simulations studied, we
find that the dynamo mechanism is universal in the kinematic regime because
energy is transferred from the turbulent flow to the magnetic field from
wavenumbers in the inertial range of the energy spectrum. The addition of
physical effects relevant to the solar near-surface layers, including
stratification, compressibility, partial ionization, and radiative energy
transport, does not appear to affect the nature of the dynamo mechanism. The
role of inertial-range shear stresses in magnetic field amplification is
independent from outer-scale circumstances, including forcing and
stratification. Although the shell-to-shell energy transfer functions have
similar properties to those seen in mean-flow driven dynamos in each simulation
studied, the saturated states of these simulations are not universal because
the flow at the driving wavenumbers is a significant source of energy for the
magnetic field.Comment: 16 pages, 9 figures, accepted for publication in Ap
Reentrant and Whirling Hexagons in Non-Boussinesq convection
We review recent computational results for hexagon patterns in non-Boussinesq
convection. For sufficiently strong dependence of the fluid parameters on the
temperature we find reentrance of steady hexagons, i.e. while near onset the
hexagon patterns become unstable to rolls as usually, they become again stable
in the strongly nonlinear regime. If the convection apparatus is rotated about
a vertical axis the transition from hexagons to rolls is replaced by a Hopf
bifurcation to whirling hexagons. For weak non-Boussinesq effects they display
defect chaos of the type described by the two-dimensional complex
Ginzburg-Landau equation. For stronger non-Boussinesq effects the Hopf
bifurcation becomes subcritical and localized bursting of the whirling
amplitude is found. In this regime the coupling of the whirling amplitude to
(small) deformations of the hexagon lattice becomes important. For yet stronger
non-Boussinesq effects this coupling breaks up the hexagon lattice and strongly
disordered states characterized by whirling and lattice defects are obtained.Comment: Accepted in European Physical Journal Special Topic
Boussinesq Systems of Bona-Smith Type on Plane Domains: Theory and Numerical Analysis
We consider a class of Boussinesq systems of Bona-Smith type in two space
dimensions approximating surface wave flows modelled by the three-dimensional
Euler equations. We show that various initial-boundary-value problems for these
systems, posed on a bounded plane domain are well posed locally in time. In the
case of reflective boundary conditions, the systems are discretized by a
modified Galerkin method which is proved to converge in at an optimal
rate. Numerical experiments are presented with the aim of simulating
two-dimensional surface waves in complex plane domains with a variety of
initial and boundary conditions, and comparing numerical solutions of
Bona-Smith systems with analogous solutions of the BBM-BBM system
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