470 research outputs found
Transition to finger convection in double-diffusive convection
Finger convection is observed experimentally in an electrodeposition cell in
which a destabilizing gradient of copper ions is maintained against a
stabilizing temperature gradient. This double-diffusive system shows finger
convection even if the total density stratification is unstable. Finger
convection is replaced by an ordinary convection roll if convection is fast
enough to prevent sufficient heat diffusion between neighboring fingers, or if
the thermal buoyancy force is less than 1/30 of the compositional buoyancy
force. At the transition, the ion transport is larger than without an opposing
temperature gradient
Stability problem in dynamo
It is shown, that the saturated -effect taken from the nonlinear
dynamo equations for the thin disk can still produce exponentially growing
magnetic field in the case, when this field does not feed back on the .
For negative dynamo number (stationary regime) stability is defined by the
structure of the spectra of the linear problem for the positive dynamo numbers.
Stability condition for the oscillatory solution (positive dynamo number) is
also obtained and related to the phase shift of the original magnetic field,
which produced saturated and magnetic field in the kinematic regime.
Results can be used for explanation of the similar effect observed in the shell
models simulations as well in the 3D dynamo models in the plane layer and
sphere
Tilt-over mode in a precessing triaxial ellipsoid
The tilt-over mode in a precessing triaxial ellipsoid is studied
theoretically and numerically. Inviscid and viscous analytical models
previously developed for the spheroidal geometry by Poincar\'e [Bull. Astr. 27,
321 (1910)] and Busse [J. Fluid Mech., 33, 739 (1968)] are extended to this
more complex geometry, which corresponds to a tidally deformed spinning
astrophysical body. As confirmed by three-dimensional numerical simulations,
the proposed analytical model provides an accurate description of the
stationary flow in an arbitrary triaxial ellipsoid, until the appearance at
more vigorous forcing of time dependent flows driven by tidal and/or
precessional instabilities.Comment: http://link.aip.org/link/doi/10.1063/1.350435
Some Unusual Properties of Turbulent Convection and Dynamos in Rotating Spherical Shells
The dynamics of convecting fluids in rotating spherical shells is governed at
Prandtl numbers of the order unity by the interaction between differential
rotation and roll-like convection eddies. While the differential rotation is
driven by the Reynolds stresses of the eddies, its shearing action inhibits
convection and causes phenomena such as localized convection and turbulent
relaxation oscillations. The response of the system is enriched in the case of
dynamo action. Lorentz forces may brake either entirely or partially the
geostrophic differential rotation and give rise to two rather different dynamo
states. Bistability of turbulent dynamos exists for magnetic Prandtl numbers of
the order unity. While the ratios between mean magnetic and kinetic energies
differ by a factor of 5 or more for the two dynamo states, the mean convective
heat transports are nearly the same. They are much larger than in the absence
of a magnetic field.Comment: To appear in Procs. IUTAM Symposium on Turbulence in the Atmosphere
and Oceans, 08-7 = GA.06-0
Tidal instability in a rotating and differentially heated ellipsoidal shell
The stability of a rotating flow in a triaxial ellipsoidal shell with an
imposed temperature difference between inner and outer boundaries is studied
numerically. We demonstrate that (i) a stable temperature field encourages the
tidal instability, (ii) the tidal instability can grow on a convective flow,
which confirms its relevance to geo- and astrophysical contexts and (iii) its
growth rate decreases when the intensity of convection increases. Simple
scaling laws characterizing the evolution of the heat flux based on a
competition between viscous and thermal boundary layers are derived
analytically and verified numerically. Our results confirm that thermal and
tidal effects have to be simultaneously taken into account when studying
geophysical and astrophysical flows
Viscous dissipation by tidally forced inertial modes in a rotating spherical shell
We investigate the properties of forced inertial modes of a rotating fluid
inside a spherical shell. Our forcing is tidal like, but its main property is
that it is on the large scales. Our solutions first confirm some analytical
results obtained on a two-dimensional model by Ogilvie (2005). We also note
that as the frequency of the forcing varies, the dissipation varies drastically
if the Ekman number E is low (as is usually the case). We then investigate the
three-dimensional case and compare the results to the foregoing model. These
solutions show, like their 2D counterpart, a spiky dissipation curve when the
frequency of the forcing is varied; they also display small frequency intervals
where the viscous dissipation is independent of viscosity. However, we show
that the response of the fluid in these frequency intervals is crucially
dominated by the shear layer that is emitted at the critical latitude on the
inner sphere. The asymptotic regime is reached when an attractor has been
excited by this shear layer. This property is not shared by the two-dimensional
model. Finally, resonances of the three-dimensional model correspond to some
selected least-damped eigenmodes. Unlike their two-dimensional counter parts
these modes are not associated with simple attractors; instead, they show up in
frequency intervals with a weakly contracting web of characteristics. Besides,
we show that the inner core is negligible when its relative radius is less than
the critical value 0.4E^{1/5}. For these spherical shells, the full sphere
solutions give a good approximation of the flows (abridged abstract).Comment: 32 pages, 19 figs, accepted in J. Fluid Mec
Linear optical properties of one-dimensional Frenkel exciton systems with intersite energy correlations
We analyze the effects of intersite energy correlations on the linear optical
properties of one-dimensional disordered Frenkel exciton systems. The
absorption line width and the factor of radiative rate enhancement are studied
as a function of the correlation length of the disorder. The absorption line
width monotonously approaches the seeding degree of disorder on increasing the
correlation length. On the contrary, the factor of radiative rate enhancement
shows a non-monotonous trend, indicating a complicated scenario of the exciton
localization in correlated systems. The concept of coherently bound molecules
is exploited to explain the numerical results, showing good agreement with
theory. Some recent experiments are discussed in the light of the present
theory.Comment: 18 pages, 3 figues, REVTeX, to appear in Physical Review
Dynamo action at low magnetic Prandtl numbers: mean flow vs. fully turbulent motion
We compute numerically the threshold for dynamo action in Taylor-Green
swirling flows. Kinematic calculations, for which the flow field is fixed to
its time averaged profile, are compared to dynamical runs for which both the
Navier-Stokes and the induction equations are jointly solved. The kinematic
instability is found to have two branches, for all explored Reynolds numbers.
The dynamical dynamo threshold follows these branches: at low Reynolds number
it lies within the low branch while at high kinetic Reynolds number it is close
to the high branch.Comment: 4 pages, 4 figure
Saturation and time dependence of geodynamo models
In this study we address the question under which conditions a saturated
velocity field stemming from geodynamo simulations leads to an exponential
growth of the magnetic field in a corresponding kinematic calculation. We
perform global self-consistent geodynamo simulations and calculate the
evolution of a kinematically advanced tracer field. The self-consistent
velocity field enters the induction equation in each time step, but the tracer
field does not contribute to the Lorentz force. This experiment has been
performed by Cattaneo & Tobias (2009) and is closely related to the test field
method by Schrinner et al. (2005, 2007). We find two dynamo regimes in which
the tracer field either grows exponentially or approaches a state aligned with
the actual self-consistent magnetic field after an initial transition period.
Both regimes can be distinguished by the Rossby number and coincide with the
dipolar and multipolar dynamo regimes identified by Christensen & Aubert
(2006). Dipolar dynamos with low Rossby number are kinematically stable whereas
the tracer field grows exponentially in the multipolar dynamo regime. This
difference in the saturation process for dynamos in both regimes comes along
with differences in their time variability. Within our sample of 20 models,
solely kinematically unstable dynamos show dipole reversals and large
excursions. The complicated time behaviour of these dynamos presumably relates
to the alternating growth of several competing dynamo modes. On the other hand,
dynamos in the low Rossby number regime exhibit a rather simple time dependence
and their saturation merely results in a fluctuation of the fundamental dynamo
mode about its critical state.Comment: 6 pages, 8 figure
Global dynamo models from direct numerical simulations and their mean-field counterparts
Context. The recently developed test-field method permits to compute dynamo
coefficients from global, direct numerical simulations. The subsequent use of
these parameters in mean-field models enables us to compare self-consistent
dynamo models with their mean-field counterparts. So far, this has been done
for a simulation of rotating magnetoconvection and a simple benchmark dynamo,
which are both (quasi-)stationary. Aims. It is shown that chaotically
time-dependent dynamos in a low Rossby number regime may be appropriately
described by corresponding mean-field results. Also, it is pointed out under
which conditions mean-field models do not match direct numerical simulations.
Methods. We solve the equations of magnetohydrodynamics (MHD) in a rotating,
spherical shell in the Boussinesq approximation. Based on this, we compute
mean-field coefficients for several models with the help of the previously
developed test-field method. The parameterization of the mean electromotive
force by these coefficients is tested against direct numerical simulations. In
addition, we use the determined dynamo coefficients in mean-field models and
compare the outcome with azimuthally averaged fields from direct numerical
simulations. Results. The azimuthally and time-averaged electromotive force in
fast rotating dynamos is sufficiently well parameterized by the set of
determined mean-field coefficients. In comparison to the previously considered
(quasi-)stationary dynamo, the chaotic time-dependence leads to an improved
scale separation and thus to a better agreement between direct numerical
simulations and mean-field results.Comment: 6 pages, 6 figure
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