347 research outputs found
Roll waves in mud
The stability of a viscoplastic fluid film falling down an inclined plane is explored, with the aim of determining the critical Reynolds number for the onset of roll waves. The HerschelâBulkley constitutive law is adopted and the fluid is assumed two-dimensional and incompressible. The linear stability problem is described for an equilibrium in the form of a uniform sheet flow, when perturbed by introducing an infinitesimal stress perturbation. This flow is stable for very high Reynolds numbers because the rigid plug riding atop the fluid layer cannot be deformed and the free surface remains flat. If the flow is perturbed by allowing arbitrarily small strain rates, on the other hand, the plug is immediately replaced by a weakly yielded âpseudo-plugâ that can deform and reshape the free surface. This situation is modelled by lubrication theory at zero Reynolds number, and it is shown how the fluid exhibits free-surface instabilities at order-one Reynolds numbers. Simpler models based on vertical averages of the fluid equations are evaluated, and one particular model is identified that correctly predicts the onset of instability. That model is used to describe nonlinear roll waves
Pattern formation in Hamiltonian systems with continuous spectra; a normal-form single-wave model
Pattern formation in biological, chemical and physical problems has received
considerable attention, with much attention paid to dissipative systems. For
example, the Ginzburg--Landau equation is a normal form that describes pattern
formation due to the appearance of a single mode of instability in a wide
variety of dissipative problems. In a similar vein, a certain "single-wave
model" arises in many physical contexts that share common pattern forming
behavior. These systems have Hamiltonian structure, and the single-wave model
is a kind of Hamiltonian mean-field theory describing the patterns that form in
phase space. The single-wave model was originally derived in the context of
nonlinear plasma theory, where it describes the behavior near threshold and
subsequent nonlinear evolution of unstable plasma waves. However, the
single-wave model also arises in fluid mechanics, specifically shear-flow and
vortex dynamics, galactic dynamics, the XY and Potts models of condensed matter
physics, and other Hamiltonian theories characterized by mean field
interaction. We demonstrate, by a suitable asymptotic analysis, how the
single-wave model emerges from a large class of nonlinear advection-transport
theories. An essential ingredient for the reduction is that the Hamiltonian
system has a continuous spectrum in the linear stability problem, arising not
from an infinite spatial domain but from singular resonances along curves in
phase space whereat wavespeeds match material speeds (wave-particle resonances
in the plasma problem, or critical levels in fluid problems). The dynamics of
the continuous spectrum is manifest as the phenomenon of Landau damping when
the system is ... Such dynamical phenomena have been rediscovered in different
contexts, which is unsurprising in view of the normal-form character of the
single-wave model
Inclusion of turbulence in solar modeling
The general consensus is that in order to reproduce the observed solar p-mode
oscillation frequencies, turbulence should be included in solar models.
However, until now there has not been any well-tested efficient method to
incorporate turbulence into solar modeling. We present here two methods to
include turbulence in solar modeling within the framework of the mixing length
theory, using the turbulent velocity obtained from numerical simulations of the
highly superadiabatic layer of the sun at three stages of its evolution. The
first approach is to include the turbulent pressure alone, and the second is to
include both the turbulent pressure and the turbulent kinetic energy. The
latter is achieved by introducing two variables: the turbulent kinetic energy
per unit mass, and the effective ratio of specific heats due to the turbulent
perturbation. These are treated as additions to the standard thermodynamic
coordinates (e.g. pressure and temperature). We investigate the effects of both
treatments of turbulence on the structure variables, the adiabatic sound speed,
the structure of the highly superadiabatic layer, and the p-mode frequencies.
We find that the second method reproduces the SAL structure obtained in 3D
simulations, and produces a p-mode frequency correction an order of magnitude
better than the first method.Comment: 10 pages, 12 figure
Solar-like oscillations of semiregular variables
Oscillations of the Sun and solar-like stars are believed to be excited
stochastically by convection near the stellar surface. Theoretical modeling
predicts that the resulting amplitude increases rapidly with the luminosity of
the star. Thus one might expect oscillations of substantial amplitudes in red
giants with high luminosities and vigorous convection. Here we present evidence
that such oscillations may in fact have been detected in the so-called
semiregular variables, extensive observations of which have been made by
amateur astronomers in the American Association for Variable Star Observers
(AAVSO). This may offer a new opportunity for studying the physical processes
that give rise to the oscillations, possibly leading to further information
about the properties of convection in these stars.Comment: Astrophys. J. Lett., in the press. Processed with aastex and
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