28,607 research outputs found
The effect of temperature-dependent solubility on the onset of thermosolutal convection in a horizontal porous layer
We consider the onset of thermosolutal (double-diffusive) convection of a binary fluid in a horizontal porous layer subject to fixed temperatures and chemical equilibrium on the bounding surfaces, in the case when the solubility of the dissolved component depends on temperature. We use a linear stability analysis to investigate how the dissolution or precipitation of this component affects the onset of convection and the selection of an unstable wavenumber; we extend this analysis using a Galerkin method to predict the structure of the initial bifurcation and compare our analytical results with numerical integration of the full nonlinear equations. We find that the reactive term may be stabilizing or destabilizing, with subtle effects particularly when the thermal gradient is destabilizing but the solutal gradient is stabilizing. The preferred spatial wavelength of convective cells at onset may also be substantially increased or reduced, and strongly reactive systems tend to prefer direct to subcritical bifurcation. These results have implications for geothermal-reservoir management and ore prospecting
Transient convective instabilities in directional solidification
We study the convective instability of the melt during the initial transient
in a directional solidification experiment in a vertical configuration. We
obtain analytically the dispersion relation, and perform an additional
asymptotic expansion for large Rayleigh number that permits a simpler
analytical analysis and a better numerical behavior. We find a transient
instability, i.e. a regime in which the system destabilizes during the
transient whereas the final unperturbed steady state is stable. This could be
relevant to growth mode predictions in solidification.Comment: 28 pages, 5 figures. The following article has been accepted for
publication in Physics of Fluids. After it is published, it will be found at
http://pof.aip.or
Turbulent Cells in Stars: I. Fluctuations in Kinetic Energy and Luminosity
Three-dimensional (3D) hydrodynamic simulations of shell oxygen burning
(Meakin and Arnett, 2007b) exhibit bursty, recurrent fluctuations in turbulent
kinetic energy. These are shown to be due to a general instability of the
convective cell, requiring only a localized source of heating or cooling. Such
fluctuations are shown to be suppressed in simulations of stellar evolution
which use mixing-length theory (MLT).
Quantitatively similar behavior occurs in the model of a convective roll
(cell) of Lorenz (1963), which is known to have a strange attractor that gives
rise to chaotic fluctuations in time of velocity and, as we show, luminosity.
Study of simulations suggests that the behavior of a Lorenz convective roll may
resemble that of a cell in convective flow. We examine some implications of
this simplest approximation, and suggest paths for improvement.
Using the Lorenz model as representative of a convective cell, a
multiple-cell model of a convective layer gives total luminosity fluctuations
which are suggestive of irregular variables (red giants and supergiants
(Schwarzschild 1975)), and of the long secondary period feature in semi-regular
AGB variables (Stothers 2010, Wood, Olivier and Kawaler 2004). This
"tau-mechanism" is a new source for stellar variability, which is inherently
non-linear (unseen in linear stability analysis), and one closely related to
intermittency in turbulence. It was already implicit in the 3D global
simulations of Woodward, Porter and Jacobs (2003). This fluctuating behavior is
seen in extended 2D simulations of CNeOSi burning shells (Arnett and Meakin
2011b), and may cause instability which leads to eruptions in progenitors of
core collapse supernovae PRIOR to collapse.Comment: 30 pages, 13 figure
Boundary knot method: A meshless, exponential convergence, integration-free, and boundary-only RBF technique
Based on the radial basis function (RBF), non-singular general solution and
dual reciprocity principle (DRM), this paper presents an inheretnly meshless,
exponential convergence, integration-free, boundary-only collocation techniques
for numerical solution of general partial differential equation systems. The
basic ideas behind this methodology are very mathematically simple and
generally effective. The RBFs are used in this study to approximate the
inhomogeneous terms of system equations in terms of the DRM, while non-singular
general solution leads to a boundary-only RBF formulation. The present method
is named as the boundary knot method (BKM) to differentiate it from the other
numerical techniques. In particular, due to the use of non-singular general
solutions rather than singular fundamental solutions, the BKM is different from
the method of fundamental solution in that the former does no need to introduce
the artificial boundary and results in the symmetric system equations under
certain conditions. It is also found that the BKM can solve nonlinear partial
differential equations one-step without iteration if only boundary knots are
used. The efficiency and utility of this new technique are validated through
some typical numerical examples. Some promising developments of the BKM are
also discussed.Comment: 36 pages, 2 figures, Welcome to contact me on this paper: Email:
[email protected] or [email protected]
Transient Rayleigh-Benard-Marangoni Convection due to Evaporation : a Linear Non-normal Stability Analysis
The convective instability in a plane liquid layer with time-dependent
temperature profile is investigated by means of a general method suitable for
linear stability analysis of an unsteady basic flow. The method is based on a
non-normal approach, and predicts the onset of instability, critical wave
number and time. The method is applied to transient Rayleigh-Benard-Marangoni
convection due to cooling by evaporation. Numerical results as well as
theoretical scalings for the critical parameters as function of the Biot number
are presented for the limiting cases of purely buoyancy-driven and purely
surface-tension-driven convection. Critical parameters from calculations are in
good agreement with those from experiments on drying polymer solutions, where
the surface cooling is induced by solvent evaporation.Comment: 31 pages, 8 figure
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