scholarly journals Thermal coupling in layered convection: evidence for an interface viscosity control from mechanical experiments and marginal stability analysis

1991 ◽  
Vol 1 (6) ◽  
pp. 599-622 ◽  
Author(s):  
Ph. Cardin ◽  
H.-C. Nataf ◽  
Ph. Dewost
Keyword(s):  
Stability Analysis ◽  
Marginal Stability ◽  
Thermal Coupling

Stability of bounded rapid shear flows of a granular material

1996 ◽  
Vol 308 ◽  
pp. 31-62 ◽  
Author(s):  
Chi-Hwa Wang ◽  
R. Jackson ◽  
S. Sundaresan
Keyword(s):  
Growth Rate ◽  
Stability Analysis ◽  
Granular Material ◽  
Bulk Density ◽  
Particulate Material ◽  
Dominant Mode ◽  
Marginal Stability ◽  
Sheared Layer ◽  
The Stability ◽  
Unusual Type

This paper presents a linear stability analysis of a rapidly sheared layer of granular material confined between two parallel solid plates. The form of the steady base-state solution depends on the nature of the interaction between the material and the bounding plates and three cases are considered, in which the boundaries act as sources or sinks of pseudo-thermal energy, or merely confine the material while leaving the velocity profile linear, as in unbounded shear. The stability analysis is conventional, though complicated, and the results are similar in all cases. For given physical properties of the particles and the bounding plates it is found that the condition of marginal stability depends only on the separation between the plates and the mean bulk density of the particulate material contained between them. The system is stable when the thickness of the layer is sufficiently small, but if the thickness is increased it becomes unstable, and initially the fastest growing mode is analogous to modes of the corresponding unbounded problem. However, with a further increase in thickness a new mode becomes dominant and this is of an unusual type, with no analogue in the case of unbounded shear. The growth rate of this mode passes through a maximum at a certain value of the thickness of the sheared layer, at which point it grows much faster than any mode that could be shared with the unbounded problem. The growth rate of the dominant mode also depends on the bulk density of the material, and is greatest when this is neither very large nor very small.

scholarly journals Linear Stability of a Steady Convective Flow between Permeable Cylinders

Fluids ◽  
2021 ◽  
Vol 6 (10) ◽  
pp. 342
Author(s):  
Maksims Zigunovs ◽  
Andrei Kolyshkin ◽  
Ilmars Iltins
Keyword(s):  
Reynolds Number ◽  
Stability Analysis ◽  
Linear Stability ◽  
Chemical Reaction ◽  
Linear Stability Analysis ◽  
Convective Flow ◽  
Base Flow ◽  
Marginal Stability ◽  
Heat Sources ◽  
Rate Of Increase

Linear stability analysis of a steady convective flow in a tall vertical annulus caused by nonlinear heat sources is conducted in the paper. Heat sources are generated as a result of a chemical reaction. The effect of radial cross-flow through permeable porous walls of the annulus is analyzed. The problem is relevant to biomass thermal conversion. The base flow solution is obtained by solving nonlinear boundary value problem. Linear stability analysis is performed, using collocation method. The calculations show that radial inward or outward flow has a stabilizing effect on the flow, while the increase in the Frank–Kamenetskii parameter (proportional to the intensity of the chemical reaction) destabilizes the flow. The increase in the Reynolds number based on the radial velocity leads to the appearance of the second minimum on the marginal stability curves. The rate of increase in the critical Grashof number with respect to the Reynolds number is different for inward and outward radial flows.

Marginal stability analysis on salt-fingers convection with parabolic temperature and salinity profiles

2009 ◽  
Vol 65 (3-4) ◽  
pp. 591-598
Author(s):  
Ray-Yeng Yang ◽  
Hwung-Hweng Hwung ◽  
Igor V. Shugan
Keyword(s):  
Stability Analysis ◽  
Marginal Stability ◽  
Salt Fingers

Marginal Stability of the Convective Boundary Layer

2020 ◽  
Vol 77 (2) ◽  
pp. 435-442
Author(s):  
John Thuburn ◽  
Georgios A. Efstathiou
Keyword(s):  
Boundary Layer ◽  
Stability Analysis ◽  
Linear Stability Analysis ◽  
Convective Boundary Layer ◽  
Eddy Viscosity ◽  
Potential Temperature ◽  
Marginal Stability ◽  
Layer Depth ◽  
Convective Boundary ◽  
Layer Potential

Abstract We hypothesize that the convective atmospheric boundary layer is marginally stable when the damping effects of turbulence are taken into account. If the effects of turbulence are modeled as an eddy viscosity and diffusivity, then an idealized analysis based on the hypothesis predicts a well-known scaling for the magnitude of the eddy viscosity and diffusivity. It also predicts that the marginally stable modes should have vertical and horizontal scales comparable to the boundary layer depth. A more quantitative numerical linear stability analysis is presented for a realistic convective boundary layer potential temperature profile and is found to support the hypothesis.

scholarly journals Particle pressure and marginal stability limits for a homogeneous monodisperse gas-fluidized bed: kinetic theory and numerical simulations

1999 ◽  
Vol 400 ◽  
pp. 229-263 ◽  
Author(s):  
DONALD L. KOCH ◽  
ASHOK S. SANGANI
Keyword(s):  
Stability Analysis ◽  
Fluidized Bed ◽  
Stokes Number ◽  
Hydrodynamic Interactions ◽  
Marginal Stability ◽  
Homogeneous State ◽  
Particle Phase ◽  
Velocity Variance ◽  
Unit Cells ◽  
Dilute Suspensions

A linear stability analysis is performed for the homogeneous state of a monodisperse gas-fluidized bed of spherical particles undergoing hydrodynamic interactions and solid-body collisions at small particle Reynolds number and finite Stokes number. A prerequisite for the stability analysis is the determination of the particle velocity variance which controls the particle-phase pressure. In the absence of an imposed shear, this velocity variance arises solely due to the hydrodynamic interactions among the particles. Since the uniform state of these suspensions is unstable over a wide range of values of particle volume fraction φ and Stokes number St, full dynamic simulations cannot be used in general to characterize the properties of the homogeneous state. Instead, we use an asymptotic analysis for large Stokes numbers together with numerical simulations of the hydrodynamic interactions among particles with specified velocities to determine the hydrodynamic sources and sinks of particle-phase energy. In this limit, the velocity distribution to leading order is Maxwellian and therefore standard kinetic theories for granular/hard-sphere molecular systems can be used to predict the particle-phase pressure and rheology of the bed once the velocity variance of the particles is determined. The analysis is then extended to moderately large Stokes numbers for which the anisotropy of the velocity distribution is considerable by using a kinetic theory which combines the theoretical analysis of Koch (1990) for dilute suspensions (φ [Lt ] 1) with numerical simulation results for non-dilute suspensions at large Stokes numbers. A linear stability analysis of the resulting equations of motion provides the first a priori predictions of the marginal stability limits for the homogeneous state of a gas-fluidized bed. Dynamical simulations following the detailed motions of the particles in small periodic unit cells confirm the theoretical predictions for the particle velocity variance. Simulations using larger unit cells exhibit an inhomogeneous structure consistent with the predicted instability of the homogeneous gas–solid suspension.

The thermodynamics of the Vlasov equilibria

1985 ◽  
Vol 33 (3) ◽  
pp. 359-367 ◽  
Author(s):  
E. Minardi
Keyword(s):  
Stability Analysis ◽  
Charge Distribution ◽  
Bifurcation Theory ◽  
Statistical Procedure ◽  
Coarse Grained ◽  
Marginal Stability ◽  
Principle Of Maximum Entropy ◽  
Entropy Functional ◽  
Principle Of Maximum ◽  
Electrostatic Equilibrium

A statistical procedure is applied for constructing an entropy functional associated with a collective Vlasov equilibrium described by a given coarse-grained current and charge distribution. The functional is not at a maximum if the magnetic or electrostatic equilibrium is not unique. This property connects the principle of maximum entropy with bifurcation theory and marginal stability analysis.

Stability of Internal Modes in Circularly Cylindrical MDH Equilibria

1980 ◽  
Vol 35 (1) ◽  
pp. 75-79
Author(s):  
D. Lortz ◽  
J. Nührenberg
Keyword(s):  
Stability Analysis ◽  
Pressure Gradient ◽  
Plasma Boundary ◽  
Cylindrical Symmetry ◽  
Magnetic Axis ◽  
Marginal Stability ◽  
Stability Conditions ◽  
The Stability

Abstract The stability of internal modes, i.e. modes which leave the plasma boundary unperturbed, is discussed for magnetohydrostatic equilibria in circularly cylindrical symmetry. Stability analysis can be performed analytically by expansion near the magnetic axis. Marginal stability conditions relating the pressure gradient and the shear are determined.

On Perturbation and Marginal Stability Analysis of Magneto-Convection in Active Mushy Layer

2009 ◽  
Vol 82 (2) ◽  
pp. 385-399 ◽  
Author(s):  
Dambaru Bhatta ◽  
Mallikarjunaiah S. Muddamallappa ◽  
Daniel N. Riahi
Keyword(s):  
Stability Analysis ◽  
Marginal Stability ◽  
Mushy Layer
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