scholarly journals On the Modulation of Oscillation in Thermohaline Convection Problems Using Temperature Dependent Viscosity

2015 ◽  
Vol 45 (1) ◽  
pp. 39-52
Author(s):  
Joginder Singh Dhiman ◽  
Vijay Kumar
Keyword(s):  
Growth Rate ◽  
Linear Stability Theory ◽  
Effect Of Temperature ◽  
Sufficient Condition ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Thermohaline Convection ◽  
The Stability ◽  
Dependent Viscosity ◽  
Complex Growth Rate

Abstract The present paper mathematically investigates the effect of temperature dependent viscosity on the onset of instability in thermohaline convection problems of Veronis and Stern type configurations, using linear stability theory. A sufficient condition for the stability of oscillatory modes for thermohaline configuration is derived. When the compliment of this sufficient condition is true, the oscillatory motions of neutral or growing amplitude may exist, and hence the bounds for the complex growth rate of these neutral or unstable modes are derived, when viscosity of the fluid is an arbitrary function of temperature. Some general conclusions for the cases of linear and exponential variations of viscosity are worked out. The present analysis thus shows that the oscillations in thermohaline convection problems can be modulated or arrested by considering the temperature dependent viscosity of the fluid.

Numerical simulations of a viscous-fingering instability in a fluid with a temperature-dependent viscosity

2006 ◽  
Vol 84 (4) ◽  
pp. 273-287 ◽  
Author(s):  
Kristi E Holloway ◽  
John R Bruyn
Keyword(s):  
Growth Rate ◽  
Numerical Simulations ◽  
Viscosity Ratio ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Cell Width ◽  
Inlet Velocity ◽  
Fingering Instability ◽  
Dependent Viscosity ◽  
Hele Shaw Cell

We have performed numerical simulations of the flow of hot glycerine as it displaces colder, more viscous glycerine in a radial Hele–Shaw cell. We find that fingering occurs for sufficiently high inlet velocities and viscosity ratios. The wavelength of the instability is independent of inlet velocity and viscosity ratio, but depends weakly on cell width. The growth rate of the fingers is found to increase with inlet velocity and decrease with the cell width. We compare our results with those from experiments.PACS No.: 47.54.–r

Effect of temperature-dependent viscosity on mantle convection

2014 ◽  
Vol 49 (3) ◽  
pp. 249-263 ◽  
Author(s):  
Lukács Benedek Kuslits ◽  
Márton Pál Farkas ◽  
Attila Galsa
Keyword(s):  
Mantle Convection ◽  
Effect Of Temperature ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Dependent Viscosity

Dynamics of cooling domes of viscoplastic fluid

2000 ◽  
Vol 422 ◽  
pp. 225-248 ◽  
Author(s):  
N. J. BALMFORTH ◽  
R. V. CRASTER
Keyword(s):  
Thin Layer ◽  
Yield Stress ◽  
Stability Theory ◽  
Constitutive Relations ◽  
Linear Stability Theory ◽  
Viscoplastic Fluid ◽  
Surface Cooling ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Dependent Viscosity

A non-isothermal viscoplastic thin-layer theory is developed to explore the effects of surface cooling, yield stress, and shear thinning on the evolution of non-isothermal domes of lava and laboratory fluids. The fluid is modelled using the Herschel–Bulkley constitutive relations, but modified to have temperature-dependent viscosity and yield stress. The thin-layer equations are solved numerically to furnish models of expanding, axisymmetrical domes. Linear stability theory reveals the possibility of non-axisymmetrical, fingering-like instability in these domes. Finally, the relevance to lava and experiments is discussed.

Onset of Thermogravitational Convection in a Ferrofluid Layer With Temperature Dependent Viscosity

2011 ◽  
Vol 134 (1) ◽  
Author(s):  
I. S. Shivakumara ◽  
Jinho Lee ◽  
C. E. Nanjundappa
Keyword(s):  
Perturbation Technique ◽  
Temperature Dependent ◽  
Regular Perturbation ◽  
Temperature Dependent Viscosity ◽  
Stability Parameters ◽  
Thermogravitational Convection ◽  
Different Types ◽  
The Stability ◽  
Dependent Viscosity ◽  
Bounding Surfaces

The onset of thermogravitational convection in a horizontal ferrofluid layer is investigated with viscosity depending exponentially on temperature. The bounding surfaces of the ferrofluid layer are considered to be either stress free or rigid-ferromagnetic and insulated to temperature perturbations. The resulting eigenvalue problem is solved numerically using the Galerkin technique and also by a regular perturbation technique for different types of velocity boundary conditions, namely free-free, rigid-rigid, and lower rigid- upper free. It is observed that increasing the viscosity parameter, Λ, and the magnetic number, M1, is to hasten the onset of ferroconvection, while the nonlinearity of fluid magnetization, M3, is found to have no influence on the stability of the system. The critical stability parameters are found to be the same in the limiting cases of either no magnetic forces or no buoyancy forces.

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