Effect of Low-Frequency Modulation on Thermal Convection Instability

2001 ◽  
Vol 56 (6-7) ◽  
pp. 509-522 ◽  
Author(s):  
P. K. Bhatia ◽  
B. S. Bhadauria
Keyword(s):  
Asymptotic Solution ◽  
Temperature Difference ◽  
Frequency Modulation ◽  
Thermal Convection ◽  
Low Frequency ◽  
Horizontal Layer ◽  
Time Dependent ◽  
Stability Criteria ◽  
Steady Temperature ◽  
The Stability

Abstract The stability of a horizontal layer of fluid heated from below is examined when, in addition to a steady temperature difference between the horizontal walls of the layer a time-dependent low-frequency per­ turbation is applied to the wall temperatures. An asymptotic solution is obtained which describes the be­ haviour of infinitesimal disturbances to this configuration. Possible stability criteria are analyzed and the results are compared with the known experimental as well as numerical results.

Low-frequency modulation of thermal instability

1970 ◽  
Vol 43 (2) ◽  
pp. 385-398 ◽  
Author(s):  
S. Rosenblat ◽  
D. M. Herbert
Keyword(s):  
Temperature Gradient ◽  
Asymptotic Solution ◽  
Frequency Modulation ◽  
Thermal Instability ◽  
Low Frequency ◽  
Experimental Results ◽  
Stability Criteria ◽  
The Stability ◽  
Boussinesq Fluid

A Boussinesq fluid is heated from below. The applied temperature gradient is the sum of a steady component and a low-frequency sinusoidal component. An asymptotic solution is obtained which describes the behaviour of infinitesimal disturbances to this configuration. The solution is discussed from the viewpoint of the stability or otherwise of the basic state, and possible stability criteria are analyzed. Some comparison is made with known experimental results.

scholarly journals Effect of modulation on the onset of thermal convection

1969 ◽  
Vol 35 (2) ◽  
pp. 243-254 ◽  
Author(s):  
Giulio Venezian
Keyword(s):  
Temperature Field ◽  
Applied Field ◽  
Critical Rayleigh Number ◽  
Perturbation Expansion ◽  
Horizontal Layer ◽  
Time Dependent ◽  
Steady Temperature ◽  
Onset Of Convection ◽  
Time Modulation ◽  
The Stability

The stability of a horizontal layer of fluid heated from below is examined when, in addition to a steady temperature difference between the walls of the layer, a time-dependent sinusoidal perturbation is applied to the wall temperatures. Only infinitesimal disturbances are considered. The effects of the oscillating temperature field are treated by a perturbation expansion in powers of the amplitude of the applied field. The shift in the critical Rayleigh number is calculated as a function of frequency, and it is found that it is possible to advance or delay the onset of convection by time modulation of the wall temperatures.

Stability of time-dependent rotational Couette flow Part 2. Stability analysis

1971 ◽  
Vol 48 (2) ◽  
pp. 365-384 ◽  
Author(s):  
C. F. Chen ◽  
R. P. Kirchner
Keyword(s):  
Growth Rate ◽  
Stability Analysis ◽  
Kinetic Energy ◽  
Initial Value Problem ◽  
Basic Flow ◽  
The Other ◽  
Time Dependent ◽  
Stability Criteria ◽  
Initial Value ◽  
The Stability

The stability of the flow induced by an impulsively started inner cylinder in a Couette flow apparatus is investigated by using a linear stability analysis. Two approaches are taken; one is the treatment as an initial-value problem in which the time evolution of the initially distributed small random perturbations of given wavelength is monitored by numerically integrating the unsteady perturbation equations. The other is the quasi-steady approach, in which the stability of the instantaneous velocity profile of the basic flow is analyzed. With the quasi-steady approach, two stability criteria are investigated; one is the standard zero perturbation growth rate definition of stability, and the other is the momentary stability criterion in which the evolution of the basic flow velocity field is partially taken into account. In the initial-value problem approach, the predicted critical wavelengths agree remarkably well with those found experimentally. The kinetic energy of the perturbations decreases initially, reaches a minimum, then grows exponentially. By comparing with the experimental results, it may be concluded that when the perturbation kinetic energy has grown a thousand-fold, the secondary flow pattern is clearly visible. The time of intrinsic instability (the time at which perturbations first tend to grow) is about ¼ of the time required for a thousandfold increase, when the instability disks are clearly observable. With the quasi-steady approach, the critical times for marginal stability are comparable to those found using the initial-value problem approach. The predicted critical wavelengths, however, are about 1½ to 2 times larger than those observed. Both of these points are in agreement with the findings of Mahler, Schechter & Wissler (1968) treating the stability of a fluid layer with time-dependent density gradients. The zero growth rate and the momentary stability criteria give approximately the same results.

Thermal convection in gas–droplet mixtures with phase transition

1975 ◽  
Vol 70 (1) ◽  
pp. 89-112
Author(s):  
T. Kambe ◽  
R. Takaki
Keyword(s):  
Water Vapour ◽  
Density Gradient ◽  
Thermal Convection ◽  
Fluid Layer ◽  
Travelling Waves ◽  
Horizontal Layer ◽  
Phase Changes ◽  
Droplet Growth ◽  
The Stability ◽  
Droplet Density

Thermal convection in a three-component fluid consisting of an inert carrier gas, a condensable vapour and small liquid droplets dispersed throughout the gaseous components has been investigated both theoretically and experimentally. The theoretical study is concerned with the stability of a horizontal fluid layer subject to gradients of both temperature and droplet density. The stability is characterized by four parameters: two material constants, that is, a modified Prandtl number P and a constant Q proportional to Dm − κ (Dm is the mutual mass diffusivity of the two gaseous constituents, κ the thermometric conductivity of the gas phase), a modified Rayleigh number R and a parameter S defined as the ratio of the droplet density gradient to the gas density gradient. It is shown for positive R that, irrespective of the value of R, the system is stable for S > S∞ (S∞ is a constant dependent on P and Q) and unstable for S < Q (Q is normally less than S∞) and that for the intermediate range Q < S < S∞ a transition from stability to instability occurs via an oscillatory state as R is increased through a critical value depending on S. It is shown that the stability is governed largely by both vapour diffusion through the inert gas and droplet growth or decay due to phase changes.In the experiments, thermal convection in a three-component fluid consisting of air, water vapour and water droplets was investigated. The cloud of droplets was mainly formed by injecting cigarette smoke into a horizontal layer of air saturated with water vapour. After the injection several phases of motion were observed successively. Among them there were travelling waves and steady cellular convection. Measurements were made of the critical Rayleigh numbers for the onset of the phases, the scale of the steady convection cells and the speed of the travelling waves. It is found that all the qualitative features of the experiment are explained by the theory.

scholarly journals Effects of modulation on Rayleigh-Benard convection. Part I

2004 ◽  
Vol 2004 (19) ◽  
pp. 991-1001 ◽  
Author(s):  
B. S. Bhadauria ◽  
Lokenath Debnath
Keyword(s):  
Rayleigh Number ◽  
Linear Stability ◽  
Fluid Layer ◽  
Critical Rayleigh Number ◽  
Horizontal Layer ◽  
Time Dependent ◽  
Steady Temperature ◽  
Prandtl Numbers ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

The linear stability of a horizontal layer of fluid heated from below and above is considered. In addition to a steady temperature difference between the walls of the fluid layer, a time-dependent periodic perturbation is applied to the wall temperatures. Only infinitesimal disturbances are considered. Numerical results for the critical Rayleigh number are obtained at various Prandtl numbers and for various values of the frequency. Some comparisons have been made with the known results.

The Effect of Impurity ions on the stability of drift Waves

1971 ◽  
Vol 6 (1) ◽  
pp. 201-209 ◽  
Author(s):  
R. S. B. Ong ◽  
M. Y Yu
Keyword(s):  
Cyclotron Frequency ◽  
Low Frequency ◽  
Drift Waves ◽  
Electron Drift ◽  
Stability Criteria ◽  
Homogeneous Plasma ◽  
Impurity Ions ◽  
The Stability ◽  
Impurity Ion ◽  
Low Frequency Waves

The propagation and stability of ion and electron drift waves in a non-homogeneous plasma containing impurity ions is considered. It is shown that the presence of impurities in the plasma may significantly affect the stability criteria of these low frequency waves. Furthermore, perturbations at frequencies which are multiples of the impurity ion cyclotron frequency may also be unstable when ½K2u R21 > 1.

The effect of viscous heating on the stability of Taylor–Couette flow

2002 ◽  
Vol 462 ◽  
pp. 111-132 ◽  
Author(s):  
U. A. AL-MUBAIYEDH ◽  
R. SURESHKUMAR ◽  
B. KHOMAMI
Keyword(s):  
Stability Analysis ◽  
Secondary Flow ◽  
Linear Stability ◽  
Couette Flow ◽  
Temperature Difference ◽  
Time Dependent ◽  
Viscous Heating ◽  
Taylor Couette ◽  
The Stability ◽  
Taylor Couette Flow

The influence of viscous heating on the stability of Taylor–Couette flow is investigated theoretically. Based on a linear stability analysis it is shown that viscous heating leads to significant destabilization of the Taylor–Couette flow. Specifically, it is shown that in the presence of viscous dissipation the most dangerous disturbances are axisymmetric and that the temporal characteristic of the secondary flow is very sensitive to the thermal boundary conditions. If the temperature difference between the two cylinders is small, the secondary flow is stationary as in the case of isothermal Taylor–Couette flow. However, when the temperature difference between the two cylinders is large, time-dependent secondary states are predicted. These linear stability predictions are in agreement with the experimental observations of White & Muller (2000) in terms of onset conditions as well as the spatiotemporal characteristics of the secondary flow. Nonlinear stability analysis has revealed that over a broad range of operating conditions, the bifurcation to the time-dependent secondary state is subcritical, while stationary states result as a consequence of supercritical bifurcation. Moreover, the supercritically bifurcated stationary state undergoes a secondary bifurcation to a time-dependent flow. Overall, the structure of the time-dependent state predicted by the analysis compares very well with the experimental observations of White & Muller (2000) that correspond to slowly moving vortices parallel to the cylinder axis. The significant destabilization observed in the presence of viscous heating arises as the result of the coupling of the perturbation velocity and the base-state temperature gradient that gives rise to fluctuations in the radial temperature distribution. Due to the thermal sensitivity of the fluid these fluctuations greatly modify the fluid viscosity and reduce the dissipation of disturbances provided by the viscous stress terms in the momentum equation.

A note on the stability of an infinite fluid heated from below

1967 ◽  
Vol 29 (3) ◽  
pp. 461-464 ◽  
Author(s):  
J. L. Robinson
Keyword(s):  
Growth Rate ◽  
Temperature Profile ◽  
Constant Temperature ◽  
Temperature Difference ◽  
Rate Of Change ◽  
Time Dependent ◽  
Initial Value ◽  
Horizontal Boundary ◽  
Boundary Case ◽  
The Stability

The problem of the stability of a fluid with time-dependent heating has been investigated by Morton (1957), Lick (1965) and Foster (1965). Morton and Lick assumed that the rate of change of the temperature profile is small compared with the growth rate of the disturbances (quasi-static assumption). This assumption is invalid near the onset of instability (as defined by ∂/∂t = 0), and Foster has therefore used an initial-value approach.In this paper the range of validity of the quasi-static assumption is discussed, and results of a time-scaled analysis and calculations based on this are compared with the work of Foster; the agreement is found to be good. We restrict our attention to a semi-infinite fluid initially at a constant temperature; at time t = 0 a temperature difference ΔT is applied at the (lower) horizontal boundary (case (A) of Foster).

scholarly journals On the instability of a fluid when heated from below

1935 ◽  
Vol 152 (877) ◽  
pp. 586-594 ◽  
Keyword(s):  
Critical Temperature ◽  
Temperature Difference ◽  
Fluid Layer ◽  
Physical Constant ◽  
Horizontal Layer ◽  
Free Surfaces ◽  
The Stability ◽  
Small Disturbances

It has been known for some times that when a horizontal layer of fluid is heated from below the fluid stationary, if initially at rest, until a certain temperature difference, depending on the physical constant of the fluid and the depth of the fluid layer, is reached. The equilibrium, which becomes less and less stable as the temperature rises, then becomes unstable for infinitely small disturbances, so that the fluid begins to move. Rayleigh,* in 1916, put forward a theory which gave the temperature at which motion first occurs when the top and bottom layers are free surfaces. The results agreed qualitatively with previous experiments due to Bérnard. Later Jeffreys calculated a critical temperature for the stability of a fluid between two rigid horizontal conducting planes. The investigation has since been revised by Jeffreys§ and also by Low.¶

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