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).

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.

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.

Confined Buckling Analysis of a Viscoelastic Ring Subjected to Constant Temperature Difference

2011 ◽  
Vol 295-297 ◽  
pp. 1804-1810 ◽  
Author(s):  
Min Yang ◽  
Shi Fu Xiao
Keyword(s):  
Galerkin Method ◽  
Critical Load ◽  
Constant Temperature ◽  
Temperature Difference ◽  
Evolutionary Trend ◽  
Buckling Behavior ◽  
Viscoelastic Theory ◽  
Confined Buckling ◽  
The Stability ◽  
Stability Of The Solution

Based on Boltzmann’s viscoelastic theory, the confined buckling behavior of a viscoelastic ring subjected to constant temperature difference is investigated by assumed modes method, Galerkin method and numeric method. The critical load and the stability of the solution are investigated. The evolutionary trend of the system is also analyzed.

Improving Temperature Probe Calibration Accuracy in Constant Temperature Baths With a Novel Data Processing Method

2019 ◽  
Author(s):  
Mustafa Koz ◽  
Thomas Visalli
Keyword(s):  
Data Processing ◽  
Constant Temperature ◽  
Sampling Rate ◽  
Processing Method ◽  
Time Dependent ◽  
Calibration Data ◽  
Temperature Probe ◽  
Data Processing Method ◽  
Probe Calibration ◽  
The Stability

Abstract The accuracy of temperature probe calibration in a constant temperature bath is governed by the stability and uniformity of the bath. In the available literature, there have been efforts in designing baths with better stability and uniformity. This work is distinguished from the previous efforts by presenting a novel data processing method that improves the calibration performance without the need to improve the inherent qualities of the bath. The stability limitation is addressed by filtering out the time dependent components of temperature readings, and then the resulting calibration performance becomes limited only by the uniformity. This work provides the theory and guidelines for filtering the time dependent signal components such as sampling rate and duration based on the stability of the bath. The method is experimentally validated by applying it to a baseline bath and the results are compared to those from a high-end bath. As a figure of merit, the probability of obtaining a calibration value within ±0.75 mK of the high-end bath is reported. In a calibration scenario in which the uncertainty is predominantly governed by the stability, only 10% of the calibration values are within the aforementioned limits with the conventional method. With the application of the novel method, all of the calibration data meets the criterion.

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.

On the stability of slowly varying flow: the divergent channel

1975 ◽  
Vol 69 (2) ◽  
pp. 241-262 ◽  
Author(s):  
P. M. Eagles ◽  
M. A. Weissman
Keyword(s):  
Growth Rate ◽  
Rate Of Change ◽  
Ray Method ◽  
Constant Frequency ◽  
Neutral Curves ◽  
Divergent Channel ◽  
Walled Channel ◽  
The Stability ◽  
Flow Quantity

The linear stability of a slowly varying flow, the flow in a diverging straight-walled channel, is studied using a modification of the ‘WKB’ or ‘ray’ method. It is shown that ‘quasi-parallel’ theory, the usual method for handling such flows, gives the formally correct lowest-order growth rate; however, this growth rate can be substantially in error if its magnitude is comparable to that of the rate of change of the basic state. The method used clearly demonstrates the dependence of the growth rate, wavenumber, neutral curves, etc., on the cross-stream variable and on the flow quantity under consideration. When applied to the divergent channel, the method yields a much wider ‘unstable’ region and a much lower ‘critical’ Reynolds number (depending on the flow quantity used) than those predicted by quasi-parallel theory. The determination of the downstream development of waves of constant frequency shows that waves of all frequencies eventually decay.

Growth and adaptation to sea water in 'underyearling' sockeye (Oncorhynchus nerka) and coho (O. kisutch) salmon subjected to regimes of constant or changing temperature and day length

1978 ◽  
Vol 56 (11) ◽  
pp. 2413-2421 ◽  
Author(s):  
W. C. Clarke ◽  
J. E. Shelbourn ◽  
J. R. Brett
Keyword(s):  
Growth Rate ◽  
Environmental Factors ◽  
Constant Temperature ◽  
Sea Water ◽  
Rate Of Change ◽  
Day Length ◽  
Artificial Photoperiod ◽  
Final Length ◽  
Temperature Controlled ◽  
Rate Of Response

Growth and hypoosmoregulatory ability of 'underyearling' sockeye and coho were studied in relation to the influence of constant as well as changing temperature and day length. Both environmental factors influenced growth and osmoregulatory performance. Temperature controlled the rate of response to photoperiod so that changes in growth rate caused by photoperiod treatments were apparent sooner at higher temperatures than at lower ones. Changing temperatures did not alter the final length or weight achieved in comparison with a constant temperature of the same mean.The sensitivity of the fry to photoperiod varied seasonally. The characteristics of photoperiod which formed the most important cues were direction of change and rate of change of day length.It is concluded that artificial photoperiod treatments are not required to produce 'underyearling' sockeye smolts in spring, provided that water temperatures are sufficient to allow growth to a weight of 3–4 g. However, coho smoltify at a larger size and thus would require a substantially greater thermal input to produce 'underyearling' smolts in spring.

Symmetrizable Difference Dchemes

2005 ◽  
Vol 5 (1) ◽  
pp. 3-50 ◽  
Author(s):  
Alexei A. Gulin
Keyword(s):  
Initial Data ◽  
Difference Scheme ◽  
Difference Schemes ◽  
Time Dependent ◽  
Stability Boundaries ◽  
Typical Representative ◽  
Variable Weight ◽  
The Stability ◽  
Conditions Of Stability ◽  
The Right

AbstractA review of the stability theory of symmetrizable time-dependent difference schemes is represented. The notion of the operator-difference scheme is introduced and general ideas about stability in the sense of the initial data and in the sense of the right hand side are formulated. Further, the so-called symmetrizable difference schemes are considered in detail for which we manage to formulate the unimprovable necessary and su±cient conditions of stability in the sense of the initial data. The schemes with variable weight multipliers are a typical representative of symmetrizable difference schemes. For such schemes a numerical algorithm is proposed and realized for constructing stability boundaries.

COVID-19: Time-Dependent Effective Reproduction Number and Sub-notification Effect Estimation Modeling (Preprint)

2020 ◽  
Author(s):  
Eduardo Atem De Carvalho ◽  
Rogerio Atem De Carvalho
Keyword(s):  
New York ◽  
Reproduction Number ◽  
Moving Average ◽  
Real Data ◽  
Time Dependent ◽  
Initial Value ◽  
Health Authorities ◽  
Reproduction Numbers ◽  
Effect Estimation ◽  
The Impact

BACKGROUND Since the beginning of the COVID-19 pandemic, researchers and health authorities have sought to identify the different parameters that govern their infection and death cycles, in order to be able to make better decisions. In particular, a series of reproduction number estimation models have been presented, with different practical results. OBJECTIVE This article aims to present an effective and efficient model for estimating the Reproduction Number and to discuss the impacts of sub-notification on these calculations. METHODS The concept of Moving Average Method with Initial value (MAMI) is used, as well as a model for Rt, the Reproduction Number, is derived from experimental data. The models are applied to real data and their performance is presented. RESULTS Analyses on Rt and sub-notification effects for Germany, Italy, Sweden, United Kingdom, South Korea, and the State of New York are presented to show the performance of the methods here introduced. CONCLUSIONS We show that, with relatively simple mathematical tools, it is possible to obtain reliable values for time-dependent, incubation period-independent Reproduction Numbers (Rt). We also demonstrate that the impact of sub-notification is relatively low, after the initial phase of the epidemic cycle has passed.

scholarly journals High-Speed Video Analysis of the Process Stability in Plasma Spraying

2021 ◽  
Author(s):  
K. Bobzin ◽  
M. Öte ◽  
M. A. Knoch ◽  
I. Alkhasli ◽  
H. Heinemann
Keyword(s):  
Plasma Spraying ◽  
High Speed ◽  
Plasma Jet ◽  
Plasma Jets ◽  
Time Dependent ◽  
Acquisition Time ◽  
Fast Fourier Transformation ◽  
Frequency Spectra ◽  
Dependent Signal ◽  
The Stability

AbstractIn plasma spraying, instabilities and fluctuations of the plasma jet have a significant influence on the particle in-flight temperatures and velocities, thus affecting the coating properties. This work introduces a new method to analyze the stability of plasma jets using high-speed videography. An approach is presented, which digitally examines the images to determine the size of the plasma jet core. By correlating this jet size with the acquisition time, a time-dependent signal of the plasma jet size is generated. In order to evaluate the stability of the plasma jet, this signal is analyzed by calculating its coefficient of variation cv. The method is validated by measuring the known difference in stability between a single-cathode and a cascaded multi-cathode plasma generator. For this purpose, a design of experiment, covering a variety of parameters, is conducted. To identify the cause of the plasma jet fluctuations, the frequency spectra are obtained and subsequently interpreted by means of the fast Fourier transformation. To quantify the significance of the fluctuations on the particle in-flight properties, a new single numerical parameter is introduced. This parameter is based on the fraction of the time-dependent signal of the plasma jet in the relevant frequency range.

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