Hopf Bifurcation in the Double-Glazing Problem With Conducting Boundaries

1987 ◽  
Vol 109 (4) ◽  
pp. 894-898 ◽  
Author(s):  
K. H. Winters
Keyword(s):  
Steady State ◽  
Hopf Bifurcation ◽  
Gravity Waves ◽  
Traveling Waves ◽  
Critical Rayleigh Number ◽  
Boussinesq Approximation ◽  
Time Dependent ◽  
Oscillatory Convection ◽  
Extended System ◽  
State Equations

Oscillatory convection has been observed in recent experiments in a square, air-filled cavity with differentially heated sidewalls and conducting horizontal surfaces. We show that the onset of the oscillatory convection occurs at a Hopf bifurcation in the steady-state equations for free convection in the Boussinesq approximation. The location of the bifurcation point is found by solving an extended system of steady-state equations. The predicted critical Rayleigh number and frequency at the onset of oscillations are in excellent agreement with the values measured recently and with those of a time-dependent simulation. Four other Hopf bifurcation points are found near the critical point and their presence supports a conjectured resonance between traveling waves in the boundary layers and interior gravity waves in the stratified core.

Ideal planar fluid flow over a submerged obstacle: Review and extension

2021 ◽  
Vol 63 ◽  
pp. 377-419
Author(s):  
Larry K. Forbes ◽  
Stephen J. Walters ◽  
Graeme C. Hocking
Keyword(s):  
Fluid Flow ◽  
Free Surface ◽  
Steady State ◽  
Gravity Waves ◽  
Classical Problem ◽  
Time Dependent ◽  
Time Dependent Behaviour ◽  
Critical Overview ◽  
Dependent Behaviour ◽  
Obstacle Height

A classical problem in free-surface hydrodynamics concerns flow in a channel, when an obstacle is placed on the bottom. Steady-state flows exist and may adopt one of three possible configurations, depending on the fluid speed and the obstacle height; perhaps the best known has an apparently uniform flow upstream of the obstacle, followed by a semiinfinite train of downstream gravity waves. When time-dependent behaviour is taken into account, it is found that conditions upstream of the obstacle are more complicated, however, and can include a train of upstream-advancing solitons. This paper gives a critical overview of these concepts, and also presents a new semianalytical spectral method for the numerical description of unsteady behaviour. doi:10.1017/S1446181121000341

scholarly journals Time dependent Long's equation

2014 ◽  
Vol 1 (2) ◽  
pp. 1673-1690
Author(s):  
M. Humi
Keyword(s):  
Steady State ◽  
Gravity Waves ◽  
Experimental Analysis ◽  
Numerical Solutions ◽  
Stratified Flow ◽  
Atmospheric Modeling ◽  
Time Dependent ◽  
Two Dimensional

Abstract. Long's equation describes steady-state two-dimensional stratified flow over terrain. Its numerical solutions under various approximations were investigated by many authors. Special attention was paid to the properties of the gravity waves that are predicted to be generated as a result. In this paper we derive a time-dependent generalization of this equation and investigate analytically its solutions under some simplifications. These results might be useful in the experimental analysis of gravity waves over topography and their impact on atmospheric modeling.

scholarly journals Time-dependent Long's equation

2015 ◽  
Vol 22 (2) ◽  
pp. 133-138 ◽  
Author(s):  
M. Humi
Keyword(s):  
Steady State ◽  
Gravity Waves ◽  
Experimental Analysis ◽  
Numerical Solutions ◽  
Stratified Flow ◽  
Atmospheric Modeling ◽  
Time Dependent ◽  
Two Dimensional

Abstract. Long's equation describes steady-state two-dimensional stratified flow over terrain. Its numerical solutions under various approximations were investigated by many authors. Special attention was paid to the properties of the gravity waves that are predicted to be generated as a result. In this paper we derive a time-dependent generalization of this equation and investigate analytically its solutions under some simplifications. These results might be useful in the experimental analysis of gravity waves over topography and their impact on atmospheric modeling.

scholarly journals The steady-state form of large-amplitude internal solitary waves

2010 ◽  
Vol 666 ◽  
pp. 477-505 ◽  
Author(s):  
STUART E. KING ◽  
MAGDA CARR ◽  
DAVID G. DRITSCHEL
Keyword(s):  
Steady State ◽  
Large Amplitude ◽  
Numerical Scheme ◽  
Boussinesq Approximation ◽  
Time Dependent ◽  
Internal Solitary Waves ◽  
Buoyancy Frequency ◽  
Iterative Solver ◽  
Vorticity Field ◽  
State Form

A new numerical scheme for obtaining the steady-state form of an internal solitary wave of large amplitude is presented. A stratified inviscid two-dimensional fluid under the Boussinesq approximation flowing between horizontal rigid boundaries is considered. The stratification is stable, and buoyancy is continuously differentiable throughout the domain of the flow. Solutions are obtained by tracing the buoyancy frequency along streamlines from the undisturbed far field. From this the vorticity field can be constructed and the streamfunction may then be obtained by inversion of Laplace's operator. The scheme is presented as an iterative solver, where the inversion of Laplace's operator is performed spectrally. The solutions agree well with previous results for stratification in which the buoyancy frequency is a discontinuous function. The new numerical scheme allows significantly larger amplitude waves to be computed than have been presented before and it is shown that waves with Richardson numbers as low as 0.062 can be computed straightforwardly. The method is also extended to deal in a novel way with closed streamlines when they occur in the domain. The new solutions are tested in independent fully nonlinear time-dependent simulations and are verified to be steady. Waves with regions of recirculation are also discussed.

scholarly journals Ground- and excited-state characteristics in photovoltaic polymer N2200

RSC Advances ◽  
2021 ◽  
Author(s):  
Guanzhao Wen ◽  
Xianshao Zou ◽  
Rong Hu ◽  
Jun Peng ◽  
Zhifeng Chen ◽  
...  
Keyword(s):  
Density Functional Theory ◽  
Excited State ◽  
Steady State ◽  
Excited States ◽  
Density Functional ◽  
Density Functional Theory Calculations ◽  
Time Dependent ◽  
Functional Theory ◽  
Time Resolved ◽  
Dependent Density

Ground- and excited-states properties of N2200 have been studied by steady-state and time-resolved spectroscopies as well as time-dependent density functional theory calculations.

scholarly journals Determinants of mRNA stability in Dictyostelium discoideum amoebae: differences in poly(A) tail length, ribosome loading, and mRNA size cannot account for the heterogeneity of mRNA decay rates.

1988 ◽  
Vol 8 (5) ◽  
pp. 1957-1969 ◽  
Author(s):  
R A Shapiro ◽  
D Herrick ◽  
R E Manrow ◽  
D Blinder ◽  
A Jacobson
Keyword(s):  
Steady State ◽  
Dictyostelium Discoideum ◽  
Mrna Decay ◽  
Decay Rates ◽  
Time Dependent ◽  
Translational Efficiency ◽  
Cdna Clones ◽  
Dependent Manner ◽  
Significant Difference ◽  
Kinetics Of

As an approach to understanding the structures and mechanisms which determine mRNA decay rates, we have cloned and begun to characterize cDNAs which encode mRNAs representative of the stability extremes in the poly(A)+ RNA population of Dictyostelium discoideum amoebae. The cDNA clones were identified in a screening procedure which was based on the occurrence of poly(A) shortening during mRNA aging. mRNA half-lives were determined by hybridization of poly(A)+ RNA, isolated from cells labeled in a 32PO4 pulse-chase, to dots of excess cloned DNA. Individual mRNAs decayed with unique first-order decay rates ranging from 0.9 to 9.6 h, indicating that the complex decay kinetics of total poly(A)+ RNA in D. discoideum amoebae reflect the sum of the decay rates of individual mRNAs. Using specific probes derived from these cDNA clones, we have compared the sizes, extents of ribosome loading, and poly(A) tail lengths of stable, moderately stable, and unstable mRNAs. We found (i) no correlation between mRNA size and decay rate; (ii) no significant difference in the number of ribosomes per unit length of stable versus unstable mRNAs, and (iii) a general inverse relationship between mRNA decay rates and poly(A) tail lengths. Collectively, these observations indicate that mRNA decay in D. discoideum amoebae cannot be explained in terms of random nucleolytic events. The possibility that specific 3'-structural determinants can confer mRNA instability is suggested by a comparison of the labeling and turnover kinetics of different actin mRNAs. A correlation was observed between the steady-state percentage of a given mRNA found in polysomes and its degree of instability; i.e., unstable mRNAs were more efficiently recruited into polysomes than stable mRNAs. Since stable mRNAs are, on average, "older" than unstable mRNAs, this correlation may reflect a translational role for mRNA modifications that change in a time-dependent manner. Our previous studies have demonstrated both a time-dependent shortening and a possible translational role for the 3' poly(A) tracts of mRNA. We suggest, therefore, that the observed differences in the translational efficiency of stable and unstable mRNAs may, in part, be attributable to differences in steady-state poly(A) tail lengths.

STABILITY OF STEADY STATE AND TRAVELING WAVES SOLUTIONS IN COUPLED MAP LATTICES

2008 ◽  
Vol 18 (01) ◽  
pp. 219-225 ◽  
Author(s):  
DANIEL TURZÍK ◽  
MIROSLAVA DUBCOVÁ
Keyword(s):  
Steady State ◽  
Essential Spectrum ◽  
Traveling Waves ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Linear Operators ◽  
Coupled Map Lattices ◽  
Basic Tool ◽  
Wave Solutions ◽  
The Stability

We determine the essential spectrum of certain types of linear operators which arise in the study of the stability of steady state or traveling wave solutions in coupled map lattices. The basic tool is the Gelfand transformation which enables us to determine the essential spectrum completely.

Spin down problem of rotating stratified fluid in thermally insulated circular cylinders

1969 ◽  
Vol 37 (4) ◽  
pp. 689-699 ◽  
Author(s):  
Takeo Sakurai
Keyword(s):  
Steady State ◽  
Time Scale ◽  
Boussinesq Approximation ◽  
Circular Cylinders ◽  
Heat Conducting ◽  
Quasi Steady State ◽  
Homogeneous Fluid ◽  
Time Duration ◽  
Viscous Heat ◽  
Final Approach

A response of viscous heat-conducting compressible fluid to an abrupt change of angular velocity of a containing thermally insulated circular cylinder under the existence of stable distribution of the temperature is investigated within the framework of the Boussinesq approximation for a time duration of the order of the homogeneous-fluid spin down time in order to resolve the Holton-Pedlosky controversy. The explicit expression of the solution is obtained by the standard method and Holton's conclusion is confirmed. The secondary meridional current induced by the Ekman layers spins the fluid down to a quasi-steady state within the present time scale. However, unlike the homogeneous case, the quasi-steady state is not one of solid body rotation. The final approach to the state of rigid rotation is achieved via the viscous diffusion in the time scale of the usual diffusion time.

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