scholarly journals Horizontal Wave Number Dependence of Type II Solutions in Rayleigh?Benard Convection with Hexagonal Planform

1984 ◽  
Vol 37 (5) ◽  
pp. 531 ◽  
Author(s):  
JM Lopez ◽  
JO Murphy
Keyword(s):  
Vertical Component ◽  
Wave Number ◽  
Type I ◽  
Type Ii ◽  
Horizontal Wave ◽  
Convection Problem ◽  
Parameter Values ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard ◽  
Cyclonic Type

The horizontal wave number dependence of the hexagonal planform solutions for the RayleighBenard convection problem, which have a nonzero vertical component of vorticity (type II solutions), has been established. Over the range of wave numbers which support cellular convection, comparisons between the thermal transport characteristics of these cyclonic type solutions and those traditionally obtained from nonlinear investigations of the single horizontal mode equations (type I solutions) have been made. From the numerical results obtained, it is found that the cell aspect ratio which maximizes the heat flux of type II solutions is larger than that for type I solutions, at quivalent parameter values, and that the value of the horizontal wave number giving maximum Nusselt number for type II solutions increases with Rayleigh number and decreases with Prandtl number.

The Role of Kinetic Boundary Conditions in Generating Type II Solutions for Rayleigh-Benard Convection

1985 ◽  
Vol 6 (2) ◽  
pp. 216-219 ◽  
Author(s):  
J. O. Murphy ◽  
N. Yannios
Keyword(s):  
Vertical Component ◽  
Single Mode ◽  
Convection Cell ◽  
Type I ◽  
Type Ii ◽  
Vertical Vorticity ◽  
Bénard Convection ◽  
Benard Convection ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

A new family of solutions for stationary convection (Murphy and Lopez 1984) has been established which exists within the astrophysical range of parameter values — large Rayleigh number and low Prandtl number. These single mode Type II solutions, which have a non-zero component of vertical vorticity, apparently do not exist at higher Prandtl numbers and are characterized by a lower vertical velocity and heat flux, when compared to the equivalent single mode Type I solutions for Rayleigh — Benard convection with zero vertical vorticity. In turn the vertical component of vorticity associated with Type II solutions is responsible for modifying the horizontal components of the velocity field to establish cyclonic or swirling type solutions within the hexagonal convection cell.

Interpretation of shadowgraph patterns in Rayleigh-Bénard convection

1988 ◽  
Vol 190 ◽  
pp. 451-469 ◽  
Author(s):  
D. R. Jenkins
Keyword(s):  
Rayleigh Number ◽  
Linear Theory ◽  
Vertical Component ◽  
Fluid Flows ◽  
Bénard Convection ◽  
Benard Convection ◽  
Higher Order Terms ◽  
The Relationship ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

The relationship between observations of cellular Rayleigh-Bénard convection using shadowgraphs and theoretical expressions for convection planforms is considered. We determine the shadowgraphs that ought to be observed if the convection is as given by theoretical expressions for roll, square or hexagonal planforms and compare them with actual experiments. Expressions for the planforms derived from linear theory, valid for low supercritical Rayleigh number, produce unambiguous shadowgraphs consisting of cells bounded by bright lines, which correspond to surfaces through which no fluid flows and on which the vertical component of velocity is directed downwards. Dark spots at the centre of cells, indicating regions of hot, rising fluid, are not accounted for by linear theory, but can be produced by adding higher-order terms, predominantly due to the temperature dependence of a material property of the fluid, such as its viscosity.

scholarly journals ROBUST HETEROCLINIC CYCLES IN TWO-DIMENSIONAL RAYLEIGH–BÉNARD CONVECTION WITHOUT BOUSSINESQ SYMMETRY

2002 ◽  
Vol 12 (11) ◽  
pp. 2501-2522 ◽  
Author(s):  
ISABEL MERCADER ◽  
JOANA PRAT ◽  
EDGAR KNOBLOCH
Keyword(s):  
Rayleigh Number ◽  
Lower Boundary ◽  
Two Dimensions ◽  
External Parameter ◽  
Onset Of Convection ◽  
Current Dissipation ◽  
Parameter Values ◽  
Rayleigh Benard Convection ◽  
Spatial Resonance ◽  
Rayleigh Benard

The onset of convection in systems that are heated via current dissipation in the lower boundary or that lose heat from the top boundary via Newton's law of cooling is formulated as a bifurcation problem. The Rayleigh number as usually defined is shown to be inappropriate as a bifurcation parameter since the temperature difference across the layer depends on the amplitude of convection and hence changes as convection evolves at fixed external parameter values. A modified Rayleigh number is introduced that does remain constant even when the system is evolving, and solutions obtained with the standard formulation are compared with those obtained via the new one. Near the 1 : 2 spatial resonance in low Prandtl number fluids these effects open up intervals of Rayleigh number with no stable solutions in the form of steady convection or steadily traveling waves. Direct numerical simulations in two dimensions show that in such intervals the dynamics typically take the form of a nearly heteroclinic modulated traveling wave. This wave may be quasiperiodic or chaotic.

APPROXIMATION OF THE STATIONARY STATISTICAL PROPERTIES OF THE DYNAMICAL SYSTEM GENERATED BY THE TWO-DIMENSIONAL RAYLEIGH–BÉNARD CONVECTION PROBLEM

2011 ◽  
Vol 09 (04) ◽  
pp. 421-446 ◽  
Author(s):  
FLORENTINA TONE ◽  
XIAOMING WANG
Keyword(s):  
Dynamical System ◽  
Global Attractors ◽  
Statistical Properties ◽  
Two Dimensional ◽  
Time Step ◽  
Bénard Convection ◽  
Benard Convection ◽  
Convection Problem ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

In this article, we consider a temporal linear semi-implicit approximation of the two-dimensional Rayleigh–Bénard convection problem. We prove that the stationary statistical properties as well as the global attractors of this linear semi-implicit scheme converge to those of the 2D Rayleigh–Bénard problem as the time step approaches zero.

Energy Conservative Dissipative Particle Dynamics Simulation of Natural Convection in Liquids

2011 ◽  
Vol 133 (11) ◽  
Author(s):  
Eiyad Abu-Nada
Keyword(s):  
Natural Convection ◽  
Prandtl Number ◽  
Dissipative Particle Dynamics ◽  
Particle Dynamics ◽  
Dynamics Simulation ◽  
Wide Range ◽  
Convection Problem ◽  
Basic Features ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

Dissipative particle dynamics with energy conservation (eDPD) was used to study natural convection in liquid domain over a wide range of Rayleigh Numbers. The problem selected for this study was the Rayleigh–Bénard convection problem. The Prandtl number used resembles water where the Prandtl number is set to Pr = 6.57. The eDPD results were compared to the finite volume solutions, and it was found that the eDPD method calculates the temperature and flow fields throughout the natural convection domains correctly. The eDPD model recovered the basic features of natural convection, such as development of plumes, development of thermal boundary layers, and development of natural convection circulation cells (rolls). The eDPD results were presented by means of temperature isotherms, streamlines, velocity contours, velocity vector plots, and temperature and velocity profiles.

scholarly journals On the colour and spin of epistemic error (and what we might do about it)

2011 ◽  
Vol 15 (10) ◽  
pp. 3123-3133 ◽  
Author(s):  
K. Beven ◽  
P. J. Smith ◽  
A. Wood
Keyword(s):  
Hydrological Model ◽  
Type I ◽  
Model Structure ◽  
Calibration Data ◽  
Type Ii ◽  
Likelihood Functions ◽  
Model Residuals ◽  
Type Ii Errors ◽  
Parameter Values ◽  
Do So

Abstract. Disinformation as a result of epistemic error is an issue in hydrological modelling. In particular the way in which the colour in model residuals resulting from epistemic errors should be expected to be non-stationary means that it is difficult to justify the spin that the structure of residuals can be properly represented by statistical likelihood functions. To do so would be to greatly overestimate the information content in a set of calibration data and increase the possibility of both Type I and Type II errors. Some principles of trying to identify periods of disinformative data prior to evaluation of a model structure of interest, are discussed. An example demonstrates the effect on the estimated parameter values of a hydrological model.

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