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Effect of mean flow on Spatial patterns
Hira AffanInstitute für Theoretische Physik,
Westfälische Wilhelms Universität Münster
Natural Patterns
Spatial Patterns Non equilibrium spatial patterns may be
classified as the linear instability of an infinite spatial uniform systems.
Pattern Formation in a thin layer of fluid occurs when the vertical temperature gradient exceeds certain threshold.
Rayleigh Benard Convection
Basic Model-Swift Hohenberg Equation
),(
where
)1(
variablescaledin or
)(4
)(
22
31
2
2322
2
2
tr
gg
kk
t
ct
Simulated Pattern
Modified Model Equations
},{
)(})Pr({
)()1(
222
32
xy
t
mt
U
Uc
Ug
Numerical Scheme
trNLtr
trL
trNLtr
trL
r ,,
),(
,,
),(1
Summary The localized roll structure may be pinned or it
may shrink or grow depending upon the parameters used.
For non-potential systems having finite stream function we have spatio temporal patterns.
Strength of mean flow increases with decreasing Prandtle number.
Mean flows play essential role in maintaining the spiral defect chaos.
The speed of pseudospectral scheme permits the simulation of large aspect ratio.
Future Task The patterns will be analysed for the different
parameter values and the threshold will be computed to study the transient bahviour of the system.
Analytical tools will be developed to study the nature of patterns in the presence of streaming velocities which may be helpful in solving the defects in pattern formation systems.
Thank You for your Attention !!
