Title: Numerical modelling of the transition from laminar to turbulent stages in a simple parallel shear fl
1Numerical modelling of the transition from
laminar to turbulent stages in a simple
parallel shear flow
- M. Nagata T. Itano
- Kyoto University
- Japan
2Physical configuration
- Differentially heated side walls
- Boussinesq approxmation
- Cubic velocity profile
- Prandtl number 0
- gt purely hydrodynamic
- Periodicity in the streamwise(x) and the
spanwise(y) directions
3Neutral curve and the stability of the transverse
vortex flowby Nagata Busse (1985)
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6Decomposition of the velocity fields
?
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11DNS
12The growth rate and the wall shear rate of the
basic state, 2DTV and 3DSS
Basic
2DTV
3DSS
Basic
2DTV
3DSS
13Transient states and the final state by DNS
3DSS-I
3DPS-I
2DTV
3DPS-I
3DPS-II
2DTV
Harmonic case
Subharmonic case
14The wall shear rate by DNS
Basic
Basic
3DPS-I
3DPS-I
3DSS-I
3DTW
2DTV
2DTV
Burst
3DPS-II
3DSS-II
Subharmonic case
Harmonic case
15Sporadic burst flow
16The spectrum of the wall friction.at Gr678, 684
and 690.
173DSSII
18The vorticity on the mid-plane 3DSS-I
19The vorticity on the mid-plane 3DSS-II
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21Bifurcation diagram
22Concluding remarks
- The bifurcation of flows of a Boussinesq fluid
between two vertical plates with different
temperatures in the vanishing Prandtl number
limit has been examined. - We have confirmed the results of Nagata Busse
(1983), in which the secondary and tertiary flows
are the two-dimensional steady transverse vortex
flow and the three-dimensional steady subharmonic
flow, respectively. - We have also presented the results obtained by
the numerical experiment. In particular, several
unstable periodic solutions representing a
transient state are captured in both the harmonic
and the subharmonic cases. - At high Grashof numbers different types of motion
coexist as a stable solution of the system. - The motion becomes quasi-periodic and a chaotic
motion ensues eventually.