X. T. ZHOU ET AL.

22

be the symmetrical form, Taylor deduced the theoretical

predictions in his paper, and found that there would be a

definite speed at which the perturbation would suddenly

make the Taylor vortex appearance. Although mathema-

ticians could not make certain the condition so as to es-

timate whether the general small perturbation could grow

in the flow governed by fluid control equations, the gen-

eral small perturbation could come from the truncation

error in CFD process, so that laminar Taylor vortex can

be gained in the way of numeric solution with the small

perturbation grown. So the small perturbation equations

may be taken as a kind of condition beyond the stability.

As having proved above, there are different steady so-

lutions to the fluid control equations at the same bound-

ary condition, the same fluid property, the same mesh grid

in CFD process with the same business software except

that the flow has developed from different procedures of

GDP, GIP and SIP. It was reported in the work of Kosch-

mieder and Burkhalter [14] that the wave length of lami-

nar axisymmetric Taylor vortices was significantly dif-

ferent if a certain supercritical Taylor number was rea-

ched either by quasi-steady increasing to the given angu-

lar velocity or by sudden start to the given angular veloc-

ity. Koschmieder also found that when a wavelength was

once established by some procedure, it did not change in

some rang with subsequently increased slowly or quickly.

And the wavelength obtained from the sudden starts was

smaller than that from the slow acceleration experiments

[9]. So the developed procedure, in which the present

state has undergone, should be taken as another condition

of getting the real flow solution beyond the stability. In

other word, the present flow state may include the infor-

mation of its past, namely the flowing fluid may have the

memory to some degrees.

From the view of solving fluid control equation, steady

boundary condition has been generally accepted. The

perturbation condition has also been accepted by resear-

chers in hydrodynamic stability. What needs to be em-

phasized is that the developed procedure can leave be-

hind some information of its history in present state so

that the solutions to fluid control equations are different

when the flows undergo different developed procedures.

By distinguishing the details in the flow performance, we

may deduce what the fluid has undergone to some de-

grees. In other words, the flow between concentric rotat-

ing cylinders has somewhat memory for the procedure of

its history.

5. Conclusions

The performances of laminar Taylor-Couette flow with

different developed procedures have shown that the solu-

tions of fluid control equations are different when they

are solved in steady state with the same boundary, the

same fluid property, the same mesh grid in CFD process

with the same business software except that the flows have

developed from the procedures of GDP, GIP and SIP.

The developed procedure should be taken as the nec-

essary condition in order to make the solution of fluid

control equations become coincident with the reality be-

side the boundary condition and the perturbation in ste-

ady state. The developed procedure can leave behind so-

me information of its history in the present state.

By distinguishing the details in the flow performance,

we could deduce what the fluid has undergone to some

degrees. In other words, the flow between concentric ro-

tating cylinders has somewhat memory for the procedure.

This may be a way of understanding the history of the

present state for the fluid.

6. Acknowledgements

X. T. ZHOU thanks Prof. Pan Jiazhen and Prof. Chu Li-

angyin for their useful discussions. This work is support-

ed by the National Natural Science Foundation of China

(Grant No. 50876032).

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