NDLI: Finite-Amplitude Equilibrium Solutions for Plane Poiseuille

Content Provider	Springer Nature Link
Author	Balakumar, P.
Copyright Year	1997
Abstract	Two-dimensional nonlinear equilibrium solutions for the plane Poiseuille–Couette flow are computed by directly solving the full Navier–Stokes equations as a nonlinear eigenvalue problem. The equations are solved using the two-point fourth-order compact scheme and the Newton–Raphson iteration technique. The linear eigenvalue computations show that the combined Poiseuille–Couette flow is stable at all Reynolds numbers when the Couette velocity component σ2 exceeds 0.34552. Starting with the neutral solution for the plane Poiseuille flow, the nonlinear neutral surfaces for the combined Poiseuille–Couette flow were mapped out by gradually increasing the velocity component σ2. It is found that, for small σ2, the neutral surfaces stay in the same family as that for the plane Poiseuille flow, and the nonlinear critical Reynolds number gradually increases with increasing σ2. When the Couette velocity component is increased further, the neutral curve deviates from that for the Poiseuille flow with an appearance of a new loop at low wave numbers and at very low energy. By gradually increasing the σ2 values at a constant Reynolds number, the nonlinear critical Reynolds numbers were determined as a function of σ2. The results show that the nonlinear neutral curve is similar in shape to a linear case. The critical Reynolds number increases slowly up to σ2∼ 0.2 and remains constant until σ2∼ 0.58. Beyond σ2 > 0.59, the critical Reynolds number increases sharply. From the computed results it is concluded that two-dimensional nonlinear equilibrium solutions do not exist beyond a critical σ2 value of about 0.59.
Starting Page	103
Ending Page	119
Page Count	17
File Format	PDF
ISSN	09354964
Journal	Theoretical and Computational Fluid Dynamics
Volume Number	9
Issue Number	2
e-ISSN	14322250
Language	English
Publisher	Springer-Verlag
Publisher Date	1997-03-01
Publisher Place	Berlin Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Content Type	Text
Resource Type	Article
Subject	Fluid Flow and Transfer Processes Condensed Matter Physics Computational Mechanics

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