Linear Stability Characteristics of Wake-Shear Layers in Two-Phase Shallow Flows

Linear stability of wake-shear layers in two-phase shallow flows is analyzed in the present paper. Stability analysis is based on two-dimensional shallow water equations. It is assumed that the fluid contains uniformly distributed solid particles. No dynamic interaction between the carrier fluid and particles is expected in the initial moment. Linear stability curves are obtained for different values of the particle loading parameter, the velocity ratio and the velocity deficit. It is shown that the increase in the velocity ratio destabilizes the flow. The particle loading parameter has a stabilizing effect on the flow. The role of the velocity deficit is also destabilizing: the increase of the velocity deficit leads to less stable flow.

Authors:

• Inta Volodko
• Valentina Koliskina

Keywords:

• Linear stability
• Shallow flows
• Wake-shear flows.

References:

[1] V. H. Chu, J. H. Wu, and R. E. Khayat, "Stability of transverse shear
flows in shallow open channels," Journal of Hydraulic Engineering,
vol. 117, pp. 1370-1388, 1991.
[2] D. Chen, and G. H. Jirka, "Absolute and convective instabilities of plane
turbulent wakes in a shallow water layer," Journal of Fluid
Mechanics, vol. 338, pp. 157-172, 1997.
[3] A. A. Kolyshkin, and M. S. Ghidaoui, "Stability analysis of shallow
wake flows," Journal of Fluid Mechanics, vol. 494, pp. 355-377,
2003.
[4] M. S. Ghidaoui, A. A. Kolyshkin, J. H. Liang, F. C. Chan, O. Li, and K.
Xu, "Linear and nonlinear analysis of shallow wakes," Journal of
Fluid Mechanics, vol. 548, pp. 309-340, 2006.
[5] D. Chen, and G. H. Jirka, "Experimental study of a plane turbulent
wake in a shallow water layer," Fluid Dynamics Research, vol. 16, pp.
11-41, 1995.
[6] Y. Yang, J. N. Chung, T. R. Troutt, and C. T. Crowe, "The influence of
particles on spatial stability of two-phase shallow mixing layers,"
Physics of Fluids, vol. A2(10), pp. 1839-1845, 1990.
[7] Y. Yang, J. N. Chung, T. R. Troutt, and C. T. Crowe, "The effect of
particles on the stability of a two-phase wake flow," International
Journal of Multiphase Flow, vol. 19, pp. 137-149, 1993.
[8] A. A. Dimas, and K. T. Kiger, "Linear instability of a particle-laden
mixing layer with a dynamic dispersed phase," Physics of Fluids, vol.
10, pp. 2539-2557, 1998.
[9] F. Wen, and J. Evans, "Linear instability of a two-layer flow with
differential particle loading," Physics of Fluids, vol. 6, pp. 3893-
3905, 1994.
[10] A. A. Kolyshkin, and S. Nazarovs, "Linear and weakly nonlinear
analysis of two-phase shallow wake flows," WSEAS Transactions on
Mathematics, vol. 6, issue 1, pp. 1-8, 2007.
[11] M. M. Koochesfahani, and C. E. Frieler, "Instability of non-uniform
density free shear layers with a wake profile," AIAA paper No. 87-
0047, 1987.
[12] D. Wallace, and L. G. Redekopp, "Linear instability characteristics of
wake-shear layers," Physics of Fluids, vol. A4, pp. 189-191, 1991.
[13] I. Volodko, and V. Koliskina, "Linear instability of wake-shear layers in
shallow water", Proceedings of the 5th International WSEAS conference
on environment, ecosystems and development, Tenerife, Spain,
December 14 - 16, pp. 40 - 44, 2007.