Linear Instability of Wake-Shear Layers in Two-Phase Shallow Flows

Authors: Inta Volodko, Valentina Koliskina

Abstract:

Linear stability analysis of wake-shear layers in twophase shallow flows is performed in the present paper. Twodimensional shallow water equations are used in the analysis. 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. The stability calculations are performed for different values of the particle loading parameter and two other parameters which characterize the velocity ratio and the velocity deficit. The results show that the particle loading parameter has a stabilizing effect on the flow while the increase in the velocity ratio or in the velocity deficit destabilizes the flow.

Keywords: Linear stability, Shallow flows, Wake-shear flows.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1079656

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.