The Effect of Slow Variation of Base Flow Profile on the Stability of Slightly Curved Mixing Layers
The effect of small non-parallelism of the base flow
on the stability of slightly curved mixing layers is analyzed in the
present paper. Assuming that the instability wavelength is much
smaller than the length scale of the variation of the base flow we
derive an amplitude evolution equation using the method of multiple
scales. The proposed asymptotic model provides connection between
parallel flow approximations and takes into account slow
longitudinal variation of the base flow.
[1] V. H. Chu, J. H. Wu, and R. E. Khayat, "Stability of transverse shear
flows in shallow open channels," Journal of Hydraulic Engineering
ASCE, vol. 117, pp. 1370-1388, 1991.
[2] D. Chen, and G. H. Jirka, "Linear instability analyses of turbulent
mixing layers and jets in shallow water layers," Journal of Hydraulic
Research, vol. 36, pp. 815-830, 1998.
[3] M. S. Ghidaoui, and A. A. Kolyshkin, "Linear stability analysis of
lateral motions in compound open channels," Journal of Hydraulic
Engineering ASCE, vol. 125, pp. 871-880, 1999.
[4] A. A. Kolyshkin, and M. S. Ghidaoui, "Gravitational and shear
instabilities in compound and composite channels," Journal of
Hydraulic Engineering ASCE, vol. 128, pp. 1076-1086, 2002.
[5] B. C. van Prooijen, and W. S. J. Uijttewaal, "A linear approach for the
evolution of coherent structures in shallow mixing layers," Physics of
Fluids, vol. 14, pp. 4105-4114, 2002.
[6] V. H. Chu, and S. Babarutsi, "Confinement and bed-friction effects in
shallow turbulent mixing layers," Journal of Hydraulic Engineering
ASCE, vol. 114, pp. 1257-1274, 1988.
[7] W. S. J. Uijttewaal, and J. Tukker, "A linear approach for the evolution
of coherent structures in shallow mixing layers," Experiments in Fluids,
vol. 24, pp. 192-200, 1998.
[8] W. S. J. Uijttewaal, and R. Booij, "Effect of shallowness on the
development of free-surface mixing layers," Physics of Fluids, vol. 12,
pp. 392-402, 2000.
[9] W. W. Liou, "Linear instability of curved free shear layers," Physics of
Fluids, vol. 6, pp. 541-549, 1993.
[10] F.Q. Hu, S.R. Otto, and T.L. Jackson, "On the stability of a curved
mixing layer," in Proc. ICASE Workshop on Transition, Turbulence and
Combustion, T.R. Gatski, M.Y. Hussaini, and T.L. Jackson, Eds. New
York: Kluwer, 1993, pp. 107-116.
[11] M. M. Gibson, and B. A. Jounis, "Turbulence measurements in a
developing mixing layer with mild destabilizing curvature," Experiments
in Fluids, vol. 1, pp. 23-30, 1983.
[12] C. Godréche, and P. Manneville, Hydrodynamics and nonlinear
instabilities, Cambridge, Cambridge University Press, 1998.
[13] A. A. Kolyshkin, and S. Nazarovs, "Stability of slowly diverging flows
in shallow water," Mathematical modeling and analysis, no. 1, pp. 101-
106, 2007.
[14] D. Crighton, and M. Gaster, "Stability of slowly diverging jet flow,"
Journal of Fluid Mechanics, vol. 77, pp. 397-413, 1976.
[1] V. H. Chu, J. H. Wu, and R. E. Khayat, "Stability of transverse shear
flows in shallow open channels," Journal of Hydraulic Engineering
ASCE, vol. 117, pp. 1370-1388, 1991.
[2] D. Chen, and G. H. Jirka, "Linear instability analyses of turbulent
mixing layers and jets in shallow water layers," Journal of Hydraulic
Research, vol. 36, pp. 815-830, 1998.
[3] M. S. Ghidaoui, and A. A. Kolyshkin, "Linear stability analysis of
lateral motions in compound open channels," Journal of Hydraulic
Engineering ASCE, vol. 125, pp. 871-880, 1999.
[4] A. A. Kolyshkin, and M. S. Ghidaoui, "Gravitational and shear
instabilities in compound and composite channels," Journal of
Hydraulic Engineering ASCE, vol. 128, pp. 1076-1086, 2002.
[5] B. C. van Prooijen, and W. S. J. Uijttewaal, "A linear approach for the
evolution of coherent structures in shallow mixing layers," Physics of
Fluids, vol. 14, pp. 4105-4114, 2002.
[6] V. H. Chu, and S. Babarutsi, "Confinement and bed-friction effects in
shallow turbulent mixing layers," Journal of Hydraulic Engineering
ASCE, vol. 114, pp. 1257-1274, 1988.
[7] W. S. J. Uijttewaal, and J. Tukker, "A linear approach for the evolution
of coherent structures in shallow mixing layers," Experiments in Fluids,
vol. 24, pp. 192-200, 1998.
[8] W. S. J. Uijttewaal, and R. Booij, "Effect of shallowness on the
development of free-surface mixing layers," Physics of Fluids, vol. 12,
pp. 392-402, 2000.
[9] W. W. Liou, "Linear instability of curved free shear layers," Physics of
Fluids, vol. 6, pp. 541-549, 1993.
[10] F.Q. Hu, S.R. Otto, and T.L. Jackson, "On the stability of a curved
mixing layer," in Proc. ICASE Workshop on Transition, Turbulence and
Combustion, T.R. Gatski, M.Y. Hussaini, and T.L. Jackson, Eds. New
York: Kluwer, 1993, pp. 107-116.
[11] M. M. Gibson, and B. A. Jounis, "Turbulence measurements in a
developing mixing layer with mild destabilizing curvature," Experiments
in Fluids, vol. 1, pp. 23-30, 1983.
[12] C. Godréche, and P. Manneville, Hydrodynamics and nonlinear
instabilities, Cambridge, Cambridge University Press, 1998.
[13] A. A. Kolyshkin, and S. Nazarovs, "Stability of slowly diverging flows
in shallow water," Mathematical modeling and analysis, no. 1, pp. 101-
106, 2007.
[14] D. Crighton, and M. Gaster, "Stability of slowly diverging jet flow,"
Journal of Fluid Mechanics, vol. 77, pp. 397-413, 1976.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:64148", author = "Irina Eglite and Andrei A. Kolyshkin", title = "The Effect of Slow Variation of Base Flow Profile on the Stability of Slightly Curved Mixing Layers", abstract = "The effect of small non-parallelism of the base flow
on the stability of slightly curved mixing layers is analyzed in the
present paper. Assuming that the instability wavelength is much
smaller than the length scale of the variation of the base flow we
derive an amplitude evolution equation using the method of multiple
scales. The proposed asymptotic model provides connection between
parallel flow approximations and takes into account slow
longitudinal variation of the base flow.", keywords = "shallow water, parallel flow assumption, weaklynonlinear analysis, method of multiple scales", volume = "5", number = "4", pages = "694-4", }