Non-uniqueness Of Flow Research Articles

Flow Theory for Sand During Rotation of Principal Stress Direction

The paper presents the results of a series of tests using the hollow cylindrical apparatus on the flow of sand during loadings involving rotation of principal stress direction. The results establish an important feature of the flow of sand during principal stress rotation, namely, nonuniqueness of flow or the dependency of the plastic strain increment direction on the stress increment direction. This feature contradicts the usual assumption in plasticity theory of a unique flow during loadings causing plastic deformations in a material. Guided by the results of the experiments, a plastic potential theory capable of representing the dependency of the flow of sand on the stress increment direction is proposed. Comparisons with the experimental results and the outcome of stress probe experiments show the validity of the proposed theory.

Two-dimensional wave regimes in a thin layer of a viscous fluid

uniqueness of fluid flows in rotating spherical layers," Dokl. Akad. Nauk SSSR, 241, 52 (1978). 7. N. M. Astaf'eva and I. M. Yavorskaya, "The numerical study of nonlinear axisymmetric motions of fluid in spherical layers," in: Numerical Methods in the Dynamics of a Viscous Fluid [in Russian], Novosibirsk (1979), pp. 3-14. 8. I. M. Yavorskaya and N. M. Astaf'eva, "Numerical analysis of the stability and nonuniqueness of spherical Couette flow," Proc. Third GA_MM--Conf. on numerical methods in fluid mechanics, 1979; in: Notes Numer. Fluid Mech., No. 2 (1980), pp. 305-315. 9. F. Bartels and E. Krause, "Taylor vortices in spherical gaps," Laminar-turbuie1~t transition Symposium, Stuttgart, 1979, Springer-Verlag, Berlin (1980), pp. 415--425. i0. F. Bartels, "Taylor vortices between two concentric rotating spheres," J. Fluid Mech., 119, 1 (1982). Ii. N. M. Astaf'eva and V. A. Parshev, "The numerical solution of the Navier--Stokes equations in problems with spherical geometry," in: Numerical Methods in the Mechanics of a Continuous Medium, Vol. 9 [~n Russian], Novosihirsk (1978), pp. ].2-18. 12. I. M. Yavorskaya, Yu. N. Belyaev, and A. A. Monakhov, "The experimental study of spherical Couette flow," Dokl. Akad. Nauk SSSR, 221, 1059 (1975). 13. Yu. N. Belyaev, A. A. Monakhov, and I. M. Yavorskaya, "The stability of spherical Couette flow in thick layers during rotation of the internal sphere," Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 2, 9 (1978). 14. Yu. N. Belyaev, A. A. Monakhov, G. N. Khlebutin, and I. M. Yavorskaya, "The stability and non-uniqueness of flow in rotating spherical layers," Preprint No. 567 [in Russian], Institute of Cosmic Research, USSR Academy of Sciences, Moscow (1980).