On the diffusion of a rigid viscoplastic vortex layer

    Received 27 November 2017; accepted 20 December 2017

    2018, Vol. 14, no. 1, pp.  63-67

    Author(s): Georgievsky D. V.

    This paper is concerned with obtaining the parameters of a nonsteady shear rigid viscoplastic flow in a half-plane initially at rest. Beginning with the initial time moment, the constant tangent stress exceeding a yield stress is given on the boundary. The diffusion-vortex solution holds true inside an extending layer with an a priori unknown boundary. The remaining half-plane is immovable in this case. A two-dimensional picture of disturbances is imposed on the obtained flow; the picture may then evolve over time. The upper estimates of velocity disturbances by the integral measure of the space $H_2$ are constructed. It is shown that, in a certain range of parameters, the estimating function may decrease up to some point of minimum and only then increase exponentially. The fact of its initial decrease is interpreted as a stabilization of the main flow on a finite time interval.
    Keywords: viscoplastic solid, rigid domain, yield stress, diffusion, vortex layer, nonsteady shear, disturbance, quadratic functional
    Citation: Georgievsky D. V., On the diffusion of a rigid viscoplastic vortex layer, Rus. J. Nonlin. Dyn., 2018, Vol. 14, no. 1, pp.  63-67

    Download File
    PDF, 273.08 Kb


    [1] Георгиевский Д. В., “Диффузия разрыва касательного напряжения на границе вязкопластической полуплоскости”, ПММ, 70:5 (2006), 884–892; Georgiyevskii D. V., “The diffusion of a discontinuity of the shear stress at the boundary of a viscoplastic half-plane”, J. Appl. Math. Mech., 70:5 (2006), 796–803  crossref
    [2] Козырев О. Р., Степанянц Ю. А., “Метод интегральных соотношений в линейной теории гидродинамической устойчивости”, Механика жидкости и газа: Сб. ст., Итоги науки и техн. Сер. Механика жидкости и газа, 25, ВИНИТИ, Москва, 1991, 3–89 [Kozyrev O. R., Stepanyants Yu. A., Method of integral relations in the linear theory of hydrodynamical stability, VINITI, Moscow, 1991 (Russian)]
    [3] Георгиевский Д. В., “Устойчивость нестационарного сдвига среды Бингама в плоcком слое”, ПММ, 2018 (в печати); Georgiyevskii D. V., “Stability of the nonsteady shear of the Bingham medium in plane layer”, J. Appl. Math. Mech., 2018 (to appear)

    Creative Commons License
    This work is licensed under a Creative Commons Attribution-NoDerivs 3.0 Unported License