UPPER ESTIMATES OF THE GROWTH OF PERTURBATIONS BY TRIAXIAL SPREADING-DRAIN IN INFINITE VISCOUS SPACE

The development over time of a system of small perturbations imposed on a triaxial homogeneous spreading-drain in an infinite three-dimensional space of a Newtonian incompressible fluid is investigated. In the first part of the work, it is assumed that the main motion is stationary and the velocity field is defined by only two constants. In this case, the linearized problem with respect to velocity and pressure perturbations is reduced to a spectral problem in which the real part of the spectral parameter is related to the nature of the exponential decay or growth of the initial perturbations. Based on the method of integral relations for quadratic functionals, an upper bound for this parameter is performed. In the second part of the paper, a more general case of unsteady triaxial spreading-drain is considered. An upper integral estimate of the growth of perturbations is derived, which includes a time function completely determined by the velocity field of the main fluid flow.

viscous fluid, spreading, drain, incompressibility, unsteady process, perturbation, method of integral relations, stability estimate, quadratic functional, Friedrichs inequalities