S. N. Aristov

Bio: S. N. Aristov is an academic researcher from Russian Academy of Sciences. The author has contributed to research in topics: Navier–Stokes equations & Couette flow. The author has an hindex of 12, co-authored 24 publications receiving 359 citations. Previous affiliations of S. N. Aristov include Uppsala University.

Exact solutions of the Navier-Stokes equations with the linear dependence of velocity components on two space variables

Abstract: A wide class of two-dimensional and three-dimensional steady-state and non-steady-state flows of a viscous incompressible fluid is considered. It is assumed that the components of the velocity of a fluid linearly depend on two spatial coordinates. The three-dimensional Navier-Stokes equations in this case are reduced to a closed determining system that consists of six equations with partial derivatives of the third and second orders. A brief review of the known exact solutions of this system and the respective flows of a fluid (Couette-Poiseuille, Ekman, Stokes, Karman, and other flows) is given. The cases of reducing a determining system to one or two equations are described. Many new exact solutions of two-dimensional and three-dimensional nonstationary Navier-Stokes equations containing arbitrary functions and arbitrary parameters are derived. Periodic (both in spatial coordinates and in time) and some other solutions that are expressed in terms of elementary functions are described. The problems of the nonlinear stability of solutions are studied. A number of new hydrodynamic problems are considered. A general interpretation of the solutions as the main terms of the Taylor series expansion in terms of radial coordinates is given.

A new class of exact solutions for three-dimensional thermal diffusion equations

Abstract: A new class of exact solutions has been obtained for three-dimensional equations of themal diffusion in a viscous incompressible liquid. This class enables the description of the temperature and concentration distribution at the boundaries of a liquid layer by a quadratic law. It has been shown that the solutions of the linearized set of thermal diffusion equations can describe the motion of a liquid at extreme points of hydrodynamic fields. A generalization of the classic Couette flow with a quadratic temperature and concentration distribution at the lower boundary has been considered as an example. The application of the presented class of solutions enables the modeling of liquid counterflows and the construction of exact solutions describing the flows of dissipative media.

Unsteady layered vortical fluid flows

Abstract: An exact time-dependent solution of the system of Navier–Stokes equations governing large-scale viscous vortical incompressible flows is derived The solution generalizes that describing the Couette flow Two ways of preassigning the boundary conditions at the upper boundary of a fluid layer are considered These are the time-dependent variation of the velocity value with the conservation of its direction and the variation of the angle at which the velocities parallel to the coordinate axes are directed It is shown that at certain values of vorticity, viscosity, and the layer thickness the velocities within the layer can be severalfold greater than the given velocity at the boundary

On the upper layer circulation in the Alboran Sea

Abstract: We present new experimental results and assemble them with previous results in order to develop an improved picture of the upper layer circulation in the Alboran Sea. It is suggested that the key idea to understanding this upper layer circulation is the tendency of the Atlantic jet (AJ) to have negative curvature. Local interactions with the western Alboran gyre (WAG) or the African coast can, however, counterbalance this tendency and modify the anticyclonic path of the AJ. It is also proposed that the density gradients in the WAG can be maintained in part by means of an intermittent surface cross-gyre current which results in an input, mixing, and renewal of Atlantic water. The static stability at the bottom of the gyre increases because of the mixing of Atlantic water with Western Mediterranean Deep Water which is uplifted close to the African coast. This mixing process thereby acts as a local source of potential vorticity. We also report the existence in the Alboran Sea of subsurface anticyclonic eddies (located between 100 and 400 m) of relatively cold water that appear to be detached from the Iberian shelf. Regarding the large-scale variability of the AJ-WAG system, we present evidence of an eastward migration of the WAG and the subsequent formation of a new anticyclonic gyre in the western Alboran basin on a timescale of 1 month. This eastward gyre migration process temporarily allows the simultaneous presence of three anticyclonic gyres in the Alboran Sea.

A new class of exact solutions for three-dimensional thermal diffusion equations

Abstract: A new class of exact solutions has been obtained for three-dimensional equations of themal diffusion in a viscous incompressible liquid. This class enables the description of the temperature and concentration distribution at the boundaries of a liquid layer by a quadratic law. It has been shown that the solutions of the linearized set of thermal diffusion equations can describe the motion of a liquid at extreme points of hydrodynamic fields. A generalization of the classic Couette flow with a quadratic temperature and concentration distribution at the lower boundary has been considered as an example. The application of the presented class of solutions enables the modeling of liquid counterflows and the construction of exact solutions describing the flows of dissipative media.

Plane Marangoni-Poiseille flow of two immiscible fluids

Abstract: Abstract Plane Poiseuille flow of two immiscible fluids in a non-isothermal “capillary” channel under the combined action of pressure gradients, gravitational fields and surface tension gradients is studied. Conditions for attaining a Poiseuille-type regime are derived. Closed form solutions are obtained and discussed.