Konstantin Shvarts
Publications:
Shvarts K. G.
PlaneParallel Advective Flow in a Horizontal Layer of Incompressible Permeable Fluid
2023, Vol. 19, no. 2, pp. 219226
Abstract
In this paper a new exact solution of the Navier – Stokes equations in the Boussinesq approximation
describing advective flow in a horizontal liquid layer with free boundaries, where the
vertical velocity component is a constant value, is obtained. The temperature is linear along the
boundaries of the layer. Solutions of this kind are used to close threedimensional equations averaged
across the layer in the derivation of twodimensional models of nonisothermal largescale
flows in a thin layer of liquid or incompressible gas. The properties of advective flow at different
values of Reynolds number and Prandtl number are investigated.

Shvarts K. G.
Advective Flow of a Rotating Fluid Layer in a Vibrational Field
2019, Vol. 15, no. 3, pp. 261270
Abstract
This paper presents a derivation of new exact solutions to the Navier – Stokes equations in
Boussinesq approximation describing two advective flows in a rotating thin horizontal fluid layer
with noslip or free boundaries in a vibrational field. The layer rotates at a constant angular
velocity; the axis of rotation is aligned with the vertical axis of coordinates. The temperature is
linear along the boundaries of the layer. The case of longitudinal vibration is considered. The
resulting solutions are similar to those describing the advective flows in a rotating fluid layer with
solid or free boundaries without vibration. In both cases, the velocity profile is antisymmetric.
Thus, in particular, in the absence of rotation, the longitudinal vibration in the presence of
advection can be considered as a kind of “onedimensional” rotation. The presence of rotation
initiates the vortex motion of the fluid in the layer. Longitudinal vibration has a stronger effect
on the xth component of the velocity than on the yth component. At large values of the Taylor
number and (or) the vibration analogue of the Rayleigh number thin boundary layers of velocity,
temperature and amplitude of the pulsating velocity component arise, the thickness of which is
proportional to the root of the fourth degree from the sum of these numbers.
