We consider incompressible Navier-Stokes equations in a bounded 3D regular domain, coupled with the so-called dynamic boundary condition. rigorously establish principle of linearized stability. Namely, given smooth stationary state, we prove that equation has complete basis generalized eigenfunctions, and non-linear stability depends on supremum real part spectrum usual way. work class weak sol...

We consider a fluid-structure interaction system composed by rigid ball immersed into viscous in-compressible fluid. The motion of the structure satisfies Newton laws and fluid equations are standard Navier-Stokes system. At boundary domain, we use Tresca conditions, that permit to slip tangentially on under some conditions stress tensor. More precisely, there is threshold determining if can or...

An artificial dissipation scheme using the concepts of SLIP and CUSP is implemented on top of a baseline three-dimensional turbomachinery flow code. The original baseline code uses a finite-volume method for the Navier-Stokes equations with classical Jameson-Schmidt-Turkel(JST) scalar dissipation scheme. This paper focuses on the comparison of the performance of the CUSP scheme with the origina...

We consider the problem of oscillation damping in air of a thermally actuated microlever as it gradually approaches an infinite wall in parallel geometry. As the gap is decreased from 20 microm down to 400 nm, we observe the increasing damping of the lever Brownian motion in the fluid laminar regime. This manifests itself as a linear decrease in the lever quality factor accompanied by a dramati...

This investigation deals with the combined effects of Navier slip, suction/injection, convective cooling and temperature dependent viscosity on an unsteady third grade fluid flow in a porous channel filled with saturated porous medium. The heat exchange with the ambient at the channel surfaces is assumed to obey Newton’s law of cooling. The model equations governing the flow system are solved u...

In this paper we present several results from our recent work 1] concerning feedback control of the three-dimensional Navier-Stokes system on a bounded domain with non-slip boundary conditions. The feedback is introduced in the form of an additional nonlinear viscosity term which is nonvanishing only on a subdomain of the main domain and is proportional to the energy dissipation functional on t...

Exact coherent structures are three-dimensional, nonlinear traveling wave solutions of the Navier-Stokes equations. These solutions are typically unstable from onset, yet they capture the basic statistical and structural features of low Reynolds number turbulent shear flows remarkably well. These exact coherent structures have now been found in all canonical shear flows: plane Couette, Poiseuil...