Related papers: On tangential stabilization in curvature driven fl…
The non-perturbative curvature inhomogeneities induced by relativistic viscous fluids are not conserved in the large-scale limit. However when the bulk viscosity is a function of the total energy density of the plasma (or of the trace of…
A novel route to instabilities and turbulence in fluid and plasma flows is presented in kinetic Vlasov-Maxwell model. New kind of flow instabilities is shown to arise due to the availability of new kinetic energy sources which are absent in…
Using extensive particle-based simulations, we investigate out-of-equilibrium pattern dynamics in an oppositely driven binary particle system in two dimensions. A surprisingly rich dynamical behavior including lane formation, jamming,…
We consider a motion of non-closed planar curves with infinite length. The motion is governed by a steepest descent flow for the geometric functional which consists of the sum of the length functional and the total squared curvature. We…
We study the stability of a type of stratified flows of the two dimensional inviscid incompressible MHD equations with velocity damping. The exponential stability for the perturbation near certain stratified flow is investigated in a…
In our previous papers we proposed a continuum model for the dynamics of the systems of self-propelling particles with conservative kinematic constraints on the velocities. We have determined a class of stationary solutions of this…
The dynamics of transitional flows are governed by an interplay between the non-normal linear dynamics and quadratic nonlinearity in the incompressible Navier-Stokes equations. In this work, we propose a framework for nonlinear stability…
In channel flows a step on the route to turbulence is the formation of streaks, often due to algebraic growth of disturbances. While a variation of viscosity in the gradient direction often plays a large role in laminar-turbulent transition…
Using dynamic models of tensegrity structures, we derive provable, distributed control laws for stabilizing and changing the shape of a formation of vehicles in the plane. Tensegrity models define the desired, controlled, multi-vehicle…
The linear stability of rapid granular flow on a slope under gravity against the longitudinal perturbation is analyzed using hydrodynamic equations. It is demonstrated that the steady flow uniform along the flow direction becomes unstable…
Turbulent fluid flows exhibit a complex small-scale structure with frequently occurring extreme velocity gradients. Particles probing such swirling and straining regions respond with an intricate shape-dependent orientational dynamics,…
A solution to a given equation is structurally stable if it suffers only an infinitesimal change when the equation (not the solution) is perturbed infinitesimally. We have found that structural stability can be used as a velocity selection…
Hydrodynamic instability of a gravity-driven flow down an inclined plane is investigated in the presence of a floating elastic plate which rests on the top surface of the flow. Linear instability of the system with respect to infinitesimal…
We introduce novel finite element schemes for curve diffusion and elastic flow in arbitrary codimension. The schemes are based on a variational form of a system that includes a specifically chosen tangential motion. We derive optimal $L^2$-…
This paper examines the linearized stability of plane Couette flow for stress-power law fluids, which exhibit non-monotonic stress-strain rate behavior. The constitutive model is derived from a thermodynamic framework using a non-convex…
Recent research has shed light on the role of coherent structures in forming layers when stably stratified turbulence is forced with horizontal shear (Lucas, Caulfield & Kerswell, J. Fluid Mech., vol. 832, 2017, pp. 409-437). Here we extend…
This article presents a modelling of the formation of spanwise vorticity in the turbulent streaks of the oblique bands and spots of transitional plane Couette flow. A functional model is designed to mimic the coherent flow in the streaks.…
Two dimensional flows on fixed smooth surfaces have been studied in the point of view of vorticity dynamics. Firstly, the related deformation theory including kinematics and kinetics is developed. Secondly, some primary relations in…
Nonlinear dynamics of fluid conveying pipe, rotating with constant velocity about its longitudinal axis is analyzed. Considering boundary conditions and internal damping, the nonlinear equation of motion is derived, and it is discretized…
We investigate the nonlinear dynamics of turbulent shear flows, with and without rotation, in the context of a simple but physically motivated closure of the equation governing the evolution of the Reynolds stress tensor. We show that the…