Navier–Stokes equations

About: Navier–Stokes equations is a research topic. Over the lifetime, 18180 publications have been published within this topic receiving 552555 citations. The topic is also known as: Navier-Stokes equations.

Internal stabilization of Navier-Stokes equations with finite-dimensional controllers

Abstract: The steady-state solutions to Navier-Stokes equations on Ω ⊂ R d , d = 2, 3, with no-slip boundary conditions, are locally exponentially stabilizable by a finite-dimensional feedback controller with support in an arbitrary open subset w ⊂ Ω of positive measure. The (finite) dimension of the feedback controller is related to the largest algebraic multiplicity of the unstable eigenvalues of the linearized equation.

Simulation of the motion of flexible fibers in viscous fluid flow

Abstract: A model for flexible fibers in viscous fluid flow is proposed, and its predictions compared with experiments found in the literature. The incompressible three-dimensional Navier–Stokes equations are employed to describe the fluid motion, while fibers are modeled as chains of fiber segments, interacting with the fluid through viscous and dynamic drag forces. Fiber segments, from the same or from different fibers, interact with each other through normal, frictional, and lubrication forces. Momentum conservation is enforced on the system to capture the two-way coupling between phases. Quantitative predictions could be made, and showed good agreement with experimental data, for the period of Jeffery orbits in shear flow, as well as for the amount of bending of flexible fibers in shear flow. Simulations, using the proposed model, also successfully reproduced the different regimes of motion for threadlike particles, ranging from rigid fiber motion to complicated orbiting behavior, including coiling and self-entanglement.

Statistical Structure at the Wall of the High Reynolds Number Turbulent Boundary Layer

Abstract: The paper reports on the application of the Time-dependent Reynolds-Averaged Navier-Stokes (T-RANS) approach to analysing the effects of magnetic force and bottom-wall configuration on the reorganisation of a large coherent structure and its role in the transport processes in Rayleigh-Benard convection. The large-scale deterministic motion is fully resolved in time and space, whereas the unresolved stochastic motion is modelled by a `subscale' model for which the conventional algebraic stress/flux expressions were used, closed with the low-Re number - - three-equation model. The applied method reproduces long-term averaged mean flow properties, turbulence second moments, and all major features of the coherent roll/cell structure in classic Rayleigh-Benard convection in excellent agreement with the available DNS and experimental results. Application of the T-RANS approach to Rayleigh-Benard convection with wavy bottom walls and a superimposed magnetic field yielded the expected effects on the reorganisation of the eddy structure and consequent modifications of the mean and turbulence parameters and wall heat transfer.