We derive a hierarchy of PDEs for the leading-order evolution of wall-based quantities, such as the skin-friction and the wall-pressure gradient, in two-dimensional fluid flows. The resulting Reduced Navier-Stokes (RNS ) equations are defined on the boundary of the flow, and hence have reduced spatial dimensionality compared to the Navier-Stokes equations. This spatial reduction speeds up numer...

In this paper, we study the solvability of inhomogeneous boundary value problems for the three-dimensional Oseen and Navier–Stokes equations in the following formulation: given function spaces for Dirichlet boundary conditions, initial values, and right-hand side forcing functions, find function spaces for solutions such that the operator generated by the boundary value problem for the Oseen eq...

We address the problem of the uniqueness of the particle trajectories corresponding to a weak solution of the two-dimensional Navier-Stokes equations with square integrable initial condition and regular enough forcing function. In order to do this we obtain an estimate for H-norm of the weak solutions of the Navier-Stokes equations and show that t‖D3/2u‖ is bounded which provides a bound on the...

This paper is devoted to the study of a stationary problem consisting of the Boussinesq approximation of the Navier–Stokes equations and two convection–diffusion equations for the temperature and concentration, respectively. The equations are considered in 3D and a velocity–pressure formulation of the Navier–Stokes equations is used. The problem is complicated by nonstandard boundary conditions...

This paper considers the analysis and control of fluid flows using tools from dynamical systems and control theory. The employed tools are derived from the spectral analysis of various linear operators associated with the Navier–Stokes equations. Spectral decomposition of the linearized Navier-Stokes operator, the Koopman operator, the spatial correlation operator and the Hankel operator provid...

We formulate a stochastic least-action principle for solutions of the incompressible Navier-Stokes equation, which formally reduces to Hamilton’s principle for the incompressible Euler solutions in the case of zero viscosity. We use this principle to give a new derivation of a stochastic Kelvin Theorem for the Navier-Stokes equation, recently established by Constantin and Iyer, which shows that...

For increasingly rarefied flowfields, the predictions from continuum formulation, such as the Navier–Stokes equations lose accuracy. These inaccuracies are attributed primarily to the linear approximations of the stress and heat flux terms in the Navier– Stokes equations. The inclusion of higher order terms, such as Burnett, or high-order moment equations, could improve the predictive capabilit...

In this paper, we study the dynamic stability of the 3D axisymmetric NavierStokes Equations with swirl. To this purpose, we propose a new one-dimensional (1D) model which approximates the Navier-Stokes equations along the symmetry axis. An important property of this 1D model is that one can construct from its solutions a family of exact solutions of the 3D Navier-Stokes equations. The nonlinear...

In this paper, we study the Navier-Stokes equation in which the unknown functions are the vorticity and the streamfunction. Our goal is to estimate the long-time innuence of a small error in the initial data. In order to do this, we write down the symmetrized linearized Navier-Stokes equation and we estimate the eigenvalues of the corresponding operator. A comparison between these estimates and...

In this project report I present my research and accompanying implementation of the unconditionally stable Navier-Stokes partial differential equation (PDE) solver presented to the computer graphics community by Jos Stam at the 1999 SIGGRAPH conference [Stam 1999]. I give a brief introduction to computational fluid dynamics (CFD), the governing Navier-Stokes equations and an overview of previou...