This work is concerned with the ill-posed inverse problem of estimating turbulent flows from the observation of an image sequence. From a Bayesian perspective, a divergence-free isotropic fractional Brownian motion (fBm) is chosen as a prior model for instantaneous turbulent velocity fields. This self-similar prior characterizes accurately second-order statistics of velocity fields in incompres...

We devise and analyze a new local discontinuous Galerkin (LDG) method for the Stokes equations of incompressible fluid flow. This optimally convergent method is obtained by using an LDG method to discretize a vorticity-velocity formulation of the Stokes equations and by applying a new hybridization to the resulting discretization. One of the main features of the hybridized method is that it pro...

In this paper we propose a new motion estimator for image sequences depicting fluid flows. The proposed estimator is based on the Helmholtz decomposition of vector fields. This decomposition consists in representing the velocity field as a sum of a divergence free component and a curl free component. The objective is to provide a low-dimensional parametric representation of optical flows by dep...

In a natural environment, saccade and vergence eye movements shift gaze in different directions and distances. In a laboratory setting, targets can be positioned precisely to elicit symmetrical vergence movements; however, saccades occur during the vergence movement even though the stimulus should not stimulate a saccadic response. These saccades may facilitate the response when the kinematics ...

In this paper, we study a system of equations that is known to extend Navier-Stokes dynamics in a well-posed manner to velocity fields that are not necessarily divergencefree. Our aim is to contribute to an understanding of the role of divergence and pressure in developing energy estimates capable of both controlling the nonlinear terms, and being useful at the time-discrete level. We address q...

In this work an approach is described to efficiently reduce inaccuracies of flow data acquired with reduced data acquisition methods based on the physical prior knowledge of zero divergence in 3D velocity vector fields. The divergence-free condition is implemented using a synergistic combination of normalized convolution and divergence-free radial basis functions. The efficacy of the method is ...

This paper describes an innovative approach to estimate motion from image observations of divergence-free flows. Unlike most stateof-the-art methods, which only minimize the divergence of the motion field, our approach utilizes the vorticity-velocity formalism in order to construct a motion field in the subspace of divergence free functions. A 4DVAR-like image assimilation method is used to gen...

We investigate the existence of weak solutions to a certain system partial differential equations, modeling behavior compressible non-Newtonian fluid for small Reynolds number. construct despite lack L ∞ $$ {L}^{\infty } estimate on divergence velocity field. The result was obtained by combining regularity theory singular operators with logarithmic integral inequality B M O BMO functions, which...

Divergence-free vector field interpolants properties are explored on uniform and scattered nodes, and also their application to fluid flow problems. These interpolants may be applied to physical problems that require the approximant to have zero divergence, such as the velocity field in the incompressible Navier-Stokes equations and the magnetic and electric fields in the Maxwell’s equations. I...

This paper studies the influence of convection by periodic or cellular flows on the effective diffusivity of a passive scalar transported by the fluid when the molecular diffusivity is small. The flows are generated by two-dimensional, steady, divergence-free, periodic velocity fields.