About interface conditions for coupling hydrostatic and nonhydrostatic Navier-Stokes flows

Comparing Hydrostatic and Nonhydrostatic Navier-stokes Models of Internal Waves

Internal waves occur at a variety of temporal and spatial scales and are mechanisms by which momentum, energy, nutrients and biota are transported in lakes, estuaries and coastal oceans. In stratified systems, accurate prediction of water quality effects requires modeling internal wave evolution and propagation. Lake, estuary, and coastal ocean models typically apply the hydrostatic approximati...

Generalized Navier - Stokes Flows

We introduce a notion of generalized Navier-Stokes flows on mani-folds, that extends to the viscous case the one defined by Brenier. Their kinetic energy extends the kinetic energy for classical Brownian flows, defined as the L 2 norm of their drift. We prove that there exists a generalized flow which realizes the infimum of kinetic energies among all generalized flows with prescribed initial a...

Stochastic Navier-Stokes Equations for Turbulent Flows

This paper concerns the fluid dynamics modelled by the stochastic flow    η̇ (t, x) = u (t,η (t, x)) + σ (t,η (t, x)) ◦ Ẇ η(0, x) = x where the turbulent term is driven by the white noise Ẇ . The motivation for this setting is to understand the motion of fluid parcels in turbulent and randomly forced fluid flows. Stochastic Euler equations for the undetermined components u(t, x) and σ(t, x) o...

Optimal Control of Navier-Stokes Fluid Flows

The Inviscid Limit and Boundary Layers for Navier-Stokes flows

The validity of the vanishing viscosity limit, that is, whether solutions of the Navier-Stokes equations modeling viscous incompressible flows converge to solutions of the Euler equations modeling inviscid incompressible flows as viscosity approaches zero, is one of the most fundamental issues in mathematical fluid mechanics. The problem is classified into two categories: the case when the phys...