We report on the structure of the scalar index-of-refraction field generated by turbulent, gas-phase, incompressible and compressible shear-layers and incompressible jets, and on associated beam-propagation aero-optical phenomena. Using simultaneous imaging of the optical-beam distortion and the turbulent-flow index-ofrefraction field, wavefront-phase functions were computed for optical beams e...

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...

We present a global existence theory for strong solution to the Cucker–Smale–Navier–Stokes system in a periodic domain, when initial data is sufficiently small. To model interactions between flocking particles and an incompressible viscous fluid, we couple the kinetic Cucker–Smale model and the incompressible Navier–Stokes system using a drag force mechanism that is responsible for the global f...

Incompressible ~magic! states that result from many-body effects in vertically coupled quantum dots submitted to strong magnetic fields such that only the lowest Landau level is relevant are studied within an exact diagonalization calculation for N53, 5, and 6, electrons. We find that the sequences of total angular momentum M for which these incompressible states exist depend on the interplay b...

The study of incompressible magnetohydrodynamic (MHD) turbulence gives useful insights on many astrophysical problems. We describe a pseudo-spectral MHD code suitable for the study of incompressible turbulence. We review our recent works on direct three-dimensional numerical simulations for MHD turbulence in a periodic box. In those works, we use a pseudo-spectral code to solve the incompressib...

In this work three branches of Immersed Boundary Methods (IBM) are described and validated for incompressible aerodynamics and fluid-structure interactions. These three approaches are: Cut Cell method, Vortex-Penalization method and Forcing method. Two first techniques are validated for external bluff-body flows and the last one is used for fluid-structure interactions. The paper confirms the a...

An incompressible surface F on the boundary of a compact orientable 3manifold M is arc-extendible if there is an arc γ on ∂M − IntF such that F ∪ N(γ) is incompressible, where N(γ) is a regular neighborhood of γ in ∂M . Suppose for simplicity that M is irreducible, and F has no disk components. If M is a product F × I, or if ∂M − F is a set of annuli, then clearly F is not arc-extendible. The m...

converge almost everywhere to a finite limit f*(x). It then follows that the limit function/* is integrable and that/*(7x) =/*(x) almost everywhere. This result can be applied to certain cases in which the given measure m is not preserved by the transformation T. In order to discuss this application, we recall some terminology for measures and transformations. If (X, S) is a measurable space, a...

A direct numerical simulation of a supersonic turbulent boundary layer has been performed. We take advantage of a technique developed by Spalart for incompressible ow. In this technique, it is assumed that the boundary layer grows so slowly in the stream-wise direction that the turbulence can be treated as approximately homogeneous in this direction. The slow growth is accounted for by a coordi...

We present and analyze a simpliied, scale-separated, anelastic uid model which is designed to assess the innuence of weak compressibility in the diiusive transport of a passive scalar. Our model incorporates a slowly varying, density induced, anisotropy into a xed, rapidly varying (small scale) uid ow. This anisotropy is physically motivated through the anelastic mass balance which retains vert...