Related papers: Exact Second-Order Structure-Function Relationship…
We are concerned with the "transfer of regularity" phenomenon for the incompressible Navier--Stokes Equations (NSE) in dimension $n \geq 3$; that is, the strong solutions of NSE on $\mathbb{R}^n$ can be nicely approximated by those on…
A hydrodynamic description for an $s$-component mixture of inelastic, smooth hard disks (two dimensions) or spheres (three dimensions) is derived based on the revised Enskog theory for the single-particle velocity distribution functions. In…
We present a numerical scheme for approximating the incompressible Navier-Stokes equations based on an auxiliary variable associated with the total system energy. By introducing a dynamic equation for the auxiliary variable and…
The so-called 2/15-law for two-point, third-order velocity statistics in isotropic turbulence with helicity is computed for the first time from a direct numerical simulation of the Navier-Stokes equations in a 512^3 periodic domain. This…
We study the statistical properties of orientation and rotation dynamics of elliptical tracer particles in two-dimensional, homogeneous and isotropic turbulence by direct numerical simulations. We consider both the cases in which the…
We present a fully discrete approximation technique for the compressible Navier-Stokes equations that is second-order accurate in time and space, semi-implicit, and guaranteed to be invariant domain preserving. The restriction on the time…
The Heisenberg inequality \Delta X \Delta P \geq \hbar/2 can be replaced by an exact equality, for suitably chosen measures of position and momentum uncertainty, which is valid for all wavefunctions. The statistics of complementary…
We present results on the trace regularity of the stress vector on the boundary of an elastic solid satisfying the time-dependent, displacement-traction problem for the Navier equations of linear elasticity in a bounded domain of…
The numerical solution of the Stokes equations on an evolving domain with a moving boundary is studied based on the arbitrary Lagrangian-Eulerian finite element method and a second-order projection method along the trajectories of the…
We derive from the Navier-Stokes equation an exact equation satisfied by the dissipation rate correlation function. We exploit its mathematical similarity to the corresponding equation derived from the 1-dimensional stochastic Burgers…
By using recent developments for the Langevin dynamics of spatially asymmetric systems, we routinely generalize the Onsager-Machlup fluctuation theory of the second order in time. In this form, it becomes applicable to fluctuating…
To capture the dynamics of macroscopic non-relativistic fluids consisting of very many atoms, it is typically sufficient to truncate the gradient expansion at order zero, leading to ideal fluid dynamics, or at order one, leading to the…
The scale-invariant inverse energy cascade is a hallmark of 2D turbulence, with its theoretical energy spectrum observed in both direct numerical simulations (DNS) and laboratory experiments. Under this scale-invariance assumption, the…
We study the numerical performance of a continuous data assimilation (downscaling) algorithm, based on ideas from feedback control theory, in the context of the two-dimensional incompressible Navier--Stokes equations. Our model problem is…
In the present paper we study slow-fast systems of coupled equations from fluid dynamics, where the fast component is perturbed by additive noise. We prove that, under a suitable limit of infinite separation of scales, the slow component of…
We consider two-dimensional homogeneous shear turbulence within the context of optimal control, a multi-scale turbulence model containing the fluctuation velocity and pressure correlations up to the fourth order; The model is formulated on…
Non-local models of stellar convection can account for mixing effects in regions adjacent to convectively unstable layers and for changes to the mean temperature structure caused by free, buoyancy driven convection. The physical…
Recent analysis of the divergence constraint in the incompressible Stokes/Navier--Stokes problem has stressed the importance of equivalence classes of forces and how it plays a fundamental role for an accurate space discretization. Two…
We prove the convergence of certain second-order numerical methods to weak solutions of the Navier-Stokes equations satisfying in addition the local energy inequality, and therefore suitable in the sense of Scheffer and…
Unstable periodic orbits are believed to underpin the dynamics of turbulence, but by their nature are hard to find computationally. We present a family of methods to converge such unstable periodic orbits for the incompressible…