Related papers: Vortex boundaries as barriers to diffusive vortici…
Complex spatial and temporal structures are inherent characteristics of turbulent fluid flows and comprehending them poses a major challenge. This comprehesion necessitates an understanding of the space of turbulent fluid flow…
Vorticity plays a prominent role in the dynamics of incompressible viscous flows. In two-dimensional freely decaying turbulence, after a short transient period, evolution is essentially driven by interactions of viscous vortices, the…
We study the two-dimensional stationary Navier-Stokes equations describing the flows around a rotating obstacle. The unique existence of solutions and their asymptotic behavior at spatial infinity are established when the rotation speed of…
We use the recent frame-indifferent theory of diffusive momentum transport to identify internal barriers in wall-bounded turbulence. Formed by the invariant manifolds of the Laplacian of the velocity field, the barriers block the viscous…
We show that a vortex matter, that is a dense assembly of vortices in an incompressible two-dimensional flow, such as a fast rotating superfluid or turbulent flows with sign-like eddies, exhibits (i) a boundary layer of vorticity (vorticity…
As a model for vortex-wall interactions, we consider the two-dimensional incompressible Navier--Stokes equations in the half-plane $R^2_+$ with no-slip boundary condition and point vortices as initial data. We focus on the paradigmatic…
Large-eddy simulations of a flat-plate boundary layer, without a leading edge, subject to multiple levels of incoming free stream turbulence are considered in the present work. Within an input-output model where non-linear terms of 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 consider the inviscid limit for the two-dimensional incompressible Navier-Stokes equation in the particular case where the initial flow is a finite collection of point vortices. We suppose that the initial positions and the circulations…
Consider the steady neutron transport equation in 2D convex domains with in-flow boundary condition. In this paper, we establish the diffusive limit while the boundary layers are present. Our contribution relies on a delicate decomposition…
We present experimental and theoretical results on formation of quantum vortices in a laser beam propagating in a nonlinear medium. Topological constrains richer than the mere conservation of vorticity impose an elaborate dynamical behavior…
We investigate a mechanism to manipulate wall-bounded flows whereby wave-like undulations of the wall topography drives the creation of bespoke longitudinal vortices. A resonant interaction between the ambient vorticity of the undisturbed…
Fractional Navier-Stokes equations -- featuring a fractional Laplacian -- provide a `bridge' between the Euler equations (zero diffusion) and the Navier-Stokes equations (full diffusion). The problem of whether an initially smooth flow can…
Vortex is a central concept in the understanding of turbulent dynamics. Objective algorithms for the detection and extraction of vortex structures can facilitate the physical understanding of turbulence regeneration dynamics by enabling…
To produce a vortex, a torque must be applied to the fluid. In viscous fluids, the torques that produce turbulent vortices result from the loss of symmetry of the stress tensor, once the viscous friction exceeds the shear stress resistance…
In this paper, the solutions of Navier-Stokes equations with Dirichlet boundary conditions governing 2-D incompressible fluid flows are considered. A condition for boundary layer separation, which is determined by initial values and…
We formulate a quantum theory of vorticity (hydro)dynamics on a general two-dimensional bosonic lattice. In the classical limit of a bosonic condensate, it reduces to conserved plasma-like vortex-antivortex dynamics. The nonlocal…
This is the second of two papers devoted to the asymptotic behavior of solutions to the incompressible Navier-Stokes equations in a half-space with point vortex initial data. A major difficulty stems from the interaction between the point…
In fairly general conditions we give explicit (smooth) solutions for the potential flow. We show that, rigorously speaking, the equations of the fluid mechanics have not rotational solutions. However, within the usual approximations of an…
The question of whether significant sub-volumes of a turbulent flow can be identified by automatic means, independently of a-priori assumptions, is addressed using the example of two-dimensional decaying turbulence. Significance is defined…