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In this short review we examine two interesting aspects of the two-dimensional dynamics. On the one hand, we document the non-homogeneous/non-local description of the two-dimensional flows. On the other hand, we discuss the anomalous energy transfer properties of the non-linear term of the 2D Navier-Stokes equations induced by the nonlocal dynamics.
This paper presents a selection of numerical methods among the most currently used to solve the Navier Stokes equation in a vorticity formulation. The paper focuses on the connection that exists between vorticity boundary condition and the divergence free condition. The different methods has been cast in two classes : the methods which are based on divergence free approximations of the vorticity fields,...
A theoretical overview of local flow models such as hyperbolic point flows or localized vorticity structures is presented. Vortex layers and tubes are particularly emphazised. Various exact Navier-Stokes or Euler solutions are introduced to analyse generic features of vorticity dynamics: vorticity gradients, vorticity stretching, interplay between axial and azimuthal vorticity, effect of a large scale...
We study the structure, dynamics, and the instabilities of a stretched vortex in two different experiments: The first experiment generates a vortex by stretching the vorticity of a laminar boundary layer on a plane wall in a water channel. The second experiment generates a vortex between two co-rotating discs with a suction through a hole in the center of each disc. These vortices model the filaments...
The local injection of a viscoelastic liquid into the vortex street produced by a circular cylinder drastically modifies its two- and three-dimensional structure. At low injection rates, a stabilization of mode A (3D instability) is observed while the primary wavelength of the vortex street (2D instability) remains identical to that of the Newtonian case. There is also a flattening of the vortices...
The present study is aimed at understanding the mechanisms which lead coherent vortex structures to burst, as observed in fully turbulent flows [2]. A single structure is considered here, modeled by a Batchelor-vortex flow. The linear and nonlinear evolution of an initially localized perturbation is followed by DNS. As already known [5], the flow is linearly unstable towards helicoidal disturbances...
Understanding decaying two-dimensional turbulence has important consequences for geophysics,meteorology and astrophysics. Various aspects appear in a recurrent way: from an initially unorganized two-dimensional flow, vorticity rapidly concentrates in localized regions called coherent structures and also in vorticity filaments. In this framework,the computation of a nonlinear equilibrium between the...
The instability of a vortex subject to a stationary n-fold constraint is studied experimentally. Such a vortex is obtained by the rotation of a deformable cylinder wall on which two or three rolls are pressed. The two control parameters of the flow are the aspect ratio and the Reynolds number. Different regimes of instability are observed in the parameter space. The wavelength and frequency of the...
Airplane trailing vortices have a destabilizing effect on ensuing aircrafts. Security spacings,related to the trailing vortices “lifetime” are actually enforced between take-offs and landings. This spacing limits the maximum take-o. and landing frequency in saturated airports [19]. A number of studies have been devoted to the understanding of vortex wake dynamics,usually modeled by a pair of counterrotating...
Most of flows found in nature belong to the class of spatially developing open flows. In this hydrodynamic class,fluid particles enter and leave the flow boundaries of the observation domain continuously. It is the case of boundary layers [1],jets [3,4] and notably wakes [5]. Actually,concepts of absolute and convective instability have proved to be useful to classify the different types of...
The elliptic instability developing in a laminar vortex pair with a high ratio of the vortex core size to the separation distance between the vortices is studied by direct numerical simulations. The computations allows the prediction of both the linear regime of the instability development and the non-linear regime including the transition to a locally turbulent flow.
Two distinct mechanisms of three-dimensional instability in compressible planar vortices in an ideal gas are presented. Both mechanisms have been obtained with the geometrical optics (WKB) stability theory which consists in studying the evolution of short-wavelength disturbances localized along the trajectories of the vortex. The first one corresponds to parametric resonances arising when a vortex...
The dynamics of a pair of parallel counter-rotating vortices has been the object of a large number of studies in the last three decades. The continued interest in this flow is,to a great extent,due to its relevance to the problem of aircraft trailing wakes. In addition,the counterrotating vortex pair represents one of the simplest flow configurations for the study of elementary vortex interactions,...
A new experimental device is presented, that allows to isolate and control a stretched vortex in an “infinite” medium. Acoustic measurements based on the ultrasound-flow interaction yield the main vortex characteristics (position, circulation, core size). This global and non-invasive method also allows a dynamical tracking of the vortex. Experimental results on the mean vortex characteristics as a...
We investigate experimentally the interaction between two parallel laminar vortices of equal circulation. They are created by the impulsive displacement of two flat plates in a fluid initially at rest. The temporal evolution of the pair is analyzed with dye visualizations and quantitative measurements using Particle Image Velocimetry. For low Reynolds numbers, the vortices remain two-dimensional and...
We report new results obtained with a strong laboratory vortex, generated between rotating disks with an axial stretching, providing a model of strong vortex structures present in turbulent flows. We first characterize the strength of the vortex in this geometry by means of a global pressure measurement, and give direct evidence of a mechanism of stretching saturation due to strong rotation. Pressure...
We report new observations of low-pressure filaments in a turbulent flow between counter-rotating disks [1]. Cavitation from microscopic gas bubbles seeding the water is used to probe the structure of the pressure field. The spatial structure of the low-pressure events, mainly vertical filaments standing along the disks axis, are visualized using a high speed video system. The negative tail of the...
It is known since pioneering work by Taylor [1] that vortex stretching,namely the fact that rotation is amplified by conservation of the angular momentum when the streamlines locally converge,is one of the most important mechanisms acting in vortex dynamics. The Burgers’ vortex [2] is a well-known model of stretched vortex where the stretching γ is kept constant in space and time,the meridional velocity...
A number of studies have referred to the existence of a vortex cell within an urban street canyon when ambient winds aloft are perpendicular to the street. The understanding of vortex dynamics or vorticity distribution in a such configuration is of great interest. Vortex structures play an important role in the dynamics of pollutant dispersion. This configuration was simulated by the interaction between...
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