VORTEX DYNAMICS 1. Introduction

VORTEX DYNAMICS1. IntroductionA VORTEX is commonly associated with the rotating motion of uid around acommon centerline. It is de ned by thevorticityin the uid, which measuresthe rate of local uid rotation. Typically, the uid circulates around the VORTEX ,the speed increases as the VORTEX is approached and the pressure decreases. Vor-tices arise in nature and technology in a large range of sizes as illustrated by theexamples given in Table 1. The next section presents some of the mathematicalbackground necessary to understand VORTEX formation and evolution. Section 3describes sample ows, including important instabilities and reconnection pro-cesses. Section 4 presents some of the numerical methods used to simulate these uid vortices10 8cm (= 1 A)trailing VORTEX of Boeing 7271{2 mdust devils1{10 mtornadoes10{500 mhurricanes100{2000 kmJupiter's Red Spot25,000 kmspiral galaxiesthousands of light yearsTABLE 1: Sample vortices and typical BackgroundLetDbe a region in 3D space containing a uid, and letx=(x; y; z)Tbe apoint inD.}}}}

function in the plane, and the induced velocity is obtained from the Biot-Savart law. For a point vortex at the origin this reduces to the radial velocity fleld u(x)=K2d ⁄– = K2d(x). Corresponding particle trajectories are shown in Fig. 2(a). The particle speed juj =1=r increases unboundedly as the vortex center is

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  Introduction, Dynamics, Vortex, Obit, Biot savart law, Savart, Vortex dynamics 1

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