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Old   November 27, 1999, 12:07
Default Vortex vs Spiral
Ashok grover
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Dear All:

Is a vortex simply a collection of logarithmic spirals. If not what is the mathematical definition of a vortex or where can I find it. Thanks a million
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Old   November 28, 1999, 13:16
Default Re: Vortex vs Spiral
John Chien
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(1). The definition of a vortex, or a more general definition of the vorticity vector, can be found in any college level fluid mechanics text book. (2). For an isolated fluid flow, it is possible to talk about a vortex. But for the general flow motion, the definition of the vorticity vector field is used. The vorticity vector field is defined as the Curl vector of the velocity vector field. The Curl vector field is always perpendicular to the velocity vector field. (3). Without the vorticity (zero vorticity), the study of fluid dynamics would be pushed back at least 100 years into 19th century. In those days, the study of fluid dynamics is related to the study of potential flows, which has zero vorticity. (4). In modern days, the handling of the vortex (or vortices) can be approached in two directions, namely the continuous approach and the discret approach. The former deals with the vorticity equations, and the latter tracts the influence or motion of individual vortex. (5). Unfortunately, most current formulations in CFD applications are written in terms of the momentum equations, rather than the vorticity equations. (6). The use of the momentum equations to solve the fluid flows based on the force and momentum balance can not directly compute the vorticity of the flow field, thus is a less accurate approach than solving the vorticity equations directly. (7). I don't have a fluid dynamics text book with me right now, so, it is a good idea for you to check out one at your library.
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