A.A.Gourjii, H.Peerhossaini Local stretching maps: an application for an advection problem in an arbitrary velocity field |
Applied hydromechanics, Vol. 2 (74) ¹ 1, (2000) |
| The local stirring properties of a passive fluid domain with arbitrary borders in known velocity field are discussed. Analytical solution for local stretching permits to single out an exponential coefficient that describes stretching of the domain studied and is analogous to the largest Lyapunov exponent used in chaotic dynamics. This coefficient exist in all solutions; it does not depend on the shape of the contour, and is determined by the gradients of the velocity field components only. Another local mechanism of stirring is determined by integral characteristics of the flow and the shape of contour under consideration. Construction of maps for local stretching values in fixed moments allows to analyze informatively an evolution of regions, in which an intensive stirring takes place. The stirring process is explored in a sample of an advection problem of a passive impurity in the velocity field induced by a system of point vortices moved periodically. This interaction regime generates a chaotic motion of passive fluid particles. Local stretching maps show that the regions of chaotic motion of fluid particles and of intensive stirring do not coincide. Chaotic region has a zone of weak stirring, in which contours are transported from one intensive stretching zone to another without any deformation. |
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| TEXT LANGUAGE: Russian |