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The Lecture Notes in Physics Part 3

Vật lý có quan hệ mật thiết với toán học. Các lý thuyết vật lý là bất biến khi biểu diễn dưới dạng các quan hệ toán học, và sự xuất hiện của toán học trong các thuyết vật lý cũng thường phức tạp hơn trong các ngành khoa học khác. | 32 G.J.F. van Heijst Fig. 1.24 Sequence of dye-visualization pictures showing the evolution of two counter-rotating pancake vortices released at small separation distance from 26 they created vortices by the tangential-injection method while they systematically changed the distance between the confining cylinders. A remarkable result was obtained for counter-rotating vortices at the closest possible separation distance viz. with the cylinders touching. After vertically withdrawing the cylinders the vortices showed an interesting behaviour shown by the sequence of dye-visualization pictures displayed in Fig. 1.24. Apparently the two monopolar vortices finally give rise to two dipole structures moving away from each other. The explanation for this behaviour lies in the fact that the vortices generated with this tangential-injection device are isolated i.e. their net circulation is zero because of the no-slip condition at the inner cylinder wall each vortex has a vorticity core surrounded by a ring of oppositely signed vorticity. The dye visualization clearly shows that the cores quickly combine into one dipolar vortex while the shields of opposite vorticity are advected forming a second weaker dipolar vortex moving in opposite direction. 1 Dynamics of Vortices in Rotating and Stratified Fluids 33 1.3 Concluding Remarks In the preceding sections we have discussed some basic dynamical features of vortices in rotating fluids Sect. 1.1 and stratified fluids Sect. 1.2 . By way of illustration of the theoretical issues a number of laboratory experiments on vortices were highlighted. Given the scope of this chapter we had to restrict ourselves in the discussion and the selection and presentation of the material was surely biased by the author s involvement in a number of studies of this type of vortices. For example much more can be said about vortex instability. What about the dynamics of tall vortices in a stratified fluid What about interactions of pancake-shaped .