Vortex Images and q-Elementary Functions
نویسنده
چکیده
In the present paper problem of vortex images in annular domain between two coaxial cylinders is solved by q-elementary functions. We show that all images are determined completely as poles of q-logarithmic function, where dimensionless parameter q = r 2/r 2 1 is determined by square ratio of the cylinder radiuses. The resulting solution for the complex potential is represented in terms of the Jackson q-exponential function. By composing pairs of q-exponents as the first Jacobi theta function and conformal mapping to rectangular domain we link our solution with result of Johnson and McDonald. We found that one vortex cannot remain at rest except at the geometric mean distance, but must orbit the cylinders with constant angular velocity which is related with q-geometric series. Vortices in two particular geometries in q → ∞ limit are studied.
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تاریخ انتشار 2008