Nonlinearity of energy of Rankine flows on a torus

✍ Scribed by M. Ito; M. Shiba

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 409 KB
• Volume: 47
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/s0362-546x(01)00651-4

✦ Synopsis

We study an ideal fluid flow on a torus described by the Weierstrass (\zeta)-function. In spite of the analogy of this function to the Joukowski transformation on the plane the convex (planar) domain bounded by two streamlines passing through the stagnation points is not a disk. The energy of the flow outside the convex domain is generally nonlinear function of the strength of the dipole; in fact the energy is in only two cases a linear function of the strength, and otherwise it is a quadratic function.