Resonance of the geotrophic mode in a torus. (Étude de la résonance du mode géostrophique dans un tore.) (French. Abridged English version) Zbl 0981.76102

Adou, Jérôme

C. R. Acad. Sci., Paris, Sér. II, Fasc. b, Méc. Phys. Astron. 327, No. 14, 1391-1396 (1999).

Summary: We investigate the oscillations of air contained in a pneumatic tyre; we assume that the tyre is a torus with generating circle of radius \(R\), while a characteristic size of the area of contact with ground is \(a\). We show that when \(\Omega R/c_0\ll 1\) and \(a/R\ll 1\) (here \(\Omega\) is the constant angular velocity, and \(c_0\) is sound speed), the air motion in the torus can be considered as inertial oscillations excited by a perturbation on the torus’ surface. This excitation makes one of the inertial oscillation modes resonant with the geostrophic mode, which increases proportionally to time when \(t\to\infty\).

MSC:

76U05

General theory of rotating fluids

Keywords:

air oscillations; resonance; pneumatic tyre; torus; inertial oscillations; perturbation; geostrophic mode