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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

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
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