## 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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