Abstract
We present a study of secondary instabilities of parametrically generated standing waves in a horizontal layer of fluid submitted to vertical vibrations. The fluid is contained in a thin annulus, and thus the basic standing wave behaves as a one-dimensional spatial structure. When the driving frequency is increased (respectively, decreased), the system bifurcates abruptly to another standing wave pattern by nucleation (respectively, annihilation) of one wavelength. When the driving amplitude is increased, the standing-wave pattern undergoes various instabilities, and in particular an oscillatory instability that corresponds to a one-dimensional compression mode of the periodic structure. This secondary instability is understood in the framework of the amplitude equation formalism.