We report on laboratory experiments of wave-driven rotating turbulence. A set of wave makers produces inertial-wave beams that interact nonlinearly in the central region of a water tank mounted on a rotating platform. The forcing thus injects energy into inertial waves only. For moderate forcing amplitude, part of the energy of the forced inertial waves is transferred to subharmonic waves, through a standard triadic resonance instability. This first step is broadly in line with the theory of weak turbulence. Surprisingly however, stronger forcing does not lead to an inertial-wave turbulence regime. Instead, most of the kinetic energy condenses into a vertically invariant geostrophic flow, even though the latter is unforced. We show that resonant quartets of inertial waves can trigger an instability—the “quartetic instability”—that leads to such spontaneous emergence of geostrophy. In the present experiment, this instability sets in as a secondary instability of the classical triadic instability.

中文翻译：

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波浪驱动的湍流中地球物理的捷径：二次不稳定

我们报告了波浪驱动的旋转湍流的实验室实验。一组造波器产生的惯性波光束在安装在旋转平台上的水箱的中心区域中发生非线性相互作用。因此，强迫仅将能量注入惯性波。为了获得适度的强迫振幅，通过标准的三重共振不稳定性，被强迫的惯性波的一部分能量会转换为次谐波。第一步与弱湍流理论基本相符。然而，令人惊讶的是，更强的强迫不会导致惯性波湍流状态。取而代之的是，即使动静力没有作用，大部分动能会凝结成垂直不变的地转流。我们表明，惯性波的共振四重态可以触发不稳定性，即“四次不稳定性”，从而导致地球动力学的这种自发出现。在本实验中，这种不稳定性是经典三重性不稳定性的次要不稳定性。