The subcritical transition to turbulence of Faraday waves in miscible fluids

We study the development and the breaking process of standing waves at the interface between two miscible fluids of small density contrast. In our experiment, a subharmonic wave is generated by a time-periodic vertical acceleration via the Faraday instability. It is shown that its wavelength may be selected not only by the linear process predicted by the Floquet theory and favouring the most unstable modes allowed by the tank geometry, but also by a nonlinear mode competition mechanism giving the preference to subcritical modes. Subsequently, as the standing wave amplitude grows, a secondary destabilization process occurs at smaller scales and produces turbulent mixing at the nodes. We explain this phenomenon as a subcritical parametric resonance instability. Different approaches derived from local and global stability analysis are proposed to predict the critical wave steepness. These theories are then assessed against various numerical and experimental data varying the frequencies and amplitudes of the forcing acceleration.

Automated summary

This study investigates the development and breaking process of standing waves at the interface between two miscible fluids with small density contrast. Experimental findings reveal that the wavelength of the standing waves is determined not only by linear processes and tank geometry, but also by nonlinear mode competition mechanism. Another destabilization process occurs at smaller scales as the standing wave amplitude grows, leading to turbulent mixing at the nodes. Various approaches using local and global stability analysis are proposed to predict the critical wave steepness.