  Spontaneous emergence of periodic oscillations due to self-organization is
ubiquitous in turbulent flows. The emergence of such oscillatory instabilities
in turbulent fluid mechanical systems is often studied in different
system-specific frameworks. We uncover the existence of a universal scaling
behaviour during self-organization in turbulent flows leading to oscillatory
instability. Our experiments show that the spectral amplitude of the dominant
mode of oscillations scales inversely with the Hurst exponent of a fluctuating
state variable following an inverse power law relation. Interestingly, we
observe the same power law behaviour with a constant exponent near -2 across
various turbulent systems such as aeroacoustic, thermoacoustic and aeroelastic
systems.
