  Energy cascade is ubiquitous in systems far from equilibrium. Facilitated by
particle interactions and external forces, it can lead to highly complex
phenomena like fully developed turbulence, characterized by power law velocity
correlation functions. Yet despite decades of research, how these power laws
emerge from first principle remains unclear. Recently, experiments show that
when a Bose condensate is subjected to periodic shaking, its momentum
distribution exhibits a power law behavior. The flexibility of cold atom
experiments has provided new opportunities to explore the emergence of these
power laws, and to disentangle different sources of energy cascade. Here, we
point out that recent experiments in cold atoms imply that classical turbulence
is part of a larger family of scale invariant phenomena that include ideal
gases. Moreover, the property of the entire family is contained in the
structure of its Floquet states. For ideal gases, we show analytically that its
momentum distribution acquires a $1/q^2$ tail in each dimension when it is
shaken periodically.
