Universal energy spectrum in decaying quasi-two-dimensional turbulence

We study experimentally the time evolution of energy and its spectrum in decaying quasi-two-dimensional (quasi-2-D) turbulence with different damping rates gamma γ γ . The thin-layer fluid flow is forced electromagnetically and decays freely after cessation of the forcing. We found that energy does not exhibit an exponential decay associated with linear damping, but an algebraic decay which can be described by a quadratic drag model. This represents the first experimental evidence of the quadratic drag in (quasi-) 2-D turbulence. The energy spectrum upper E left parenthesis k right parenthesis E ( k ) $E(k)$ undergoes two decay stages. In the initial stage, the shape of upper E left parenthesis k right parenthesis E ( k ) $E(k)$ changes with time and is notably dependent on gamma γ γ . In the late stage, upper E left parenthesis k right parenthesis E ( k ) $E(k)$ evolves in a self-preserving manner and exhibits an unexpected universal form that is independent of gamma γ γ . This universal spectrum is characterised by a dual scaling: a k Superscript negative 3 k − 3 k⁻³ scaling at large scales and k Superscript negative 5 divided by 3 k − 5 / 3