Scale-invariant fluxes are the defining property of turbulent cascades, but their direct measurement is a notorious problem. Here we perform such a measurement for a direct energy cascade in a turbulent quantum gas. Using a time-periodic force, we inject energy at a large lengthscale and generate a cascade in a uniformly-trapped Bose gas. The adjustable trap depth provides a high-momentum cutoff $k_{\textrm{D}}$ , which realises a synthetic dissipation scale. This gives us direct access to the particle flux across a momentum shell of radius $k_{\textrm{D}}$ , and the tunability of $k_{\textrm{D}}$ allows for a clear demonstration of the zeroth law of turbulence. Moreover, our time-resolved measurements give unique access to the pre-steady-state dynamics, when the cascade front propagates in momentum space.Scale-invariant fluxes are the defining property of turbulent cascades, but their direct measurement is a notorious problem. Here we perform such a measurement for a direct energy cascade in a turbulent quantum gas. Using a time-periodic force, we inject energy at a large lengthscale and generate a cascade in a uniformly-trapped Bose gas. The adjustable trap depth provides a high-momentum cutoff $k_{\textrm{D}}$, which realises a synthetic dissipation scale. This gives us direct access to the particle flux across a momentum shell of radius $k_{\textrm{D}}$, and the tunability of $k_{\textrm{D}}$ allows for a clear demonstration of the zeroth law of turbulence. Moreover, our time-resolved measurements give unique access to the pre-steady-state dynamics, when the cascade front propagates in momentum space.

Jan 15, 201918 citations

k_{\textrm{D}}

, which realises a synthetic dissipation scale. This gives us direct access to the particle flux across a momentum shell of radius

k_{\textrm{D}}

, and the tunability of

k_{\textrm{D}}

allows for a clear demonstration of the zeroth law of turbulence. Moreover, our time-resolved measurements give unique access to the pre-steady-state dynamics, when the cascade front propagates in momentum space.