Quad-cascade picture of electrokinetic turbulence

Turbulence, ubiquitous in nature and across various disciplines, exhibits chaotic and intermittent fluctuations in space and time, defying precise prediction. For nearly a century, extensive efforts have been made to uncover the underlying universality and invariant laws from the immense disorder and chaotic nature of turbulence. While the celebrated Kolmogorov −5/3 law stands as a robust cornerstone, it falls short in capturing the diverse scaling behavior exhibited in turbulence influenced by external volume forces, like thermal convection and electrokinetic flows. This study proposes a general framework that couples the fluxes of kinetic energy and scalar variance, culminating in the formulation of a universal conservation law. This framework offers a comprehensive quad-cascade depiction of turbulence, enabling predictions that go beyond the limitations of existing models. We illustrate this framework with microfluidic experiments on electrokinetic turbulence, wherein power spectra of concentration and velocity fluctuations exhibit the predicted scaling behaviors, providing remarkable agreement with theory. These findings not only deepen our understanding of the complete cascades in turbulence driven by external volume forces but also hold promise for insights into other turbulent phenomena.