Cascades of turbulent kinetic energy and multicomponent scalars in a momentum-scalar coupling turbulence driven by multiple mechanisms under homogeneous and isotropic hypotheses

Abstract

Momentum-scalar coupling turbulence, a phenomenon observed in both natural and engineering contexts, involves the intricate interaction between multicomponent scalars and multiscale forces (i.e., multiple coupling mechanisms), resulting in a wide array of manifestations. Despite its importance, limited research has been conducted to comprehend the influence of these multicomponent and multiple coupling mechanisms on turbulence cascades. Hence, this study aims to provide a preliminary and theoretical exploration into how these multiple coupling mechanisms govern the cascades of turbulent kinetic energy and multicomponent scalars. To simplify the mathematical analysis, homogeneous and isotropic hypotheses of flow field have been applied. The key findings of this study can be summarized as follows. The first is validation of quad-cascade processes. The second is an examination of various cases involving single scalar components but multiple coupling mechanisms. Of particular interest is the coexistence of buoyancy-driven turbulence and electrokinetic turbulence, which introduces a new variable flux (VF) subrange resulting from their nonlinear interaction. Another extension considers an exponential modulation function, equivalent to the coexistence of multiple coupling mechanisms acting on a single scalar. The study identifies two new VF subranges. Third, binary scalar components and coupling mechanisms are investigated, indicating coupling mechanisms with significantly different strengths that can also induce complex interactions and new VF subranges. Fourth is the complexity when three or more different scalar components and coupling mechanisms coexist simultaneously: with the exception of certain special cases, closure of the problem becomes unattainable. This highlights the challenges inherent in addressing the simultaneous presence of multiple scalar components and coupling mechanisms. This research endeavor illuminates the theoretical understanding of the diverse scaling properties observed in momentum-scalar coupling turbulence across different scenarios.