Energy Flow of Homogeneous Isotropic Turbulence at Sub-scale Eddies

Understanding the flow of energy at the smallest eddy scale can provide insights into energy cascade. Much work has been done on investigating the energy flow at the level of the smallest eddies using different Navier-Stokes (NS) based techniques. However, resorting to NS based methods to understand the impact of the smallest eddies on the energy flow is tedious due to the strong coupling between the translational and rotational motion of the eddies. Therefore, a higher order morphing continuum theory (MCT) is employed. MCT treats the continuum not as a set of volume-less points as NS, but as a set of small-scale structures that possess their own rotational motion and inertia. The current study derives the MCT conservation laws under a translational symmetry. The resulting conservation laws reveal the existence of new routes for energy transfer among translation, rotation and internal energy. It broadens the view on the energy cascade phenomena in homogeneous isotropic turbulence as an example. The energy analysis shows that the energy flux (positive or negative) is highly dependent on the rotation of the small-scale structure as well as their translational motion.