Abstract
The modeling of turbulence cascade has been executed using a multitude of methods, among which we utilized the multifractal representation for a more precise portrayal of turbulence. Typically, energy dissipation characteristics are dictated by specific partial differential equations such as the Navier-Stokes Equations. However, in climate modeling, the Kolmogorov turbulence cascading approximation often leads to an isotropic representation. In recent years, a shift from the Kolmogorov assumptions has been proposed by Meneveau et al., advocating for multifractal models that accommodate a novel anisotropic representation. Our research is geared towards using Direct Numerical Simulations (DNS) from the JHU Turbulence Database and Large Eddy Simulations (LES) that we created via OpenFOAM. This is to ascertain the accuracy of these simulations in mirroring the experimental procedures of Meneveau, employing numerical simulations that adhere to the same rigorous mathematical paradigms. We hope that the modeling of turbulence cascading using higher fidelity data will yield advancements in the field, and generate quicker, superior remote sensing metrics. We have developed computer code to scrutinize DNS and LES data, delving into the multifractal nature of energy dissipation. We employed the box-counting method to discern the multifractal dimension spectrum of the DNS and LES data in all directions. This aligns with Meneveau's work and facilitates a more accurate representation of turbulence-cascading effects within the atmosphere.
*We acknowledge the U.S. Department of Defense (AFOSR Grant Number #FA9550-19-1-0304, FA9550-17-1-0253, FA9550-12-1-0242, FA9550-17-1-0393, SFFP, AFTC, HAFB/HSTT, AFRL, HPCMP), U.S. Department of Energy(GRANT13584020, DE-SC0022957, DE-FE0026220, DE-FE0002407, NETL, Sandia, ORNL, NREL), Systems Plus, and several other individuals at these agencies for partially supporting our research financially or through mentorship. We would also like to thank NSF ((HRD-1139929, XSEDE Award Number ACI-1053575), TACC, DOE, DoD, Microsoft, HPCMP, University of Texas STAR program, UTEP(Research Cloud, Department of Mechanical Engineering, Graduate School & College of Engineering) for generously providing financial support or computational resources. Without their generous support, completing the milestones would have been almost impossible.
