n partial fulfillment of the requirements for the degree of 

Doctor of Philosophy in Physics 

School of Physics Thesis Dissertation Defense

Mateo Reynoso

Dr. Roman Grigoriev, School of Physics, Georgia Institute of Technology (Advisor)

Dynamical Mechanisms of Nonuniversality in 2D Turbulence in the Presence of Coherent Structures

Date: Tuesday, April 21, 2026

Time: 1:00 p.m.

Location: Howey Physics Building, Room N110 

Virtual: https://gatech.zoom.us/j/98641369716

Committee members:

Dr. Predrag Cvitanović, School of Physics, Georgia Institute of Technology

Dr. Michael Schatz, School of Physics, Georgia Institute of Technology

Dr. Alexander Blumenthal, School of Mathematics, Georgia Institute of Technology

Dr. Rafael de La Llave, School of Mathematics, Georgia Institute of Technology

Abstract:

Turbulence is one of the most important problems in physics and applied mathematics, with applications ranging from astrophysics and engineering to plumbing and more. It is fundamentally a multiscale phenomenon, characterized by cascades that dynamically transfer energy and other invariants across a wide range of length scales. While these interactions are often described through a statistical framework, a more holistic understanding requires accounting for the spatial structure of the flow. Aspects such as the coherence of large-scale structures cannot be captured by statistical assumptions alone; therefore, a more general theory for scaling in turbulence must explicitly account for the dynamical role of coherent structures.

This dissertation examines how coherent structures shape scale generation and nonuniversality in two-dimensional turbulence, with an emphasis on both the direct enstrophy cascade in steady turbulence and the inverse energy transferr in freely decaying turbulence. Although classical Kraichnan–Leith–Batchelor theory predicts universal scaling under assumptions of homogeneity, isotropy, and locality, the results presented here show that the observed scaling is instead governed by the geometry and interactions of coherent structures, often organized as large-scale flows. By combining direct numerical simulations, reduced-order modeling, and statistical closure arguments, this work demonstrates that a predictive theory of turbulence scaling must move beyond statistical assumptions and account for the transport and lifecycle of coherent structures.