Title: Dynamos in Stably Stratified Fluids Authors: Skoutnev, Valentin Advisors: Bhattacharjee, Amitava Contributors: Astrophysical Sciences—Plasma Physics Program Department Subjects: AstrophysicsPlasma physics Issue Date: 2022 Publisher: Princeton, NJ : Princeton University Abstract: While magnetic fields are thought to play a dominant role in transport processes in stellar radiative zones, present theory of radiative zone dynamos and even properties of stellar stably stratified turbulence is fragmented and incomplete. This thesis examines the fundamentals of small-scale and large-scale dynamo theory in the conditions of a stellar radiative zone: turbulence, stable stratification, and mean shear. The simultaneous operation of several effects and instabilities requires sequentially examining fluid dynamical systems of increasing complexity. A stably stratified fluid forced on a horizontal length $L$ and velocity scale $U\,$ leads to turbulence with emergent outer vertical scales and energy cascade set by the physical parameters of the fluid \{$N$, $\nu$, $\kappa$\}. These are the Brunt-V\"ais\"al\"a frequency, viscosity, and thermal diffusivity, respectively. From dimensional analysis, only three dimensionless parameters characterize the fluid: the Reynolds number $Re=UL/\nu$, the Froude number $Fr=U/NL$, and the Prandtl number $Pr=\nu/\kappa$. Understanding the scaling of the emergent outer vertical scales, the structure of the subsequent anisotropic energy cascade (see an artist's concept in Figure \ref{fig:ArtistConcept}), and possible dynamo instability is an important theoretical goal. We first develop a new theory for the anisotropic energy cascade of hydrodynamic, stably stratified turbulence in the astrophysical regime of asymptotically small Prandtl number, $Pr$. Dominant balance arguments suggest that as $Pr$ is decreased from $Pr=O(1)$ in the geophysical regime, a transition in turbulence regimes occurs when \$Pr