# Scaling laws and bounds for the turbulent G.O. Roberts dynamo

## TL;DR

This paper presents numerical simulations of the G.O. Roberts dynamo, deriving bounds for total energy consistent with turbulence theory, and analyzing the scaling laws governing dynamo behavior with and without mean fields.

## Contribution

It introduces exact energy bounds for the G.O. Roberts dynamo and compares numerical results with theoretical inequalities, advancing understanding of turbulence in dynamo systems.

## Key findings

- Numerical simulations produce dynamos with and without significant mean fields.
- Derived bounds for total energy align with Kolmogorov turbulence phenomenology.
- Numerical data fits match theoretical inequalities, confirming the scaling laws.

## Abstract

Numerical simulations of the G.O. Roberts dynamo are presented. Dynamos both with and without a significant mean field are obtained. Exact bounds are derived for the total energy which conform with the Kolmogorov phenomenology of turbulence. Best fits to numerical data show the same functional dependences as the inequalities obtained from optimum theory.