In the realm of energy and environmental sciences, understanding fluid dynamics and magnetic fields is crucial. Researchers Julian Koellermeier, Michael Redle, and Manuel Torrilhon from the Institute of Aerodynamics at RWTH Aachen University have been delving into this complex interplay, with their latest findings published in the Journal of Fluid Mechanics.
The team has been working on the magnetic rotating shallow water (MRSW) model, originally developed to describe transitions in stars but now widely used in solar physics and geophysics. This model, derived from the 3-D incompressible magnetohydrodynamic system, simplifies these complex systems by averaging velocities and magnetic fields over depth. While this depth-averaging approach boosts computational efficiency, it comes at the cost of losing vertical information, which can limit the model’s predictive power.
To address this issue, the researchers have introduced higher-order vertical moments into the model, specifically for conductive fluids. This enhancement allows the model to maintain non-constant vertical profiles of both horizontal magnetic fields and horizontal velocities, all while keeping the computational benefits of a 2-D framework. The team has successfully extended the derivation of shallow water moment equations to create a new MRSW moment system of arbitrary order. This means they can represent vertical profiles of velocities and magnetic fields using polynomial expansions of any order, and close the 2-D system with evolution equations for these polynomial coefficients, found via Galerkin projection.
Through numerical experiments with MRSW moment systems up to third-order, the researchers have demonstrated that these moment approximations can reduce model error without significantly compromising computational efficiency. This advancement could have practical applications in the energy sector, particularly in improving the accuracy of models used in solar physics and geophysics, which are essential for understanding and predicting space weather and its impacts on power grids and other energy infrastructure.
This article is based on research available at arXiv.