Classes of Hydrodynamic and Magnetohydrodynamic Turbulent Decay

Area of Science:

• Fluid dynamics
• Plasma physics
• Computational physics

Background:

• Turbulence plays a crucial role in various physical phenomena, from astrophysical systems to laboratory plasmas.
• Understanding the decay of turbulence and its scaling properties is essential for modeling complex systems.
• Previous studies have focused on specific types of turbulence, but a comprehensive classification of evolutionary tracks is lacking.

Purpose of the Study:

• To classify time-dependent solutions of decaying hydrodynamic and magnetohydrodynamic turbulence based on their evolutionary tracks.
• To identify the key factors determining these evolutionary trajectories.
• To investigate the role of initial conditions and helical properties on turbulent decay.

Main Methods:

• Performing numerical simulations of decaying hydrodynamic and magnetohydrodynamic turbulence.
• Classifying solutions using parametric plots of instantaneous scaling exponents.
• Analyzing the evolutionary trajectories of different turbulent cases.

Main Results:

• Identified distinct classes of solutions with specific evolutionary trajectories.
• Demonstrated that trajectories converge towards a line of self-similar solutions.
• Found that underlying physics governs trajectories, with initial conditions playing a minor role.
• Observed that helical turbulence evolves similarly regardless of the initial spectrum's infrared slope.

Conclusions:

• The decay of turbulence follows predictable paths determined by its physical nature.
• Self-similarity in turbulence is an attractor state, reached through diverse initial conditions.
• Helical turbulence exhibits robust evolutionary behavior, independent of initial spectral details.