Lecture

Turbulence in Astrophysics: Reynolds Decomposition

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In course

PHYS-753: Dynamics of astrophysical fluids and plasmas

The dynamics of ordinary matter in the Universe follows the laws of (magneto)hydrodynamics. In this course, the system of equations that describes astrophysical fluids will be discussed on the basis of selected astrophysical examples, from the physics of s ...

Description

This lecture covers the modeling of fluid instabilities with linear perturbation theory, focusing on the Rayleigh-Taylor instability at the interface of two fluids. It delves into chaotic motion and the closure problem of turbulence, exploring the origin of unpredictability through the Navier-Stokes equations. The lecture discusses the statistical approach to turbulence, the two-point correlation function, and the special case of homogeneous, isotropic, incompressible turbulence. It also introduces the concept of mean-field theory and turbulent viscosity, emphasizing its importance in stellar structure models and the interstellar medium driven by supernova explosions and galactic shear.

Official source

Ontological neighbourhood

Physics

Mechanics: Fluid mechanics

Astronomy

Astrophysics: Stellar astronomy

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In fluid dynamics, turbulence or turbulent flow is fluid motion characterized by chaotic changes in pressure and flow velocity. It is in contrast to a laminar flow, which occurs when a fluid flows in parallel layers, with no disruption between those layers. Turbulence is commonly observed in everyday phenomena such as surf, fast flowing rivers, billowing storm clouds, or smoke from a chimney, and most fluid flows occurring in nature or created in engineering applications are turbulent.

Mean-field theory

In physics and probability theory, Mean-field theory (MFT) or Self-consistent field theory studies the behavior of high-dimensional random (stochastic) models by studying a simpler model that approximates the original by averaging over degrees of freedom (the number of values in the final calculation of a statistic that are free to vary). Such models consider many individual components that interact with each other. The main idea of MFT is to replace all interactions to any one body with an average or effective interaction, sometimes called a molecular field.

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