Recent Developments in Theories of Inhomogeneous and Anisotropic Turbulence

TL;DR

This paper reviews recent theoretical advances in modeling inhomogeneous and anisotropic turbulence, emphasizing quasilinear approximations and their statistical formulations, and discusses open questions in the field.

Contribution

It provides a comprehensive overview of recent developments in quasilinear theories for inhomogeneous and anisotropic turbulence, highlighting underexplored areas and framing open research questions.

Findings

Identification of key quasilinear approximation methods

Discussion of statistical formulations for complex turbulence

Highlighting open questions in turbulence theory

Abstract

Understanding inhomogeneous and anisotropic fluid flows require mathematical and computational tools that are tailored to such flows and distinct from methods used to understand the canonical problem of homogeneous and isotropic turbulence. We review some recent developments in the theory of inhomogeneous and anisotropic turbulence, placing special emphasis on several kinds of quasilinear approximations and their corresponding statistical formulations. Aspects of quasilinear theory that have received insufficient attention in the literature are discussed, and open questions are framed.