On flow-field decomposition in fluid dynamics

TL;DR

This paper critically examines the theoretical foundations of flow-field decomposition in fluid dynamics, highlighting issues with current methods and questioning common assumptions about turbulence and flow disturbances.

Contribution

It offers a critique of traditional flow decomposition techniques and challenges the physical validity of common turbulence modeling assumptions.

Findings

Flow decomposition methods are imprecise and problematic.

Disturbances in flow are ill-defined in classical analysis.

Current turbulence models rely on unjustified statistical assumptions.

Abstract

In the theory of hydrodynamic stability, the procedure to decompose an incompressible flow field into its basic motion and disturbances is imprecise and problematic because the disturbances, infinitesimal or finite, are ill-defined quantities in analysis. The linearised equations contravene the first principles of classical mechanics while the disturbance-driven non-linear formulation can hardly be considered as exact science. The notion that unstable and amplified disturbances precipitating the early stages of laminar-turbulent transition is vague, speculative or fundamentally flawed. Similarly, turbulence is unjustifiably assumed to involve a statistical mean, and zero-on-average fluctuations. This simplistic postulation is unpromising, and inevitably renders turbulent flows to a recondite dynamics of self-contradiction. By consequence, the closure problem of turbulence modelling the Reynolds stresses deals with issues of no physical relevance.