The universality of the law of the wall: A long-lasting controversial debate

TL;DR

This paper examines the longstanding debate on whether the law of the wall in fluid mechanics is universal, arguing that physically consistent models support its universality and highlight its importance for turbulence modeling.

Contribution

The paper clarifies misconceptions about the law of the wall's universality, demonstrating that realistic models inherently support its universal applicability.

Findings

Nonuniversality results from simplified, unrealizable models.

Realizable models consistent with physics imply universality.

Universal law aids turbulence model design and theory validation.

Abstract

The discovery of the law of the wall, the log-law including the von Karman constant, is seen to be one of the biggest accomplishments of fluid mechanics. However, after more than ninety years there is still a controversial debate about the validity and universality of the law of the wall. Clarity about this question matters: in absence of alternatives, a reliable and universal theory involving the law of the wall is needed to provide essential guideline for the validation of theory, computational methods, and experimental studies of very high Reynolds number (Re) flows. The paper presents an analysis of concepts used to derive controversial conclusions. It is shown that nonuniversality is a consequence of simplified modeling concepts, which leads to unrealizable models. On the other hand, realizability implies universality: models in consistency with physical requirements do not need to be adjusted to different flows. There are essential advantages of a universal law of the wall: it enables the design of accurate turbulence models and it provides a bridge between finite Re observations and asymptotic structural theories of turbulence.