Inner/Outer Ratio Similarity Scaling for 2-D Wall-bounded Turbulent Flows

TL;DR

This paper investigates the conditions under which similarity in wall-bounded turbulent flows can be identified through the constancy of the inner/outer ratio, proposing a new integral moment-based ratio as a similarity criterion.

Contribution

It introduces a new thickness ratio based on the integral moment method that must change proportionally for similarity, challenging previous assumptions about the Rotta ratio.

Findings

The integral moment-based ratio is a valid similarity criterion.

Complete similarity cannot occur if the inner and outer scaling parameters do not change proportionally.

The Rotta ratio alone is not sufficient to determine similarity.

Abstract

The turbulent boundary layer scaling parameters for the velocity profile are usually associated with either the inner viscous region or the outer boundary layer region. It has been a long-held view that complete similarity of the velocity profile can only occur if the inner and outer region scaling parameters change proportionally as one moves from station to station along the wall. However, it appears that complete similarity is not possible for the wall-bounded turbulent boundary layer. Hence, the outer/inner ratio would seem to be of little use. However, recent revelations revive the need for identifying likely experimental datasets that display outer region similarity. It is our contention that likely datasets can be identified by finding datasets in which the inner-outer thickness ratio is almost constant. This inner-outer thickness ratio is usually associated with the Rotta scaling ratio. Unfortunately, the Rotta ratio proportional change condition has never been shown to be a similarity requirement. In contrast, we show that a recently developed thickness ratio based on the integral moment method must change proportionately from station to station if similarity is present.