On Virk's asymptote

TL;DR

This paper clarifies that Virk's asymptote is not a new law but part of the existing wall layer profile, extended in drag reduction flows, and discusses its implications for flow behavior and drag reduction limits.

Contribution

It demonstrates that Virk's asymptote is similar to the Karman buffer layer and explains its role in flow relaminarization and drag reduction.

Findings

Virk's asymptote is part of the wall layer profile.

Maximum drag reduction suppresses the law of the wake.

Flow fully relaminarizes at maximum drag reduction.

Abstract

The Virk asymptote is shown to be similar in nature to the Karman buffer layer profile and does not represent a new log-law with a modified mixing-length. It is simply part of the wall layer velocity profile but is extended because of the increase in wall layer thickness in drag reduction flows. The friction factors at the maximum drag reduction asymptote correspond to velocity profiles consisting of a wall layer and a law of the wake sub-region. Maximum drag reduction results in the suppression of the law of the wake and full relaminarisation of the flow.