A comment on the theory of turbulence without pressure proposed by Polyakov

TL;DR

This paper critically examines Polyakov's pressureless turbulence theory, focusing on the elusive nature of the dissipative anomaly operator and its implications for conservation laws.

Contribution

It provides arguments suggesting that anomalies in the first conservation law cannot be ruled out within Polyakov's framework.

Findings

Dissipative anomaly operator in pressureless turbulence is elusive.

Anomalies in the first conservation law may exist.

Challenges in deriving the anomaly operator explicitly.

Abstract

Owing to its lack of derivability, the dissipative anomaly operator appearing in the theory of turbulence without pressure recently proposed by Polyakov appears to be quite elusive. In particular, we give arguments that seem to lead to the conclusion that an anomaly in the first equation of the sequence of conservation laws cannot be {\it a priori} excluded.