# Two-point correlation in wall turbulence according to the attached-eddy hypothesis

## TL;DR

This paper theoretically investigates two-point velocity correlations in wall turbulence using the attached-eddy hypothesis, deriving general forms without extra assumptions and analyzing related spectra and transfer rates.

## Contribution

It derives the most general forms of correlation functions in wall turbulence based solely on the attached-eddy hypothesis, avoiding additional assumptions.

## Key findings

- Derived general forms of two-point correlation functions.
- Analyzed energy spectra and transfer rate correlations.
- Provided a framework for assessing the attached-eddy hypothesis.

## Abstract

For the constant-stress layer of wall turbulence, two-point correlations of velocity fluctuations are studied theoretically by using the attached-eddy hypothesis, i.e., a phenomenological model of a random superposition of energy-containing eddies that are attached to the wall. While the previous studies had invoked additional assumptions, we focus on the minimum assumptions of the hypothesis to derive its most general forms of the correlation functions. They would allow us to use or assess the hypothesis without any effect of those additional assumptions. We also study the energy spectra and the two-point correlations of the rate of momentum transfer and of the rate of energy dissipation.