---
abstract: 'We propose a minimal spectral theory for boundary layer turbulence that captures very well the profile of the mean square velocity fluctuations in the stream-wise direction, and gives a quantitative prediction of the Townsend-Perry constants. The phenomenological model is based on connecting the statistics in the streamwise direction with the energy spectrum of the streamvise velocity fluctuations. The original spectral theory was proposed in Ref. [@gioia2006turbulent] to explain the friction factor and von Kármán law in Ref. [@GGGC10]. We generalized it by including fluctuations in the wall-shear stress and the streamwise velocity. The predicted profiles for the mean velocity and mean square fluctuations are compared with velocity data from wind tunnel experiments.'
author:
- 'Björn Birnir $^1$, Luiza Angheluta$^2$, John Kaminsky$^1$, Xi Chen$^3$'
bibliography:
- 'referencef.bib'
title: 'Spectral link of the generalized Townsend-Perry constants in turbulent boundary layers'
---

Introduction
============

Turbulence is a ubiquitous phenomenon encountered in very diverse natural systems, from the large-scale atmosphere [@wyngaard1992atmospheric] and oceans [@toschi2009lagrangian] all the way down to quantum fluids [@vinen2002quantum], as well as in engineered systems, such as pipelines, heat exchangers, wind turbines, etc. It relates to the complex fluid dynamics that orchestrates the interactions of flow eddies spanning many 