Transport and Coherent Structures in Wall Turbulence

Sedat Tardu

• Publisher: Wiley-ISTE
• Year: 2014
• Print ISBN: 9781848213951
• eBook ISBN: 9781118576779
• Edition: 1
• Topic: Technology & Engineering
• Subtopic: Civil Engineering
• Index: Technology & Engineering

Wall bounded turbulent flows are of major importance in industrial and environmental fluid mechanics. The structure of the wall turbulence is intrinsically related to the coherent structures that play a fundamental role in the transport process. The comprehension of their regeneration mechanism is indispensable for the development of efficient strategies in terms of drag control and near wall turbulence management. This book provides an up-to-date overview on the progress made in this specific area in recent years.

1

General Points

1.1 Introduction

This book is the continuation of [TAR 11a] and [TAR 11b]. The series as a whole gives a broad-ranging presentation of the statistical properties of turbulent flows delimited by rigid walls. It is preferable, though not obligatory, for the readers to consult [TAR 11a] and [TAR 11b]. This chapter lays out the basic elements and the literature necessary for the understanding of this book. We limit ourselves to give an overview as brief as possible, without going into details, which the interested readers can find out in numerous publications referenced herein.

First, we provide a summary of the fundamental equations in fluid dynamics (the Navier–Stokes (NS) momentum balance equations and the conservation of mass equations). We then proceed to discuss the Reynolds-averaged equations. We lay down a number of exact solutions related to fully developed turbulent flows in a two dimensional (2D) channel, before providing a brief reminder about turbulent boundary layers and their overall characteristics. Wall turbulent scales are then introduced, alongside closures at a single point. We then present the characteristics of the mean velocity distribution and the effects of the Reynolds number, analyzed in detail in [TAR 11a] and [TAR 11b]. Turbulence intensities of the velocity components are discussed in a separate section. The chapter ends with some reminders concerning vorticity, and its statistical characteristics in wall turbulent flows.

1.2 General equations

It will be assumed in this book that the readers are familiar with the basic concepts of fluid dynamics. Here, we will recap the basic equations applicable to fluid dynamics, limiting our examination to incompressible flows.

1.2.1 Eulerian relations

The two local equations that are fundamental in fluid dynamics express the conservation of mass and the first law of general mechanics, which results in the momentum balance equation. They are both expressed in terms of the material derivative¹ defined by

[1.1]

The component of the instantaneous local velocity vector in direction x_i is written as U _i (

, t). The position vector is

(x₁, x₂, x₃) and t is the time. The Einstein summation notation is applied to the above relation. The material derivative expresses the variation of a physical value, tracking the particle in the flow.

1.2.1.1 Continuity equation

The continuity equation expresses the conservation of mass throughout an elementary volume of fluid. It can be written in various forms, including

[1.2]

where ρ is the density. This equation can also be written as

[1.3]

using the definition of the material derivative. In the context of the applications envisaged in this book, the density ρ is considered to be constant in this equation; so the continuity equation is reduced to

[1.4]

1.2.1.2. Momentum balance equations

We obtain the momentum balance equations by applying Newton’s first law to an elementary volume. We obtain

[1.5]

In this relation, f_ext,i represents the external forces and σ_ji is the shear stress tensor defined by

[1.6]

for a Newtonian fluid.² In this equation, P(

, t) represents the field of local instantaneous pressure, μ is the dynamic viscosity and δ_ji is the Kronecker delta (δ_ji = 1 if j = i, and 0 if not). The value D_ij is the strain tensor, which is expressed by

[1.7]

The momentum balance equation [1.4] can be reduced to the NS equation for an incompressible Newtonian flui...

Table of contents

• Cover
• Contents
• Title Page
• Copyrights
• Introduction
• Main Notations
• 1 General Points
• 2 Transport Phenomena in Wall Turbulence
• 3 Near-Wall Coherent Structures: History, Identification and Detection
• 4 Coherent Wall Structures: Dynamics and Contribution to Turbulent Activity
• 5 Regeneration and Self-Maintaining of Coherent Structures
• 6 Large- and Very Large-scale Structures
• Bibliography
• Index