Statistical Approach to Wall Turbulence

Sedat Tardu

• Publisher: Wiley-ISTE
• Year: 2013
• Print ISBN: 9781848212626
• eBook ISBN: 9781118601587
• Edition: 1
• Topic: Physical Sciences
• Subtopic: Mechanics

Wall turbulence is encountered in many technological applications as well as in the atmosphere, and a detailed understanding leading to its management would have considerable beneficial consequences in many areas. A lot of inspired work by experimenters, theoreticians, engineers and mathematicians has been accomplished over recent decades on this important topic and Statistical Approach to Wall Turbulence provides an updated and integrated view on the progress made in this area.

Wall turbulence is a complex phenomenon that has several industrial applications, such as in aerodynamics, turbomachinery, geophysical flows, internal engines, etc. Several books exist on fluid turbulence, but Statistical Approach to Wall Turbulence is original in the sense that it focuses solely on the turbulent flows bounded by solid boundaries. The book covers the different physical aspects of wall turbulence, beginning with classical phenomenological aspects before advancing to recent research in the effects of the Reynolds numbers, near wall coherent structures, and wall turbulent transport process.

This book would be of interest to postgraduate and undergraduate students in mechanical, chemical, and aerospace engineering, as well as researchers in aerodynamics, combustion, and all applications of wall turbulence.

Chapter 1

Basic Concepts

1.1. Introduction

This chapter will consider the basic concepts and general properties of homogeneous and isotropic turbulence. We have restricted ourselves entirely to concepts that will be useful later on in this book. However, this chapter is fairly detailed in order to enable the reader to follow the arguments that would be developed later, without the need to refer to other books.

We will begin by deriving the Reynolds-averaged Navier-Stokes equations, along with some initial concepts for turbulent transport. We will then analyze the dynamics of two-point correlations in homogeneous turbulence, followed by homogeneous and isotropic turbulence. This is followed by a section that discusses axi-symmetric turbulence, and another section where the Taylor hypothesis and turbulence length scales are discussed. The chapter concludes with a brief discussion related to the state-of-the-art measurement and numerical simulation of turbulent wall flows.

1.2. Fundamental equations

We will assume that the reader is familiar with the basic concepts of fluid dynamics. We will briefly recollect the fundamental equations used to describe Newtonian fluid flow, restricting ourselves to the case of incompressible fluids.

1.2.1. Euler equations

The two fundamental local equations of fluid dynamics represent the conservation of mass and Newton’s first law, which implies conservation of momentum. They are expressed in terms of the material derivative¹, which is defined as:

[1.1]

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

. The position vector is

and t represents time. The Einstein summation-convention applies to the above equation. The material derivative represents the variation of a physical quantity along the path of a particle (its path-line) within the flow.

1.2.1.1. Continuity equation

The continuity equation expresses the conservation of mass for an elementary volume of fluid. It can be expressed in a number of forms which includes:

[1.2]

where

is the fluid density. This equation can also be written in the following form:

[1.3]

by using the definition of the material derivative. In the context of the applications, which we will consider in this book, the density

can be treated as a constant in this equation, s...

Table of contents

• Cover
• Title Page
• Copyright
• Foreword
• Introduction
• Chapter 1: Basic Concepts
• Chapter 2: Preliminary Concepts: Phenomenology, Closures and Fine Structure
• Chapter 3: Inner and Outer Scales: Spectral Behavior
• Chapter 4: Reynolds Number-Based Effects
• Chapter 5: Vorticity
• Notations Used
• Bibliography
• Index