# Accession Number:

## AD0257176

# Title:

## MATHEMATICAL THEORY OF TURBULENCE. PART I. ASYMPTOTIC EXPANSIONS IN WALL-LAW LAYER

# Descriptive Note:

# Corporate Author:

## BERGEN UNIV (NORWAY)

# Personal Author(s):

# Report Date:

## 1960-07-01

# Pagination or Media Count:

## 1.0

# Abstract:

In the case of a linear differential equation an expansion in powers of a parameter may be multiplied by any power of that parameter and still be a solution of the differential equation. In general, this is not so in the case of non-linear differential equations. In the present paper this fact is exploited to derive possible asymptotic expansions compatible with Navier-Stokes equations in wall-law layer of stationary turbulent flows, i.e. turbulent flows in which all properly averaged quantities remain stationary. Three types of stationary turbulent flow are considered, i the flow between two parallel plane walls in relative motion, ii pressure flow between parallel plane walls at rest, and iii boundary layer along a flat plate. It is found that two essentially different asymptotic expansions are compatible with Navier-Stokes equations. One of these expansions may yield the above wall law whereas the other yields a possible wall law which indicates the possibility of a type of m that found in ordinary laboratory experiments. In either case the differential equations are the same in all three types of flow considered, thus indicating the same wall law in all three cases. Author