Environmental Engineering Reference
In-Depth Information
Chapter 7
The Effect of Stratification on the Aerodynamic
Roughness Length
Sergej Zilitinkevich, Ivan Mammarella, Alexander Baklanov,
and Sylvain Joffre
Abstract
The roughness length,
z
0
u
, is a fundamental concept presented in every
textbook on fluid mechanics. It characterizes the friction exerted by the rough-
ness elements on turbulent flows and provides conventional boundary condition for
a wide range of turbulent-flow problems. Classical lab experiments and theories
treated
z
0
u
as a “geometric” parameter independent of the properties of the flow.
This conclusion has been taken as granted in environmental physics. In this paper
we disclose a strong dependence of
z
0
u
on hydrostatic stability, develop the relevant
theory, validate it against experimental data and recommend it for use in meteorol-
ogy, oceanography and hydrology.
7.1 Introduction
The concept of roughness length,
z
0
u
, was introduced in the early thirties by classics,
Ludwig Prandtl (1875-1953) and Theodore von Karman (1881-1963), to parame-
terize the transfer of momentum from turbulent flows to aerodynamically rough
surfaces, i.e. those with the typical roughness-element height,
h
0
, larger than the
viscous layer height,
ν/
ν
is the molecular viscosity and
u
∗
is the friction
velocity). Classical laboratory experiments with neutrally stratified boundary-layer
flows have shown that
z
0
u
does not depend on properties of the flow and factually
represents a geometric characteristic of the surface. This conclusion was universally
accepted in dynamic meteorology and physical oceanography without any modifica-
tion and even discussion. The question whether or not
z
0
u
depends on stratification
did not attract attention, although the crucial role of stratification in atmospheric and
oceanic flows was already understood.
u
∗
(where
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