Geoscience Reference
In-Depth Information
19
Turbulent
Closure,
K Theory, and
Mixing Length
Introduction
The prognostic equations introduced in the last three chapters describe both the
instantaneous and mean values of atmospheric variables, but they are not by them-
selves sufficient to allow hydrometeorological modeling of turbulence in the ABL.
To complete the description it is necessary to introduce additional equations
which represent the process of turbulent transport. This chapter discusses how
this need arises and introduces the most common way in which it is met. Because
the nature of these additional equations is sensitive to whether the turbulent field
is generated by friction or by buoyancy, it is necessary also to define criteria to
quantify the origin of the turbulence present at each height in the ABL.
Richardson number
One obvious and commonly used way to quantify numerically the origin of
turbulence is by using the production terms in the prognostic equation for
turbulent kinetic energy. Equation (18.16) contains one term which describes the
production of turbulent kinetic energy by buoyancy, and three terms which
together describe production by frictional processes. The ratio of the buoyant
production term to the sum of the frictional production terms is called the
Richardson number
and is used to quantify the relative importance of these two
production processes.
When expressed in a coordinate system in which the X axis is selected to lie
along the direction of the mean wind, terms that involve
v
, the mean velocity along
the Y axis, are zero, and the equation for the Richardson number is then:
