238
Air Pollution and Turbulence: Modeling and Applications
9.4.3 Conclusions for the Lagrangian Experiments ..................................264
9.5 Conclusions ................................................................................................... 265
References ..............................................................................................................266
9.1 INTRODUCTION
The planetary boundary layer (PBL) is the lowest layer of the atmosphere in which
the direct effect of the earth’s surface on dynamical processes plays a relevant role,
and it is also the environment in which almost all human and biological activities
(with their consequences) take place. It is therefore clear why the study of the PBL is
a fundamental issue for environmental applications, as it can provide strategies for
air quality management.
The PBL can be considered as a continuous fl uid characterized by a mixture of
many subsidiary motions with different scales in space and time. The governing
equations of motion of a PBL fl ow are provided by the conservation principles, like
the conservation of mass and momentum. The main diffi culties in getting a general
solution for the set of equations describing turbulent motions essentially arise from
the nonlinearity of the equations of motion, the 3-D character of the velocity fi eld,
and the enormous number of scales involved in such motion.
The fi rst point means that it is not possible to fi nd analytical solutions, considering also the insuffi cient information for boundary and initial conditions. Even the
numerical approach is quite complex and expensive: the high computational cost
due to the large number of scales involved makes numerical solutions obtainable
only for quasi-stable fl ows (low Reynolds numbers). Hence, historically, attention
has shifted to statistical methods for studying a random velocity fi eld. In this context, Reynolds (1895) developed his theory based on an averaging process for eliminating the most random characteristics of the fi elds. The Reynolds approach on the
one hand determined a signifi cant and fruitful turning point, while on the other it
brought to the foreground the closure problem of turbulence, which has intrigued
researchers for over a hundred years. This remains an outstanding unsolved problem of modern physics. The limited power of computers and the closure problem
have induced researchers to use boundary-layer models to provide approximate
solutions.
Turbulence models enable effective predictions of turbulent fl ows. Despite this,
they work satisfactorily only in situations that do not differ too much from those used
to calibrate them. This means, for example, that models developed for shear fl ows
often do not work properly for convective fl ows.
It is well known that turbulence and air pollutant dispersion are interdependent
phenomena. The development of numerical simulations for turbulence in the PBL
during the last 30 years has brought enormous advantages in numerical simulations
of pollutant dispersion in the PBL.
Following the notation of Wyngaard and Peltier (1996), the word “modeling” is
usually used to represent the turbulence through approximate equations whose solutions have behavioral similarities to turbulence. The term “simulation” generally
refers to equations that are derivable from the exact set and, hence, remain faithful
to the essential physics.
© 2010 by Taylor and Francis Group, LLC
Air Pollution and Turbulence: Modeling and Applications
9.4.3 Conclusions for the Lagrangian Experiments ..................................264
9.5 Conclusions ................................................................................................... 265
References ..............................................................................................................266
9.1 INTRODUCTION
The planetary boundary layer (PBL) is the lowest layer of the atmosphere in which
the direct effect of the earth’s surface on dynamical processes plays a relevant role,
and it is also the environment in which almost all human and biological activities
(with their consequences) take place. It is therefore clear why the study of the PBL is
a fundamental issue for environmental applications, as it can provide strategies for
air quality management.
The PBL can be considered as a continuous fl uid characterized by a mixture of
many subsidiary motions with different scales in space and time. The governing
equations of motion of a PBL fl ow are provided by the conservation principles, like
the conservation of mass and momentum. The main diffi culties in getting a general
solution for the set of equations describing turbulent motions essentially arise from
the nonlinearity of the equations of motion, the 3-D character of the velocity fi eld,
and the enormous number of scales involved in such motion.
The fi rst point means that it is not possible to fi nd analytical solutions, considering also the insuffi cient information for boundary and initial conditions. Even the
numerical approach is quite complex and expensive: the high computational cost
due to the large number of scales involved makes numerical solutions obtainable
only for quasi-stable fl ows (low Reynolds numbers). Hence, historically, attention
has shifted to statistical methods for studying a random velocity fi eld. In this context, Reynolds (1895) developed his theory based on an averaging process for eliminating the most random characteristics of the fi elds. The Reynolds approach on the
one hand determined a signifi cant and fruitful turning point, while on the other it
brought to the foreground the closure problem of turbulence, which has intrigued
researchers for over a hundred years. This remains an outstanding unsolved problem of modern physics. The limited power of computers and the closure problem
have induced researchers to use boundary-layer models to provide approximate
solutions.
Turbulence models enable effective predictions of turbulent fl ows. Despite this,
they work satisfactorily only in situations that do not differ too much from those used
to calibrate them. This means, for example, that models developed for shear fl ows
often do not work properly for convective fl ows.
It is well known that turbulence and air pollutant dispersion are interdependent
phenomena. The development of numerical simulations for turbulence in the PBL
during the last 30 years has brought enormous advantages in numerical simulations
of pollutant dispersion in the PBL.
Following the notation of Wyngaard and Peltier (1996), the word “modeling” is
usually used to represent the turbulence through approximate equations whose solutions have behavioral similarities to turbulence. The term “simulation” generally
refers to equations that are derivable from the exact set and, hence, remain faithful
to the essential physics.
© 2010 by Taylor and Francis Group, LLC