Atmospheric Dispersion with a Large-Eddy Simulation
259
9.4 LAGRANGIAN DISPERSION WITH LARGE-EDDY
SIMULATIONS AND EXPERIMENTS
9.4.1 LAGRANGIAN DISPERSION
This chapter focuses on Lagrangian dispersion with LES. In particular, we investigate the problem of relative dispersion in a neutrally stratifi ed and celebrated
Richardson’s law. This equation implies that the mean square particle separation
grows in time as
= ε
2
3
2
( )
R t C t
(9.30)
where
C 2 is the so-called Richardson constant
ε is the mean energy dissipation
This study is relevant to describe small-scale motions and to provide important
information on the way to parameterize subgrid scales. It is not easy to observe the
“t 3 ” behavior of particle pair separation in a realistic PBL as it is hard to obtain a
PBL with a suffi ciently extended inertial range of scales in which one can clearly
identify the expected law. Moreover, the classical time-dependent approach in
isolating Richardson’s law with the classical statistical technique has been inconclusive due to its strong dependency on initial conditions (i.e., initial pair separations), which consequently does not permit an accurate estimate of the Richardson
constant.
To overcome this problem, we have applied, for the fi rst time in the context of
boundary layer physics, a recently established technique coming from the study of
dynamical systems theory (Gioia et al., 2004). This exit-time technique, known as
the fi nite scale Lyapunov exponents (FSLE) (Boffetta et al., 2000), has been exploited
for treating fi nite-scale Lagrangian relative dispersion as a fi nite-error predictability
problem (Lacorata et al., 2001). This new adopted strategy has given many important
results. First of all, it has permitted us to isolate a clean region of scaling showing
the occurrence of Richardson’s law. For this reason, a measure of the Richardson
constant has become possible.
9.4.2 PAIR DISPERSION IN A LES-GENERATED NEUTRAL PBL
9.4.2.1 The Simulated PBLs
We generated two types of neutral boundary layers, one with a spatial resolution
of 128 3 grid points (SN1) and the other with a spatial resolution of 96 3 grid points
(SN2). In order to obtain a stationary PBL, we advanced our LES code in time for
around six large-eddy turnover times. This time is the starting point for the successive Lagrangian analysis that will be described later. The relevant parameters characterizing our simulated PBLs at t = 6τ * are summarized in Table 9.3.
© 2010 by Taylor and Francis Group, LLC
259
9.4 LAGRANGIAN DISPERSION WITH LARGE-EDDY
SIMULATIONS AND EXPERIMENTS
9.4.1 LAGRANGIAN DISPERSION
This chapter focuses on Lagrangian dispersion with LES. In particular, we investigate the problem of relative dispersion in a neutrally stratifi ed and celebrated
Richardson’s law. This equation implies that the mean square particle separation
grows in time as
= ε
2
3
2
( )
R t C t
(9.30)
where
C 2 is the so-called Richardson constant
ε is the mean energy dissipation
This study is relevant to describe small-scale motions and to provide important
information on the way to parameterize subgrid scales. It is not easy to observe the
“t 3 ” behavior of particle pair separation in a realistic PBL as it is hard to obtain a
PBL with a suffi ciently extended inertial range of scales in which one can clearly
identify the expected law. Moreover, the classical time-dependent approach in
isolating Richardson’s law with the classical statistical technique has been inconclusive due to its strong dependency on initial conditions (i.e., initial pair separations), which consequently does not permit an accurate estimate of the Richardson
constant.
To overcome this problem, we have applied, for the fi rst time in the context of
boundary layer physics, a recently established technique coming from the study of
dynamical systems theory (Gioia et al., 2004). This exit-time technique, known as
the fi nite scale Lyapunov exponents (FSLE) (Boffetta et al., 2000), has been exploited
for treating fi nite-scale Lagrangian relative dispersion as a fi nite-error predictability
problem (Lacorata et al., 2001). This new adopted strategy has given many important
results. First of all, it has permitted us to isolate a clean region of scaling showing
the occurrence of Richardson’s law. For this reason, a measure of the Richardson
constant has become possible.
9.4.2 PAIR DISPERSION IN A LES-GENERATED NEUTRAL PBL
9.4.2.1 The Simulated PBLs
We generated two types of neutral boundary layers, one with a spatial resolution
of 128 3 grid points (SN1) and the other with a spatial resolution of 96 3 grid points
(SN2). In order to obtain a stationary PBL, we advanced our LES code in time for
around six large-eddy turnover times. This time is the starting point for the successive Lagrangian analysis that will be described later. The relevant parameters characterizing our simulated PBLs at t = 6τ * are summarized in Table 9.3.
© 2010 by Taylor and Francis Group, LLC