Stable atmospheric boundary layer (SABL) is characterized by the
presence of a layer of stably-stratified turbulence. Density
stratification has a direct effect on local turbulence and reduces the
generation of turbulent fluctuations while damping turbulent transports
in the vertical direction. Simpler turbulence models usually rely on
eddy-viscosity hypothesis (K-theory) and do not contain the relevant
physics for capturing the interaction between the turbulence and density
stratification. Therefore, the turbulence kinetic energy is typically
modelled using empirical stability correction functions that depend on
the value of gradient Richardson number. The aim of the present study is
to investigate the ability of a recently developed explicit algebraic
Reynolds-stress (EARS) model (Lazeroms et al., 2013) to predict effects
of varying levels of stratification in the SABL. We compare the model
with the high-resolution large-eddy simulation (LES) of Sullivan et al.
(2016) of the modified first GEWEX Atmospheric Boundary Layer Study
(GABLS1) where the SABL is developing over a cooled surface. The EARS
model carries three prognostic equations for the mean turbulence
properties; the turbulent kinetic energy, the rate of dissipation of
turbulent kinetic energy and half the temperature variance. Furthermore,
instead of using the K-theory, the EARS model contains algebraic
approximations of the solution to the transport equations for the
Reynolds stress and scalar fluxes. The approximation method is based on
the so-called weak-equilibrium assumption, which allows formulation of
the solution for turbulent fluxes in an explicit form and keeps the
closure model reasonably cheap in terms of computational costs. The EARS
model is used with the same initial conditions and boundary forcing as
in Sullivan et al. (2016) for four SABL simulations with different
surface cooling rates. The results of the EARS model agrees with all
four LES cases. The model predicts the height of the low-level jet (LLJ)
and SABL with a reasonably accuracy. As stratification increases the
height of the LLJ and SABL decreases. Agreement between the results of
wind turning and the LES in the surface layer indicates that the imposed
boundary-condition treatment from Želi et al. (2019) is adequate.
Without requirement of additional modelling, the EARS model is able to
predict horizontal-turbulent fluxes (e.g., correlation of fluctuations
in the horizontal direction which are related to the wind turning). In
the case of SABL horizontal turbulent fluxes are typically larger than
the vertical fluxes. This is an improvement compared to the isotropic
atmospheric turbulence models which are unable to predict (non-zero)
turbulent fluxes in the horizontal plane. Additionally, it is shown that
the EARS model is able to predict other second-order statistics such as
the turbulence anisotropy with a fairly good accuracy. In order to study
different cooling rates we introduce dimensionless alignment coefficient
that represents a normalized measure of the local production. Figure 1
shows that the horizontal wind speed profile and the LLJ for different
stratification rates. In summary, we show that the EARS model, an
intermediate-complexity closure model, with algebraic treatment of the
Reynolds stress and scalar fluxes, predicts the main effects in the SABL
such as LLJ and turbulence anisotropy. In addition, we introduce a new
type of scaling that can be further investigated to see if the scaling
has universal features.
presence of a layer of stably-stratified turbulence. Density
stratification has a direct effect on local turbulence and reduces the
generation of turbulent fluctuations while damping turbulent transports
in the vertical direction. Simpler turbulence models usually rely on
eddy-viscosity hypothesis (K-theory) and do not contain the relevant
physics for capturing the interaction between the turbulence and density
stratification. Therefore, the turbulence kinetic energy is typically
modelled using empirical stability correction functions that depend on
the value of gradient Richardson number. The aim of the present study is
to investigate the ability of a recently developed explicit algebraic
Reynolds-stress (EARS) model (Lazeroms et al., 2013) to predict effects
of varying levels of stratification in the SABL. We compare the model
with the high-resolution large-eddy simulation (LES) of Sullivan et al.
(2016) of the modified first GEWEX Atmospheric Boundary Layer Study
(GABLS1) where the SABL is developing over a cooled surface. The EARS
model carries three prognostic equations for the mean turbulence
properties; the turbulent kinetic energy, the rate of dissipation of
turbulent kinetic energy and half the temperature variance. Furthermore,
instead of using the K-theory, the EARS model contains algebraic
approximations of the solution to the transport equations for the
Reynolds stress and scalar fluxes. The approximation method is based on
the so-called weak-equilibrium assumption, which allows formulation of
the solution for turbulent fluxes in an explicit form and keeps the
closure model reasonably cheap in terms of computational costs. The EARS
model is used with the same initial conditions and boundary forcing as
in Sullivan et al. (2016) for four SABL simulations with different
surface cooling rates. The results of the EARS model agrees with all
four LES cases. The model predicts the height of the low-level jet (LLJ)
and SABL with a reasonably accuracy. As stratification increases the
height of the LLJ and SABL decreases. Agreement between the results of
wind turning and the LES in the surface layer indicates that the imposed
boundary-condition treatment from Želi et al. (2019) is adequate.
Without requirement of additional modelling, the EARS model is able to
predict horizontal-turbulent fluxes (e.g., correlation of fluctuations
in the horizontal direction which are related to the wind turning). In
the case of SABL horizontal turbulent fluxes are typically larger than
the vertical fluxes. This is an improvement compared to the isotropic
atmospheric turbulence models which are unable to predict (non-zero)
turbulent fluxes in the horizontal plane. Additionally, it is shown that
the EARS model is able to predict other second-order statistics such as
the turbulence anisotropy with a fairly good accuracy. In order to study
different cooling rates we introduce dimensionless alignment coefficient
that represents a normalized measure of the local production. Figure 1
shows that the horizontal wind speed profile and the LLJ for different
stratification rates. In summary, we show that the EARS model, an
intermediate-complexity closure model, with algebraic treatment of the
Reynolds stress and scalar fluxes, predicts the main effects in the SABL
such as LLJ and turbulence anisotropy. In addition, we introduce a new
type of scaling that can be further investigated to see if the scaling
has universal features.
References:
Lazeroms et al. 2013 J. Fluid Mech. 91:125
Sullivan et al. 2016 J. Atmospheric Sci. 1815:1840
Želi et al. 2019 Bound.-Layer Meteor. 53-77
Figure 1: Horizontal wind speed profile for different stratification rates
inside the SABL. Stratification rates are indicated by different
colors where black is the lowest and yellow corresponds to the highest
stratification rate in the SABL. Solutions of the EARS model (solid
lines) and the LES results (dashed lines) from Sullivan et al. (2016).
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