whether the heat flux is positive (daytime) or negative (night time); term IV is the
turbulent kinetic energy transport caused by u j ’; and term V is the transport or
pressure correlation which describes how the turbulent kinetic energy is redistributed by pressure fluctuations. This term is associated with the flow of large
eddies. Term VI refers to production/consumption by tangential stresses in the
surface boundary layer. Its sign is generally opposite that of the mean velocity
vector because of downward dissipation of linear momentum; and term VII corresponds to viscous dissipation and thermal conversion of kinetic energy. On
average, the transformation of kinetic energy into heat is about 2 Wm
−2 , a very low
power in the overall energy equation (e.g., Foken 2017).
At a given location, TKE storage varies with the time of day. It increases from
morning to the afternoon and thereafter decreases from afternoon to night time,
when the terms for losses, e.g., by dissipation, exceed terms for production. The
storage term in the surface boundary layer can vary throughout the daily cycle by
two orders of magnitude between values of the order of 5Â10
−5 and 5Â10
−3 m
2 s
−3 .
The advective term may in practice, be considered zero in a homogeneous area,
assuming steady-state conditions. Term III in Eq. (3.88) representing
production/consumption of buoyancy is positive in the surface boundary layer, with
maximum values of about 10
−2 m
2 s
−3 (Stull 1994), corresponding to thermal
generation of turbulence when the surface is warmer than the surrounding air.
On cloudy days, surface heating is lower negatively influencing the formation of
turbulence. The thermal output term only affects the vertical component of the
turbulent kinetic energy budget and is anisotropic. The terms for return to isotropy
in Eq. (3.72) cause part of the kinetic energy to move in different horizontal
directions. Loss of kinetic energy due to thermal effects clearly occurs under
conditions of thermal stability, for example, during situations of nighttime inversion
to the surface when colder than the surrounding air.
Term IV for vertical turbulent transport can be either loss or gain of kinetic
energy, depending on whether the flux is divergent or convergent. On the surface,
vertical transport of turbulent kinetic energy predominates relative to fluctuations of
the two horizontal components. In contrast, in the intermediate region of the mixed
layer, transport of the vertical component of wind velocity fluctuations
predominates.
Static pressure fluctuations in the surface boundary layer (term V) are negligible
of the order of 0.005 kPa. The pressure terms are, as mentioned below, usually
obtained by the difference from the remaining terms. Term VII, molecular dissipation, is more significant for smaller eddies corresponding to higher scalars of
atmospheric turbulence (Shaw 1995b). The rates for turbulent kinetic energy dissipation during daytime are higher in the superficial boundary layer, where the
turbulence generation rates are also higher. During night time, or in the presence of
thermal inversions, turbulence is caused by tangential stresses as there is less dissipation and the turbulent kinetic energy is lower. After sunrise, production of
turbulence through buoyancy increases, in addition to mechanical production, with
a concomitant increase in the dissipation rate. The variation in the dissipation rate
ranges from 10
−5 m
2 s
−3 at night to 10
−1 m
2 s
−3 during the day (Stull 1994).
3.5 Introduction to Turbulent Motion Equations
55
turbulent kinetic energy transport caused by u j ’; and term V is the transport or
pressure correlation which describes how the turbulent kinetic energy is redistributed by pressure fluctuations. This term is associated with the flow of large
eddies. Term VI refers to production/consumption by tangential stresses in the
surface boundary layer. Its sign is generally opposite that of the mean velocity
vector because of downward dissipation of linear momentum; and term VII corresponds to viscous dissipation and thermal conversion of kinetic energy. On
average, the transformation of kinetic energy into heat is about 2 Wm
−2 , a very low
power in the overall energy equation (e.g., Foken 2017).
At a given location, TKE storage varies with the time of day. It increases from
morning to the afternoon and thereafter decreases from afternoon to night time,
when the terms for losses, e.g., by dissipation, exceed terms for production. The
storage term in the surface boundary layer can vary throughout the daily cycle by
two orders of magnitude between values of the order of 5Â10
−5 and 5Â10
−3 m
2 s
−3 .
The advective term may in practice, be considered zero in a homogeneous area,
assuming steady-state conditions. Term III in Eq. (3.88) representing
production/consumption of buoyancy is positive in the surface boundary layer, with
maximum values of about 10
−2 m
2 s
−3 (Stull 1994), corresponding to thermal
generation of turbulence when the surface is warmer than the surrounding air.
On cloudy days, surface heating is lower negatively influencing the formation of
turbulence. The thermal output term only affects the vertical component of the
turbulent kinetic energy budget and is anisotropic. The terms for return to isotropy
in Eq. (3.72) cause part of the kinetic energy to move in different horizontal
directions. Loss of kinetic energy due to thermal effects clearly occurs under
conditions of thermal stability, for example, during situations of nighttime inversion
to the surface when colder than the surrounding air.
Term IV for vertical turbulent transport can be either loss or gain of kinetic
energy, depending on whether the flux is divergent or convergent. On the surface,
vertical transport of turbulent kinetic energy predominates relative to fluctuations of
the two horizontal components. In contrast, in the intermediate region of the mixed
layer, transport of the vertical component of wind velocity fluctuations
predominates.
Static pressure fluctuations in the surface boundary layer (term V) are negligible
of the order of 0.005 kPa. The pressure terms are, as mentioned below, usually
obtained by the difference from the remaining terms. Term VII, molecular dissipation, is more significant for smaller eddies corresponding to higher scalars of
atmospheric turbulence (Shaw 1995b). The rates for turbulent kinetic energy dissipation during daytime are higher in the superficial boundary layer, where the
turbulence generation rates are also higher. During night time, or in the presence of
thermal inversions, turbulence is caused by tangential stresses as there is less dissipation and the turbulent kinetic energy is lower. After sunrise, production of
turbulence through buoyancy increases, in addition to mechanical production, with
a concomitant increase in the dissipation rate. The variation in the dissipation rate
ranges from 10
−5 m
2 s
−3 at night to 10
−1 m
2 s
−3 during the day (Stull 1994).
3.5 Introduction to Turbulent Motion Equations
55