STEADY-STATE SlABLE IIOIiKDARY LAYEK
77
concept of the surface layer where it is assumed that the fluxes are independent of height. Thia approxim;ttion is valid only over a limited height interval: especially In the stable boundary layer, it is soon necessary to take the
variability of the tluxes with height into account.
A first approximation of the change of momentum flux with height is
girrn by
(12)
- c7;;lw' /sz = p- aplax
where ?ph?x is the pressure gradient in the direction of the mean wind speed
In the surface layer. If we assume that the thermal wind is negligible. we may
integrate (12) to
(13)
- d W ' = u: + p- '(Jp/Jx)z
which says that the stress linearly decreases with height and becomes zero at
a height h. where
Equations (I2)-( 14) are based on the assumption of no turning of wind
with height and, a s such, these are more representative of unstable conditions (see, e.g., DeardorfT, 1972; Wyngaard et a/.. this volume) than of
neutral and stable ones. For the latter, the stress profile is expected to
have some curvature, which increases with stability. Therefore, Eq. (14)
would considerably underestimate the height of neutral and stable boundary
layers. In the following section we present a simple model For calculating this
height as a function of stability and also for the wind and stress profiles.
3. A MODEL OF THE TURBULENT STABLE BOUNDARY LAYER
The most sophisticated models of the steady and homogeneous atmospheric boundary layer, which are capable of supplying many fine details of
turbulence structure, are those based on the threedimensional numerical
integration of thc Navier-Stokes quations (Deardorff, 1970, 1972). The
stably stratified boundary layer has remained elusive to this type of modeling because the subgrid-scale motions, which have to be parametrized due to
limitations of costs and computer capacity, are considered to dominate the
flow.
Next in hicrarchy and considerably cheaper are the models based on high
order closure techniques (Donaldson, 1973; Wyngaard ef nl., this volume:
Luniley ri ul.. this volume). Although, the lowest order closure assumptions have h e n found to be satisfactory for neutral and unstable
boundary layers, their validity under stable conditions still remains to be
77
concept of the surface layer where it is assumed that the fluxes are independent of height. Thia approxim;ttion is valid only over a limited height interval: especially In the stable boundary layer, it is soon necessary to take the
variability of the tluxes with height into account.
A first approximation of the change of momentum flux with height is
girrn by
(12)
- c7;;lw' /sz = p- aplax
where ?ph?x is the pressure gradient in the direction of the mean wind speed
In the surface layer. If we assume that the thermal wind is negligible. we may
integrate (12) to
(13)
- d W ' = u: + p- '(Jp/Jx)z
which says that the stress linearly decreases with height and becomes zero at
a height h. where
Equations (I2)-( 14) are based on the assumption of no turning of wind
with height and, a s such, these are more representative of unstable conditions (see, e.g., DeardorfT, 1972; Wyngaard et a/.. this volume) than of
neutral and stable ones. For the latter, the stress profile is expected to
have some curvature, which increases with stability. Therefore, Eq. (14)
would considerably underestimate the height of neutral and stable boundary
layers. In the following section we present a simple model For calculating this
height as a function of stability and also for the wind and stress profiles.
3. A MODEL OF THE TURBULENT STABLE BOUNDARY LAYER
The most sophisticated models of the steady and homogeneous atmospheric boundary layer, which are capable of supplying many fine details of
turbulence structure, are those based on the threedimensional numerical
integration of thc Navier-Stokes quations (Deardorff, 1970, 1972). The
stably stratified boundary layer has remained elusive to this type of modeling because the subgrid-scale motions, which have to be parametrized due to
limitations of costs and computer capacity, are considered to dominate the
flow.
Next in hicrarchy and considerably cheaper are the models based on high
order closure techniques (Donaldson, 1973; Wyngaard ef nl., this volume:
Luniley ri ul.. this volume). Although, the lowest order closure assumptions have h e n found to be satisfactory for neutral and unstable
boundary layers, their validity under stable conditions still remains to be