MODELING THE ATMOSPHERIC
BOUNDARY LAYER
J. C. WYNGAARD, 0. R. COTI?;, A N D K. S. RAO
Air Force Cambridge Rrsrorch Loharo~ories. Bedjord, Mossochusetts 01 730. L’.S. 4.
1. INTRODUCTION
Higher order closiire models, which use exact equations for the mean field
and approximate ones for the turbulence, can reproduce in remarkable
detail the structure of turbulent shear flows. Several models of this type are
discussed by Reynolds (1970), Bradshaw (1972), Mellor and Herring ( 1973),
and Donaldson (1973). The main differences between models are the closure
assumptions used for the turbulence equations.
Developing this type df madel for the atmospheric boundary layer is in
some ways more difficult. The effects of buoyancy and rotation modify the
structural relationships found in shear flows, and presumably buoyant and
rotation terms should appear in at least some of the closure assumptions.
Because the details of closure are currently rather controversial, even in
shear flows, going to the atmosphere only complicates matters. A second
difficulty is the lack of atmospheric turbulence data outside the surface layer.
Testing and refining models, checking closure assumptions, and establishing
model constants will be more difficult than with shear flows.
Lumley (1967, 1970) has suggested how closure can be done rationally.
and in Lumley and Khajeh-Nouri (this volume. p. 169). the method is
demonstrated. In contrast to other models, this approach minimizes the
need for ad hoc closure assumptions and thus represents a considerable
advance in the state of the art. Unfortunately, the model is considerably
more complex than any proposed to date and it seems that its application to
the atmosphere will first require establishing some of the model constants
through calculation of simpler flows. Our calculations here, which are based
on a simplified version of his model, are therefore only exploratory. Because
of the lack of atmospheric data, it is difficult to set model constants, and
some of them have arbitrarily been taken as zero; it is also difficult to check
predictions with observations, so we have simply compared our steady-state
193
BOUNDARY LAYER
J. C. WYNGAARD, 0. R. COTI?;, A N D K. S. RAO
Air Force Cambridge Rrsrorch Loharo~ories. Bedjord, Mossochusetts 01 730. L’.S. 4.
1. INTRODUCTION
Higher order closiire models, which use exact equations for the mean field
and approximate ones for the turbulence, can reproduce in remarkable
detail the structure of turbulent shear flows. Several models of this type are
discussed by Reynolds (1970), Bradshaw (1972), Mellor and Herring ( 1973),
and Donaldson (1973). The main differences between models are the closure
assumptions used for the turbulence equations.
Developing this type df madel for the atmospheric boundary layer is in
some ways more difficult. The effects of buoyancy and rotation modify the
structural relationships found in shear flows, and presumably buoyant and
rotation terms should appear in at least some of the closure assumptions.
Because the details of closure are currently rather controversial, even in
shear flows, going to the atmosphere only complicates matters. A second
difficulty is the lack of atmospheric turbulence data outside the surface layer.
Testing and refining models, checking closure assumptions, and establishing
model constants will be more difficult than with shear flows.
Lumley (1967, 1970) has suggested how closure can be done rationally.
and in Lumley and Khajeh-Nouri (this volume. p. 169). the method is
demonstrated. In contrast to other models, this approach minimizes the
need for ad hoc closure assumptions and thus represents a considerable
advance in the state of the art. Unfortunately, the model is considerably
more complex than any proposed to date and it seems that its application to
the atmosphere will first require establishing some of the model constants
through calculation of simpler flows. Our calculations here, which are based
on a simplified version of his model, are therefore only exploratory. Because
of the lack of atmospheric data, it is difficult to set model constants, and
some of them have arbitrarily been taken as zero; it is also difficult to check
predictions with observations, so we have simply compared our steady-state
193