the atmospheric nocturnal boundary layer. The flow evolution is investigated for combinations of the (bulk) Reynolds number and the imposed surface buoyancy flux.
First, we establish what the similarities and differences are between applying
a fixed buoyancy difference (Dirichlet) or a fixed buoyancy flux (Neumann)
as boundary conditions. Moreover, two distinct parameters were recently proposed
for the the turbulent-to-laminar transition: the Reynolds number based
on the Obukhov length; and the ’shear capacity’, a velocity scale ratio based
on the buoyancy flux-maximum. We study how these parameters relate to
each other and to the outdoor atmospheric boundary layer. The results show that in
a weakly stratified equilibrium state the flow statistics are virtually the same
between the different types of boundary condition. However, at stronger stratification
and, more generally in in non-equilibrium conditions the flow statistics
do depend on the type of boundary condition used. In the case of Neumann
boundary conditions, a clear sensitivity to the initial stratification strength
is observed due to the existence of multiple equilibria, while for Dirichlet
boundary conditions only one statistically steady turbulent equilibrium exists
for a particular set of boundary conditions. As in previous studies, we find
that when the imposed surface flux is larger than the maximum buoyancy flux
no turbulent steady-state occurs. Analytical investigation and simulation data
indicate that this maximum buoyancy flux converges for increasing Reynolds
numbers, which suggests a possible extrapolation to the atmospheric case.
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