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| Titel |
Direct Numerical Simulation of a Dry Shear-free Convective Boundary Layer |
| VerfasserIn |
J. R. Garcia, J. P. Mellado |
| Konferenz |
EGU General Assembly 2012
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 14 (2012) |
| Datensatznummer |
250063548
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| Zusammenfassung |
| Due to the thinness of the inversion layer, entrainment in the Convective Boundary Layer
(CBL) is not explicitly resolved in models and is still a major source of uncertainty. Recent
work using Large Eddy Simulations (LES) shows lack of convergence in the inversion layer
with further grid refinement, even for a vertical resolution of 2 meters. Observational
studies of entrainment in the CBL are even more problematic, whether they be
field observations or their low Reynolds number analogs in the laboratory, since
fine measurements of the three-dimensional flow field at the inversion layer are
practically unattainable. As an alternative, we use Direct Numerical Simulations (DNS),
which resolves the three-dimensional flow field down to the scale of molecular
diffusion. Faithful representation of the whole range of turbulent scales would mean
that attainable Reynolds numbers are orders of magnitude lower than that in the
atmosphere because of limited computational resources. However, the significant
increase in computing power now allows for simulations that are comparable in
size to tank experiments. Furthermore, we can invoke Reynolds number similarity
to justify the use of DNS to study an idealized convective boundary layer. As a
first step, we consider here the dry, shear-free case with constant surface buoyancy
flux B0 working against a stable background stratification with constant buoyancy
frequency N. Fixing the Prandlt number Pr = ν-κ to 1, where ν is the molecular
kinematic viscosity and κ is the molecular diffusivity, the problem is characterized by a
single non-dimensional parameter (B0-κ)-N2 which can be interpreted as the
ratio between a reference well-mixed layer height and the diffusive layer thickness.
In the atmosphere, (B0-κ)-N2 is at least O(106), while for our first simulation,
(B0-κ)-N2 ~ 40. We have done one simulation with a 1024x1024x541 grid that uses
vertical grid stretching, and another that is twice as wide (2048x2048x541) for assessing
statistical convergence and the effect of the computational domain size. Even with
vertical grid stretching, the grid spacing is smaller than the Kolmogorov length
scale. Despite the low Reynolds number, we obtain qualitatively comparable vertical
structure as in LES and observations. Relative values -¨w ′w′-©max-w*2 ~ 0.35 - 0.48,
-¨b′w′-©max-B0 ~ 0.8 - 0.9, and TKEmax-w*2 ~ 0.3 - 0.38 are within the range
found in literature. The entrainment ratio A = --¨b′w′-©min-B0 fluctuates in time
but has an increasing trend from 0.08 to 0.12, smaller than the canonical value
(A = 0.2) but close to the result from fine-resolution LES (A ~ 0.14). We explored
different definitions of the mean inversion height zi and chose the vertical location
of the buoyancy fluctuation peak at the inversion (max(brms)) because it proved
to be more robust. As a function of time, zi is approximated well by a -t curve
within 10%. The corresponding Richardson number Ribrms = (max(brms)zi)-w*2
approaches Ribrms ~ O(1) and is slightly increasing in time. To check for low
Reynolds number effects, we do a simulation that is twice as high (2048x2048x1024),
therefore increasing (B0-κ)-N2 to approximately 100 and the physical domain to
approximately a 2-meter box. After establishing DNS as a feasible tool for studying the dry
shear-free CBL, we will then use DNS data to investigate the physics of entrainment. |
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