Large-Eddy Simulation: How Large is Large Enough?

Abstract

The length scale evolution of various quantities in a clear convective boundary layer (CBL), a stratocumulustopped boundary layer, and three radiatively cooled (''smoke cloud'') convective boundary layers are studied by means of large-eddy simulations on a large horizontal domain (25.6 ϫ 25.6 km 2 ). In the CBL the virtual potential temperature and the vertical velocity fields are dominated by horizontal scales on the order of the boundary layer depth. In contrast, the potential temperature and the specific humidity fields become gradually dominated by mesoscale fluctuations. However, at the mesoscales their effects on the virtual potential temperature fluctuations nearly compensate. It is found that mesoscale fluctuations are negligibly small only for conserved variables that have an entrainment to surface flux ratio close to Ϫ0.25, which is about the flux ratio for the buoyancy. In the CBL the moisture and potential temperature flux ratios can have values that significantly deviate from this number.The geometry of the buoyancy flux was manipulated by cooling the clear convective boundary layer from the top, in addition to a positive buoyancy flux at the surface. For these radiatively cooled cases it is found that both the vertical velocity as well as the virtual potential temperature spectra tend to broaden. The role of the buoyancy flux in their respective prognostic variance equations is discussed. It is argued that in the upper part of the clear CBL, where the mean vertical stratification is stable, vertical velocity variance and virtual potential temperature variance cannot be produced simultaneously. For the stratocumulus case, in which latent heat release effects in the cloud layer play an important role in its dynamics, the field of any quantity, except for the vertical velocity, becomes dominated by mesoscale fluctuations.In general, the location of the spectral peak of any quantity becoming constrained by the domain size should be avoided. The answer to the question of how large the LES horizontal domain size should be in order to include mesoscale fluctuations will, on the one hand, depend on the type of convection to be simulated and the kind of physical question one aims to address, and, on the other hand, the time duration of the simulation. Only if one aims to study the dynamics of a dry CBL that excludes moisture, a rather small domain size suffices. In case one aims to examine either the spatial evolution of the fields of any arbitrary conserved scalar in the CBL, or any quantity in stratocumulus clouds except for the vertical velocity, a larger domain size that allows the development of mesoscale fluctuations will be necessary.

On the length‐scale of the wind profile

“…the root mean square error (RMSE) between the observed and the Kaimal-based modelled normalised w-spectrum is 0.03 for neutral conditions at 40 m. Those derived from LES modelling in Jonker et al (1999) and de Roode and Duynkerke (2004) are related to a 'spectral-weighted' length-scale and to the ogive, respectively. Although they are not the same measure, the proportionality between them, as exposed by Cuxart et al (2000) for all length-scales, is clear.…”

“…Further, Jonker et al (1999) and de Roode and Duynkerke (2004) found from LES modelling of the CBL that the z i -normalised length-scales of the wspectrum were z-dependent with maximum values ranging from 0.9 to 1.4 at z/z i =0.5-0.6, being Jonker's length-scale profile nearly identical to that of Caughey and Palmer (1979) in Figure 2.…”

Cloud Shading Effects on Characteristic Boundary-Layer Length Scales

“…We analyze in detail length scales based on both cloud optical depth (τ ) and vertical wind velocity (w) associated with cloud development and thermal circulation, respectively. Previous work on length scales of vertical wind velocity was mainly based on clear cases without a cloud-surface coupling (Lenschow and Stankov 1986;De Roode et al 2004;Dosio et al 2005;Pino et al 2006;Verzijlbergh et al 2009;Hellsten and Zilitinkevich 2013). This coupling is taken into account in this study.…”

“…The length and time scales associated with these motions are determined by using autocorrelation analysis (Lenschow and Stankov 1986;Dosio et al 2005;Verzijlbergh et al 2009) and spectral analysis (e.g. Lenschow and Stankov 1986;De Roode et al 2004;Pino et al 2006;Hellsten and Zilitinkevich 2013). These methods are less computationally intensive than for example the also recently employed cloud tracking (e.g.…”

Sheared convective boundary layers: turbulence kinetic energy and entrainment dynamics

“…For scalars, it is known that an enhanced growth of horizontal scales in CBLs is typically caused by entrainment (in particular when the entrainmnet ratio differs significantly from that of buoyancy, e.g. De Roode et al, 2004). A final characterization of this feature in relation to the CBL momentum structure (e.g.…”