1. Introduction
In their seminal paper on convective storm modeling, Klemp and Wilhelmson (1978, hereafter KW78) utilized the large-eddy simulation (LES) approach pioneered by Deardorff (1970). For LES, it is assumed that the most important scales of motion (the energy containing, or “large” eddies) are well resolved on the grid. A modified form of the Navier–Stokes equations (usually called the “filtered Navier–Stokes” equations) is used for LES. These equations contain terms involving subgrid-scale (SGS) stress, 
The purpose of this article is not to review the deficiencies of popular eddy-viscosity SGS models [see Moeng and Sullivan (2014, p. 234) and references therein], nor do we wish to rehash the arguments of Bryan et al. (2003) regarding the resolution needed for LES turbulence closures to be appropriate in convective storm simulations. Instead, this paper deals with a somewhat different problem related to the common usage of LES for convective storm simulations.
Today’s computing power makes it relatively easy to perform convective storm simulations with grid spacings of O(100) m as recommended by Bryan et al. (2003). LES would therefore seem to be justifiable. But is LES still appropriate if there are no eddies (i.e., if the flow is not turbulent)? In almost all idealized modeling studies of convective storms, the boundary layer of the storm’s environment is laminar (e.g., the region to the right of the dashed curve in Fig. 1) owing to the lack of initial (random) perturbations and/or insufficient resolution. This article explores, quantitatively, how simulating laminar flow in conjunction with an LES turbulence closure is a problem, particularly when a lower boundary condition other than free slip is used.
Horizontal cross section of vertical velocity w at 
Citation: Monthly Weather Review 144, 5; 10.1175/MWR-D-15-0439.1
2. Simulation of a turbulent boundary layer using LES
CM1 [see appendix of Bryan and Morrison (2012)], release 18, is used in this study. For the first simulation, referred to as LES-TURB, we simulate a turbulent, neutral planetary boundary layer (PBL). The domain is 10 km 
All simulations are initialized with westerly winds of 10 m s−1 over the depth of the domain. In the lowest 1 km, potential temperature θ is 300 K, above which θ increases at 1 K km−1. For this first simulation, random θ perturbations having a maximum amplitude of 
Horizontal cross section of vertical velocity w at 
Citation: Monthly Weather Review 144, 5; 10.1175/MWR-D-15-0439.1
Domain-averaged vertical profiles in the LES-TURB simulation. (a) Mean zonal wind 
Citation: Monthly Weather Review 144, 5; 10.1175/MWR-D-15-0439.1
The vertical profile of total (resolved plus SGS) shear stress is very nearly linear, as expected (Fig. 3c). A good test of whether the most important eddies are well resolved, as is assumed in LES, is a comparison of the resolved turbulent stress, 
In summary, the vertical profiles of mean wind, mean shear, and resolved and SGS stresses in the LES-TURB simulation are all in excellent qualitative agreement with theoretical expectations and prior LES results [e.g., see Moeng and Sullivan 1994 (note especially their Fig. 8); also see Mason and Thomson 1992; Andren et al. 1994; Porté-Agel et al. 2000)].
3. Simulation of a laminar boundary layer using LES
A second simulation is configured identically to LES-TURB, except that the amplitude of the random temperature perturbations added to the initial temperature field is only 0.0025 K. The vertical velocity field technically has eddies (Fig. 4), but the amplitude of the velocity perturbations is so small [e.g., vertical velocity perturbations are O(1) cm s−1] that the PBL is very nearly laminar throughout the simulation. This simulation is referred to as LES-LAM. [A related simulation (not shown) was initialized without random perturbations (given the horizontal homogeneity, CM1 was run essentially as an expensive single-column model). Its outcome was virtually identical to the results summarized below.]
As in Fig. 2, but for the LES-LAM simulation. Note that the shading scheme differs from Fig. 2, and that maximum w is two orders of magnitude smaller than in the LES-TURB simulation.
Citation: Monthly Weather Review 144, 5; 10.1175/MWR-D-15-0439.1
The vertical wind profile evolves considerably differently in the LES-LAM simulation. The mean zonal wind increases almost linearly with height from the lowest horizontal wind grid level to the top of the shear layer, with the depth of the shear layer slowly increasing in time (Fig. 5a). By 
As in Fig. 3, but for the LES-LAM simulation. In (c), the vertical profile of total stress (resolved plus SGS) lies mostly beneath the (blue) SGS stress profile.
Citation: Monthly Weather Review 144, 5; 10.1175/MWR-D-15-0439.1
Because the PBL is laminar, the resolved shear stress is negligible in the LES-LAM simulation (exactly zero when initialized without random perturbations) and the SGS shear stress dominates (Fig. 5c). The lack of vertical turbulent stress (which is presupposed to be a dominant term in the design of LES) in the lowest several hundred meters (the lowest 350 m by t = 6 h) ultimately is responsible for the unrealistically large vertical wind shear in that layer. The excessive shear in the LES-LAM simulation is far more dreadful than in the LES-TURB simulation.
Though it is perhaps not widely appreciated in the severe storms community, it is well known in the turbulence community that SGS stress above the surface is overestimated in eddy-viscosity models when the resolved flow is laminar. For example, quoting Meneveau and Katz (2000): “when the resolved flow is laminar, the standard value of (the Smagorinsky constant) overestimates the SGS stress…” (p. 9). Though they are referring to Smagorinsky–Lilly SGS model, the Deardorff SGS model suffers from the same affliction.
4. Single-column simulation using a PBL scheme
As in Fig. 3, but for the PBLSCHEME simulation. In (c), the vertical profile of total stress (resolved plus SGS) lies beneath the (blue) SGS stress profile.
Citation: Monthly Weather Review 144, 5; 10.1175/MWR-D-15-0439.1
The vertical profiles of zonal wind and vertical shear are a much better match to the profiles in the LES-TURB simulation than are the LES-LAM profiles (cf. Figs. 3a,b; 5a,b; and 6a,b). The near-surface vertical shear profile (Fig. 6b) agrees well with expectations from Monin–Obukhov similarity theory (ϕm = 1) and also lacks the 
5. Implications for severe storm modeling
There recently has been renewed interest in the effects of friction on convective storms. It is well known that surface friction can intensify tornadoes, and presumably also incipient tornadoes, by inducing radial inflow within the boundary layer, thereby promoting the convergence of angular momentum toward the axis of rotation (e.g., Rotunno 1979; Howells et al. 1988; Lewellen 1993). More recent simulations have suggested that friction might play an additional role in the development of near-surface vertical vorticity in convective storms, by acting as a source of vorticity rather than just serving to promote the intensification of vorticity generated by other processes (Schenkman et al. 2012, 2014; Xu et al. 2015). Numerical models will be essential for this investigation, given that the effects of friction are generally unobservable (mobile radars used in field projects typically cannot observe winds below 100-m altitude except very near to the radar), and there is no way to know how a storm would have evolved in the absence of friction from observations alone.
In a turbulent flow, friction influences the overlying flow primarily via the largest, energy-containing turbulent eddies, which transport depleted momentum upward, away from the surface. (Of course, by continuity, relatively high momentum air from aloft must concurrently be brought downward, where it is then influenced by surface drag, and so forth.) Thus, if one wishes to investigate the effects of friction on a simulated convective storm using an LES configuration, it seems clear that eddies need to be present (i.e., resolved). The cool low-level outflow of convective storms in high-resolution simulations [i.e., grid spacings of O(100) m or less] tends to be highly turbulent and eddies are plentiful (Fig. 1). But in the storm environment in such simulations, eddies are typically absent, either because the simulations were not initialized with random temperature or wind perturbations (as is typically done in LES of the PBL), or because the resolution is too coarse to resolve eddies. The recent simulations of supercell storms in a convective boundary layer by Nowotarski et al. (2015), in which horizontal convective rolls and turbulent eddies are explicitly resolved, are a rare exception.
The principal conclusion from the simulations presented in sections 2 and 3 is that the influence of surface drag is incorrectly represented in numerical simulations run as LES but lacking turbulent eddies. Although this demonstration used a simple wind profile, there is no reason to believe that the LES approach applied in simulations of phenomena in laminar environments of large ambient shear (e.g., severe thunderstorm environments) would not also be problematic. Simulations run as LES that include surface friction but lack well-resolved turbulent eddies are probably simulating, at best, the “worst-case scenario” of friction’s effect on storms considering that nondimensional shear is overpredicted by as much as an order of magnitude. In other words, laminar LES potentially yields unrealistic storm evolution, particularly given the abundance of evidence that severe thunderstorm dynamics (both supercells and squall lines) are especially sensitive to the vertical wind shear in the lowest few hundred meters (e.g., Rotunno et al. 1988; McCaul and Weisman 2001; Markowski et al. 2003; Weisman and Rotunno 2004; Markowski and Richardson 2014). There may be additional applications beyond severe storms modeling for which these results could be relevant (e.g., Mũnoz-Esparza et al. 2014; Schalkwijk et al. 2015).
As an aside, we note that if a free-slip lower boundary condition is employed, then an absence of boundary layer eddies is irrelevant because the SGS model is inactive [particularly if the severe storms modeler has imposed at least some stratification in the environmental sounding so that Ri 
It is possible that LES using dynamic eddy viscosity SGS models (e.g., Germano et al. 1991; Bou-Zeid et al. 2008; Kirkil et al. 2012) would not be susceptible to the issues identified above, though to our knowledge, the use of such SGS models, which add considerable computational expense, has so far been limited to simulations of the PBL. Alternatively, the results of section 4 suggest that another viable option would be to use a PBL parameterization, even at fine grid spacings, if the simulated flow is laminar. Moreover, in some applications there are regions where LES is justified (i.e., regions in which eddies are both plentiful and well resolved, such as left of the dashed curved in Fig. 1), but other regions lacking eddies (such as right of the dashed curve in Fig. 1), where the results of the LES-LAM simulation (Fig. 5) suggest unrealistic wind shear will develop if the lower boundary condition is nonfree slip. It remains to be seen what adverse consequences might result from the use of artificially lengthened mixing lengths in regions where turbulence is resolved, but assumed by the parameterization to be unresolved (i.e., where turbulence is “double counted”). In some severe thunderstorm simulations (e.g., Frame and Markowski 2010, 2013; Schenkman et al. 2012, 2014, 2016; Oberthaler and Markowski 2013), the mixing length has been lengthened only in the neutral or slightly unstable (laminar) PBL surrounding the storm, and therefore where such an increase in length scale is needed. Thus, these simulations probably did not suffer from environmental wind profiles as unrealistic as those in the LES-LAM simulation (Fig. 5b).
One might conclude that the “safest” approach, if simulating thunderstorms via LES with a nonfree-slip lower boundary condition, would be to excite turbulent eddies in the storm’s environment and use sufficiently fine resolution so that the eddies are well resolved (e.g., Mũnoz-Esparza et al. 2014). The means by which a flow can be made turbulent are legion. Random temperature (e.g., Boudjemadi et al. 1996) or velocity (e.g., Andren et al. 1994; Chow et al. 2005) perturbations in the initial conditions are one simple way if a periodic domain is used, or in the case of open lateral boundaries, random temperature perturbations can be applied at an inflow boundary (e.g., Mũnoz-Esparza et al. 2014). More complicated “synthetic-eddy methods” exist for inhomogeneous boundary layers, unstructured meshes, and complex geometries (e.g., Jarrin et al. 2006). Some model setups allow for the use of “perturbation recycling” techniques (e.g., Mayor et al. 2002). As alluded to in section 2, one would still have to grapple with the “law-of-wall problem,” that is, the overprediction of near-surface vertical wind shear owing to turbulent eddies being inadequately resolved near the surface. Though there have been some remedies that have emerged from the PBL and civil, mechanical, and aerospace engineering communities (e.g., Sullivan et al. 1994; Chow et al. 2005; many others), it remains to be seen whether any of these approaches can be successful in severe thunderstorm simulations, which are characterized by a high degree of unsteadiness, large geostrophic vertical wind shear (frequently in excess of 25 m s−1 over the PBL on tornado outbreak days), and horizontal heterogeneity in the turbulence characteristics (e.g., within the statically stable cold pool versus within the convectively unstable or neutral PBL of the storm’s surroundings).
Another issue to contend with is that quantifying the effects of friction through traditional diagnostics (e.g., the vorticity equation) in a simulation in which the turbulence is well resolved would be difficult because friction’s effects would mostly (at least above the first grid level) be manifest in the resolved flow (e.g., resolved vorticity tilting, stretching, and advection) rather than being “neatly contained” within the SGS terms. Moreover, attempts to increase the realism of a thunderstorm simulation by including a turbulent environmental boundary layer without also including radiative transfer could have unintended (negative) consequences. For example, Nowotarski et al. (2015) found that the stabilization of the surface layer beneath a storm’s forward anvil (which greatly attenuates the solar beam) can modulate the boundary layer turbulence in importance ways.
Finally, although simulations of laminar flow with a LES SGS model are always likely to be a problem, for the reasons discussed above, we note that there are situations were laminar flow is more likely to occur. For example, it can be difficult to initiate turbulence in stably stratified flows and strongly sheared flows. In addition, our experience with grid spacing in the 250–500-m range (see, e.g., Nowotarski et al. 2014) suggests that marginally resolved boundary layer turbulence can be difficult to initiate and maintain, as well. In contrast, convective boundary layers with a strong surface heat flux usually develop resolved turbulence quite easily. Consequently, results may vary depending on application and available computing resources (i.e., techniques used to initiate turbulence in some studies may not work for others).
6. Summary
This paper documented the potential perils of using LES to simulate a laminar PBL in conjunction with a nonfree-slip boundary condition. In particular, nondimensional wind shear near the surface is badly overpredicted in a laminar PBL simulated via LES compared to a turbulent PBL, theory, and a PBL simulated using a PBL scheme. LES SGS models should only be used if the flow is turbulent. Simulations of mesoscale meteorological phenomena (e.g., convective storms), that are run as LES and include surface friction, but lack well-resolved turbulent eddies, likely overestimate friction’s effects on the phenomena. The influence of unrealistic near-surface shear on simulated convective storms will be explored in a future paper.
Acknowledgments
We are grateful for numerous constructive discussions with many colleagues: Elie Bou-Zeid, Jim Brasseur, Marcelo Chamecki, Tina Chow, Johannes Dahl, Evgeni Fedorovich, Jeff Mirocha, Matt Parker, Yvette Richardson, Rich Rotunno, Alex Schenkman, Peter Sullivan, Lou Wicker, and John Wyngaard. We also thank Branko Kosović and the anonymous reviewers for their critical evaluations. This work was supported by the National Science Foundation (Grants AGS-1157646 and AGS-1536460); the National Science Foundation’s support of the National Center for Atmospheric Research also is acknowledged. The first author is indebted to the Mesoscale and Microscale Meteorology Laboratory of the National Center for Atmospheric Research, who hosted his visit during June 2015.
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Vertical velocity and shear stresses are solved at 
The semislip condition is more commonly used than the no-slip condition owing to the fact that atmospheric flows tend to be over a rough surface. Moreover, the viscous sublayer is unresolved anyway, and the first grid point for the horizontal winds falls in the log-law layer.
