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Abstract Large-eddy simulation (LES) runs are performed to understand the influence of a one-dimensional (1D) surface heating heterogeneity on organized vertical motions within and above the atmospheric boundary layer (ABL). Two knowledge gaps are of interest: (i) how updrafts develop in the low free troposphere and (ii) what parameters control updraft location and strength within the ABL? LES runs are performed for a sheared, unstable ABL driven by geostrophic winds of the same magnitude but in various directions relative to a 1D surface-heat-flux heterogeneity. Quasi-steady-state LES results are phase-averaged over time and the horizontal dimension perpendicular to the surface-heat-flux gradient to quantify secondary circulations. Regarding the first knowledge gap, the results show that organized vertical motions in the low free troposphere can be modeled as two-dimensional (2D), stationary gravity waves, whose amplitudes depend on ABL updraft strength and instability development within the free troposphere. For the second gap, the results show that organized updrafts within the ABL may form above warm surfaces or downwind of warm-to-cool transitions. These different locations are well explained by both the relative contributions of horizontal and vertical velocities to the phase-averaged vorticity fluctuations tied to secondary circulations, and the relative importance of horizontal advection and turbulent transport in the phase-averaged internal energy fluctuation equation. The main balances associated with each updraft location are used to propose empirical models of updraft strength, and it is shown that the presence of sufficiently strong organized vertical motions can potentially change parameters used by atmospheric models that do not resolve ABL turbulence. Significance StatementThe purpose of this study is to better understand how heterogeneous surface heating affects updraft location and strength in the lowest kilometers of the atmosphere. We focus on horizontal heterogeneity scales comparable to the most frequently observed cloud size, a necessary step toward the parameterization of cloud shadow effects in weather and climate models. The results show that persistent updrafts may form above either warm or cool surfaces, with their location depending on the relative importance of terms in certain budget equations. Near-surface updrafts become stronger as the background mean wind becomes more perpendicular to the surface-heat-flux gradient, but their potential to influence clouds peaks when the background mean wind is neither parallel nor perpendicular to the surface-heat-flux gradient. 

Abstract Understanding the interactions between turbulent and nonturbulent motions has been a persistent challenge faced by the community studying stably stratified turbulent flows. For flows with high Reynolds number, high Rossby number, and stable stratifications, nonturbulent motions involve physical mechanisms acting against instability development. Because turbulent motions are generated through an energy cascade via instability development, the presence of nonturbulent motions is expected to modify the energy distribution across scales compared to that of solely turbulent motions. The objective of this work is to identify in field data statistical signals of nonturbulent motions caused by stable stratification. The need to resolve energy-containing motions in both space and time requires high-frequency time series of velocity fluctuations collected using arrays of sonic anemometers. The analysis is performed using data from the Canopy Horizontal Array Turbulence Study (CHATS), during which a total of 31 sonic anemometers were deployed on a horizontal array and on a 30-m tower. Compared to other field campaigns which were also equipped with arrays of sonic anemometers, CHATS took an important advantage of already published nighttime canopy-scale waves derived from aerosol backscatter lidar images. After precluding complexities caused by nonstationarity and horizontal heterogeneity, signals of nonturbulent motions caused by stable stratification are identified from spatial autocorrelations of time-block-averaged velocity fluctuations. These signals are interpreted using existing understanding of turbulent canopy flows and two-dimensional Kelvin–Helmholtz instability development. The associated estimates of critical wavelengths and buoyancy periods agree well with the overall properties of nighttime canopy-scale waves derived from lidar images. Significance StatementThis work investigates statistical signals of nonturbulent motions caused by stable stratification in sonic anemometer measurements of near-surface atmospheric flows. The detected signals of nonturbulent motions agree with theoretical predictions of the impacts of stable stratification on turbulent canopy flows. This agreement suggests potential advantages for understanding stably stratified near-surface flows using canopy-resolving simulations. The automatic, objective, statistical detection procedures, as well as the intermediate products of the periods of statistically stationary, horizontally homogeneous, approximately two-dimensional mean flows, are useful for improving the understanding of canopy flows for various stability conditions. 

Abstract Unsteadiness and horizontal heterogeneities frequently characterize atmospheric motions, especially within convective storms, which are frequently studied using large-eddy simulations (LES). The models of near-surface turbulence employed by atmospheric LES, however, predominantly assume statistically steady and horizontally homogeneous conditions (known as the equilibrium approach). The primary objective of this work is to investigate the potential consequences of such unrealistic assumptions in simulations of tornadoes. Cloud Model 1 (CM1) LES runs are performed using three approaches to model near-surface turbulence: the “semi-slip” boundary condition (which is the most commonly used equilibrium approach), a recently proposed nonequilibrium approach that accounts for some of the effects of turbulence memory, and a nonequilibrium approach based on thin boundary layer equations (TBLE) originally proposed by the engineering community for smooth-wall boundary layer applications. To be adopted for atmospheric applications, the TBLE approach is modified to account for the surface roughness. The implementation of TBLE into CM1 is evaluated using LES results of an idealized, neutral atmospheric boundary layer. LES runs are then performed for an idealized tornado characterized by rapid evolution, strongly curved air parcel trajectories, and substantial horizontal heterogeneities. The semi-slip boundary condition, by design, always yields a surface shear stress opposite the horizontal wind at the lowest LES grid level. The nonequilibrium approaches of modeling near-surface turbulence allow for a range of surface-shear-stress directions and enhance the resolved turbulence and wind gusts. The TBLE approach even occasionally permits kinetic energy backscatter from unresolved to resolved scales. Significance Statement The traditional approach of modeling the near-surface turbulence is not suitable for a tornado characterized by rapid evolution, strongly curved air parcel trajectories, and substantial horizontal heterogeneities. To understand the influence of statistically unsteady and horizontally heterogeneous near-surface conditions on tornadoes, this work adopts a fairly sophisticated approach from the engineering community and implements it into a widely used atmospheric model with necessary modifications. Compared to the traditional approach, the newly implemented approach produces more turbulent near-surface winds, more flexible surface-drag directions, and stronger wind gusts. These findings suggest a simulated tornado is very sensitive to the modeling approach of near-surface turbulence. 

Abstract This work explores the influence of Weighted Essentially Non-Oscillatory (WENO) schemes on Cloud Model 1 (CM1) large-eddy simulations (LES) of a quasi-steady, horizontally homogeneous, fully developed, neutral atmospheric boundary layer (ABL). An advantage of applying WENO schemes to scalar advection in compressible models is the elimination of acoustic waves and associated oscillations of domain-total vertical velocity. Applying WENO schemes to momentum advection in addition to scalar advection yields no further advantage, but has an adverse effect on resolved turbulence within LES. As a tool designed to reduce numerically generated spurious oscillations, WENO schemes also suppress physically realistic instability development in turbulence-resolving simulations. Thus, applying WENO schemes to momentum advection reduces vortex stretching, suppresses the energy cascade, reduces shear-production of resolved Reynolds stress, and eventually amplifies the differences between the surface-layer mean wind profiles in the LES and the mean wind profiles expected in accordance with the filtered law of the wall (LOTW). The role of WENO schemes in adversely influencing surface-layer turbulence has inspired a concept of anti-WENO (AWENO) schemes to enhance instability development in regions where energy-containing turbulent motions are inadequately resolved by LES grids. The success in reproducing the filtered LOTW via AWENO schemes suggests that improving advection schemes is a critical component toward faithfully simulating near-surface turbulence and dealing with other "Terra Incognita" problems. 

Abstract Surface friction contributes to tornado formation and maintenance by enhancing the convergence of angular momentum. The traditional lower boundary condition in atmospheric models typically assumes an instant equilibrium between the unresolved stress and the resolved shear. This assumption ignores the physics that turbulent motions are generated and dissipated at finite rates—in effect, turbulence has a memory through its lifetime. In this work, a modified lower boundary condition is proposed to account for the effect of turbulence memory. Specifically, when an air parcel moves along a curved trajectory, a normal surface-shear-stress component arises owing to turbulence memory. In the accompanying large-eddy simulation (LES) of idealized tornadoes, the normal surface-shear-stress component is a source of additional dynamic instability, which provides an extra pathway for the development of turbulent motions. The influence of turbulence memory on the intensity of quasi-steady-state tornadoes remains negligible as long as assumptions employed by the modified lower boundary condition hold over a relatively large fraction of the flow region of interest. However, tornadoes in a transient state may be especially sensitive to turbulence memory. Significance Statement Friction between the wind and the ground can influence atmospheric phenomena in important ways. For example, surface friction can be a significant source of rotation in some thunderstorms, and it can also help to intensify rotation when rotation is already present. Unfortunately, the representation of friction’s effects in atmospheric simulations is especially error-prone in phenomena characterized by rapid temporal evolution or strong spatial variations. Our work explores a new framework for representing friction to include the effect of the so-called turbulence memory. The approach is tested in idealized tornado simulations, but it may be applied to a wide range of atmospheric vortices. 

Abstract Typical environmental conditions associated with horizontal convective rolls (HCRs) and cellular convection have been known for over 50 years. Yet our ability to predict whether HCRs, cellular convection, or no discernable organized (null) circulation will occur within a well-mixed convective boundary layer based upon easily observed environmental variables has been limited. Herein, a large database of 50 cases each of HCR, cellular convection, and null events is created that includes observations of mean boundary layer wind and wind shear, boundary layer depth; surface observations of wind, temperature, and relative humidity; and estimates of surface sensible heat flux. Results from a multiclass linear discriminant analysis applied to these data indicate that environmental conditions can be useful in predicting whether HCRs, cellular convection, or no circulation occurs, with the analysis identifying the correct circulation type on 72% of the case days. This result is slightly better than using a mean convective boundary layer (CBL) wind speed of 6 m s⁻¹to discriminate between HCRs and cells. However, the mean CBL wind speed has no ability to further separate out cases with no CBL circulation. The key environmental variables suggested by the discriminant analysis are mean sensible heat flux, friction velocity, and the Obukhov length.