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1. Modeling Near-Surface Turbulence in Large-Eddy Simulations of a Tornado: An Application of Thin Boundary Layer Equations

   https://doi.org/10.1175/MWR-D-22-0060.1  

   Wang, Aaron; Pan, Ying; Bryan, George H.; Markowski, Paul M. (June 2023, Monthly Weather Review)

   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. 

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2. The Influence of WENO Schemes on Large-Eddy Simulations of a Neutral Atmospheric Boundary Layer

   https://doi.org/10.1175/JAS-D-21-0033.1  

   Wang, Aaron; Pan, Ying; Markowski, Paul M. (September 2021, Journal of the Atmospheric Sciences)

   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. 

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3. Reynolds shear stress modeling in turbulent boundary layers subject to very strong favorable pressure gradient

   https://doi.org/https://doi.org/10.1016/j.compfluid.2020.104494  

   Saltar, German; Araya, Guillermo (January 2020, Computers fluids)

   Recent numerical predictions of turbulent boundary layers subject to very strong Favorable Pressure Gradient (FPG) with high spatial/temporal resolution, i.e. Direct Numerical Simulation (DNS), have shown a meaningful weakening of the Reynolds shear stresses with a lengthy logarithmic behavior [1,2]. In the present study, assessment of the Shear Stress Transport and Spalart-Allmaras turbulence models (hence- forth SST and SA, respectively) in Reynolds-averaged Navier-Stokes (RANS) simulations is performed. The main objective is to evaluate the ability of popular turbulence models in capturing the characteristic features present during the quasi-laminarization phenomenon in highly accelerating turbulent boundary layers. A favorable pressure gradient is prescribed by a top converging surface (sink flow) with an approximately constant acceleration parameter of K = 4 . 0 ×10 −6 . Validation of RANS results is carried out by means of a large DNS dataset [1]. Generally speaking, the SA turbulence model has demonstrated the best compromise between accuracy and quick adaptation to the turbulent inflow conditions. Turbulence models properly captured the increasing trend of the freestream and friction velocity in highly accelerated flows; however, they fail to reproduce the decreasing behavior of the skin friction coefficient, which is typical in early stages of the quasi-laminarization process. Both models have shown deficient predictions of the decreasing and logarithmic behavior of Reynolds shear stresses as well as significantly overpredicted the production of Turbulent Kinetic Energy (TKE) in turbulent boundary layers subject to very strong FPG. https://doi.org/10.1016/j.compfluid.2020.104494 

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4. Comprehensive shear stress analysis of turbulent boundary layer profiles

   https://doi.org/10.1017/jfm.2019.673  

   Womack, Kristofer M.; Meneveau, Charles; Schultz, Michael P. (November 2019, Journal of Fluid Mechanics)

   Motivated by the need for accurate determination of wall shear stress from profile measurements in turbulent boundary layer flows, the total shear stress balance is analysed and reformulated using several well-established semi-empirical relations. The analysis highlights the significant effect that small pressure gradients can have on parameters deduced from data even in nominally zero pressure gradient boundary layers. Using the comprehensive shear stress balance together with the log-law equation, it is shown that friction velocity, roughness length and zero-plane displacement can be determined with only velocity and turbulent shear stress profile measurements at a single streamwise location for nominally zero pressure gradient turbulent boundary layers. Application of the proposed analysis to turbulent smooth- and rough-wall experimental data shows that the friction velocity is determined with accuracy comparable to force balances (approximately 1 %–4 %). Additionally, application to boundary layer data from previous studies provides clear evidence that the often cited discrepancy between directly measured friction velocities (e.g. using force balances) and those derived from traditional total shear stress methods is likely due to the small favourable pressure gradient imposed by a fixed cross-section facility. The proposed comprehensive shear stress analysis can account for these small pressure gradients and allows more accurate boundary layer wall shear stress or friction velocity determination using commonly available mean velocity and shear stress profile data from a single streamwise location. 

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5. Influence of Low-Level Shear Orientation and Magnitude on the Evolution and Rotation of Idealized Squall Lines. Part II: Storm Propagation and Dynamic Feedbacks

   https://doi.org/10.1175/MWR-D-25-0240.1  

   Brown, Matthew C; Marion, Geoffrey R; Coniglio, Michael C (February 2026, Monthly Weather Review)

   Abstract Idealized simulations described in Part I investigated the importance of near-surface [low level (LL); 0–500 m] line-parallel shear, varied in both direction and magnitude, for modulation of quasi-linear convective system (QLCS) updraft and vortex attributes. Here, in Part II, we explore dynamical processes contributing to these attributes. Results indicate that LL shear strongly impacts the strength and streamwise nature of LL inflow vorticity, while free lower-tropospheric line-normal shear modulates storm propagation and LL storm-relative flow (largely through modifications to ground-relative flow). These combine to impact the storm-relative helicity (SRH) of QLCS inflow, with higher SRH for near-storm environments with increased LL hodograph curvature and length (i.e., enhanced LL line-parallel shear). Increased influx of streamwise vorticity fosters the stronger and wider rotating updrafts identified previously, which are driven by intense midlevel dynamic accelerations. When coincident with near-surface circulation, these strongly forced updrafts can support intense, long-lived mesovortices. These results demonstrate that changes to the orientation and magnitude of the ambient LL shear vector, as well as the vertical distribution of shear, can have considerable influence on the underlying dynamics governing the propagation, updrafts, and rotation within squall lines—even for a fixed line-normal environmental shear value. Altogether, this study (along with Part I) provides crucial context for understanding near-storm environmental impacts on QLCS morphology and rotation. Significance StatementResearch related to linearly organized storms has largely focused on vertical changes in winds (i.e., shear) oriented normal to squall lines, but squall lines that produce considerable rotation often have a component of low-level shear oriented parallel to storms. This study, Part II of a larger work, assesses how these shear components influence the updrafts within squall lines. Line-normal shear and ambient flow impact how storms propagate, while line-parallel shear impacts their near-surface rotation. These factors combine to influence the overall strength and rotation within updrafts of quasi-linear convective systems (QLCSs) and their ability to support near-surface vortices that often precede squall-line tornadoes. These physical relationships can help improve our understanding and prediction of QLCS evolution and associated hazards. 

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