Subgrid-scale Turbulent Mixing Research Articles

Parameterization of Vertical Turbulent Transport in the Inner Core of Tropical Cyclones and Its Impact on Storm Intensification. Part I: Sensitivity to Turbulent Mixing Length

Abstract In the inner core of a tropical cyclone, turbulence not only exists in the boundary layer (BL) but can also be generated above the BL by eyewall and rainband clouds. Thus, the treatment of vertical turbulent mixing must go beyond the conventional scope of the BL. The turbulence schemes formulated based on the turbulent kinetic energy (TKE) are attractive as they are applicable to both deep and shallow convection regimes in the tropical cyclone (TC) inner core provided that the TKE production and dissipation can be appropriately determined. However, TKE schemes are not self-closed. They must be closed by an empirically prescribed vertical profile of mixing length. This motivates this study to investigate the sensitivity of the simulated TC intensification to the sloping curvature and asymptotic length scale of mixing length, the two parameters that determine the vertical distribution of a prescribed mixing length. To tackle the problem, both idealized and real-case TC simulations are performed. The results show that the simulated TC intensification is sensitive to the sloping curvature of mixing length but only exhibits marginal sensitivity to the asymptotic length scale. The underlying reasons for such sensitivities are explored analytically based on the Mellor and Yamada level-2 turbulence model and the analyses of azimuthal-mean tangential wind budget. The results highlight the uncertainty and importance of mixing length in the numerical prediction of TCs and suggest that future research should focus on searching for physical constraints on mixing length, particularly in the low- to midtroposphere, using observations and large-eddy simulations. Significance Statement The parametric representation of subgrid-scale turbulent mixing is one of the major sources of uncertainty in numerical predictions of tropical cyclones (TCs). This study investigates how the numerical prediction of TC intensification is affected by the turbulent mixing length, a length scale that is required to close a turbulence scheme formulated based on the turbulent kinetic energy (TKE). The research highlights the uncertainty and importance of mixing length in numerical prediction of TCs and suggests that future research should focus on searching for physical constraints on the mixing length, particularly in the low- to midtroposphere, using observations and large-eddy simulations.

What Are the Balanced and Unbalanced Dynamics of a Tropical Cyclone?

Abstract Recently, Ji and Qiao took into account the unbalanced components and derived an extended Sawyer–Eliassen (SE) equation. This study developed a new derivation of this extended SE equation from the perspective of restoring forces, and gives a physical interpretation for the coefficients that appear in the SE equation. For an unbalanced vortex, we demonstrated that the thermodynamic fields are only determined by the distribution of gradient wind, and thus, the gradient wind and thermodynamic fields always remain in balance as the unbalanced vortex evolves. Consequently, we attributed the gradient wind imbalance to the agradient wind rather than to the thermodynamic fields. Subsequently, we explored the effect of the agradient wind on the secondary circulation, and showed that the agradient wind strengthens the secondary circulation in its vicinity, which can be explained as a consequence of the restoring forces and mass continuity. Furthermore, we speculated that the SE equation, together with the radial velocity equation, could reproduce the primary characteristic of the axisymmetric boundary layer dynamics by prescribing the parameterization of subgrid-scale turbulent mixing. Specifically, the noU_BL and noVa_BL experiments conducted by Fei et al. in an article published in 2021 were reinterpreted, and the oscillation wavelength of the agradient wind in the eyewall was approximated based on this framework. Additionally, a new numerical solution algorithm to overcome the hyperbolicity near the boundary layer was proposed. This study attempts to develop a complete dynamic theory for tropical cyclones in both qualitative and quantitative perspectives.

The Influence of Boundary Layer Mixing Strength on the Evolution of a Baroclinic Cyclone

AbstractSubgrid-scale turbulence in numerical weather prediction models is typically handled by a PBL parameterization. These schemes attempt to represent turbulent mixing processes occurring below the resolvable scale of the model grid in the vertical direction, and they act upon temperature, moisture, and momentum within the boundary layer. This study varies the PBL mixing strength within 4-km WRF simulations of a 26–29 January 2015 snowstorm to assess the sensitivity of baroclinic cyclones to eddy diffusivity intensity. The bulk critical Richardson number for unstable regimes is varied between 0.0 and 0.25 within the YSU PBL scheme as a way of directly altering the depth and magnitude of subgrid-scale turbulent mixing. Results suggest that varying the bulk critical Richardson number is similar to selecting a different PBL parameterization. Differences in boundary layer moisture availability, arising from reduced entrainment of dry, free tropospheric air, lead to variations in the magnitude of latent heat release above the warm frontal region, producing stronger upper-tropospheric downstream ridging in simulations with less PBL mixing. The more amplified flow pattern impedes the northeastward propagation of the surface cyclone and results in a westward shift of precipitation. In addition, trajectory analysis indicates that ascending parcels in the less-mixing simulations condense more water vapor and terminate at a higher potential temperature level than do ascending parcels in the more-mixing simulations, suggesting stronger latent heat release when PBL mixing is reduced. These results suggest that spread within ensemble forecast systems may be improved by perturbing PBL mixing parameters that are not well constrained.

A Method to Control the Environmental Wind Profile in Idealized Simulations of Deep Convection with Surface Friction

Abstract In idealized, horizontally homogeneous, cloud model simulations of convective storms, the action of surface friction can substantially modify the near-ground environmental wind profile over time owing to the lack of a large-scale pressure gradient force to balance the frictional force together with the Coriolis force. This situation is undesirable for many applications where the impact of an unchanging environmental low-level wind shear on the simulated storm behavior is the focus of investigation, as it introduces additional variability in the experiment and accordingly complicates interpretation of the results. Partly for this reason, many researchers have opted to perform simulations with free-slip lower boundary conditions, which with appropriate boundary conditions allows for more precise control of the large-scale environmental wind profile. Yet, some recent studies have advocated important roles of surface friction in storm dynamics. Here, a simple method is introduced to effectively maintain any chosen environmental wind profile in idealized storm simulations in the presence of surface friction and both resolved and subgrid-scale turbulent mixing. The method is demonstrated through comparisons of simulations of a tornadic supercell with and without surface friction and with or without invoking the new method. The method is compared with similar techniques in the literature and potential extensions and other applications are discussed.

A Grid-Refinement-Based Approach for Modeling the Convective Boundary Layer in the Gray Zone: Algorithm Implementation and Testing

Abstract A grid-refinement-based method is implemented in a community atmospheric model to improve the representation of convective boundary layer (CBL) turbulence on gray-zone [i.e., ~O(1) km] grids. At this resolution, CBL convection is partially resolved and partially subgrid scale (SGS), such that neither traditional mesoscale planetary boundary layer (PBL) schemes nor SGS closures for large-eddy simulations (LESs) are appropriate. The proposed method utilizes two-way interactive nesting to refine the horizontal resolution of the unstable surface layer of the daytime CBL. SGS turbulent mixing in the fine nest and coarse parent grids are parameterized by an LES turbulence closure and a PBL scheme, respectively. The method does not rely on predetermined empirical functions to introduce grid (scale) dependency and in theory works with any PBL scheme. Compared to the stand-alone gray-zone simulation, the proposed approach shows improvements in terms of higher-order statistics, the timing of the onset of resolved convection, and the convective structures. A deficiency of the method exists when the nest domain is limited to the surface layer; the convective structures become gradually contaminated by spurious convection on the parent gray-zone grid. A deeper nest domain alleviates the issue at increased computational costs.

A Physically Based Horizontal Subgrid-Scale Turbulent Mixing Parameterization for the Convective Boundary Layer

Abstract Compared to the representation of vertical turbulent mixing through various planetary boundary layer (PBL) schemes, the treatment of horizontal turbulent mixing in the boundary layer has received much less attention. In mesoscale and convective-scale models, subgrid-scale horizontal turbulent mixing has traditionally been associated with mesoscale circulations or eddies. Its parameterization most often adopts the gradient-diffusion model, where the horizontal mixing coefficients are usually set constant, or through the 2D Smagorinsky formulation, or in some cases based on the 1.5-order turbulence kinetic energy (TKE) closure. For horizontal turbulent mixing associated with boundary layer eddies, the traditional schemes are shown to perform poorly. This work investigates the characteristic turbulence velocity and length scales based on analysis of a well-resolved, wide-domain large-eddy simulation of a convective boundary layer (CBL). To improve the representation of horizontal turbulent mixing by CBL eddies, a class of schemes is proposed with different levels of sophistication. The first two schemes can be used together with first-order PBL schemes, while the third uses TKE to define its characteristic velocity scale and can be used together with TKE-based higher-order PBL schemes. The proposed parameterizations are tested a posteriori in idealized simulations of turbulent dispersion of a passive scalar. Comparisons show improved horizontal dispersion by the proposed schemes and further demonstrate the weakness of the existing schemes.

Homogeneity of the Subgrid-Scale Turbulent Mixing in Large-Eddy Simulation of Shallow Convection

Abstract This paper presents an approach to locally predict homogeneity of the subgrid-scale turbulent mixing in large-eddy simulation of shallow clouds applying double-moment warm-rain microphysics. The homogeneity of subgrid-scale mixing refers to the partitioning of the cloud water evaporation due to parameterized entrainment between changes of the mean droplet radius and changes of the mean droplet concentration. Homogeneous and extremely inhomogeneous mixing represent two limits of possible scenarios, where the droplet concentration and the mean droplet radius remains unchanged during the microphysical adjustment, respectively. To predict the subgrid-scale mixing scenario, the double-moment microphysics scheme is merged with the approach to delay droplet evaporation resulting from entrainment. Details of the new scheme and its application in the Barbados Oceanographic and Meteorological Experiment (BOMEX) shallow convection case are discussed. The simulated homogeneity of mixing varies significantly inside small convective clouds, from close to homogeneous to close to extremely inhomogeneous. The mean mixing characteristics become more homogeneous with height, reflecting increases of the mean droplet size and the mean turbulence intensity, both favoring homogeneous mixing. Model results are consistent with microphysical effects of entrainment and mixing deduced from field observations. Mixing close to homogeneous is predicted in volumes with the highest liquid water content (LWC) and strongest updraft at a given height, whereas mixing in strongly diluted volumes is typically close to extremely inhomogeneous. The simulated homogeneity of mixing has a small impact on mean microphysical characteristics. This result agrees with the previous study applying prescribed mixing scenarios and can be explained by the high humidity of the clear air involved in the subgrid-scale mixing.

Modeling microphysical effects of entrainment in clouds observed during EUCAARI-IMPACT field campaign

Abstract. This paper discusses aircraft observations and large-eddy simulation (LES) modeling of 15 May 2008, North Sea boundary-layer clouds from the EUCAARI-IMPACT field campaign. These clouds are advected from the northeast by the prevailing lower-tropospheric winds and featured stratocumulus-over-cumulus cloud formations. An almost-solid stratocumulus deck in the upper part of the relatively deep, weakly decoupled marine boundary layer overlays a field of small cumuli. The two cloud formations have distinct microphysical characteristics that are in general agreement with numerous past observations of strongly diluted shallow cumuli on one hand and solid marine stratocumulus on the other. Based on the available observations, a LES model setup is developed and applied in simulations using a novel LES model. The model features a double-moment warm-rain bulk microphysics scheme combined with a sophisticated subgrid-scale scheme allowing local prediction of the homogeneity of the subgrid-scale turbulent mixing. The homogeneity depends on the characteristic time scales for the droplet evaporation and for the turbulent homogenization. In the model, these scales are derived locally based on the subgrid-scale turbulent kinetic energy, spatial scale of cloudy filaments, mean cloud droplet radius, and humidity of the cloud-free air entrained into a cloud, all predicted by the LES model. The model reproduces contrasting macrophysical and microphysical characteristics of the cumulus and stratocumulus cloud layers. Simulated subgrid-scale turbulent mixing within the cumulus layer and near the stratocumulus top is on average quite inhomogeneous, but varies significantly depending on the local conditions.

Modeling of subgrid-scale cloud-clear air turbulent mixing in Large Eddy Simulation of cloud fields

This paper presents computational approach to locally predict the homogeneity of subgrid-scale turbulent mixing between a cloud and its environment in large-eddy simulation of warm (ice-free) shallow convective clouds applying a double-moment bulk microphysics scheme. The term homogenity of mixing refers to the change of the mean droplet size associated with evaporation of cloud water due to entrainment. The two contrasting limits are the homogeneous mixing, where the radius of all droplets is reduced and the concentration does not change during microscale homogenization, and the extremely inhomogeneous mixing, where the microscale homogenization leads to complete evaporation of some droplets and does not affect the rest. The novel approach is applied to simulations of shallow convective cloud field. The results show that locally the homogeneity of mixing can vary significantly because of the spatial variability of the intensity of turbulence and the mean droplet radius. On average, however, the mixing becomes more homogeneous with height because of higher turbulence intensities and larger droplet sizes aloft.

Modeling of Subgrid-Scale Mixing in Large-Eddy Simulation of Shallow Convection

Abstract This paper discusses an extension of the approach proposed previously to represent the delay of cloud water evaporation and buoyancy reversal due to the cloud–environment mixing in bulk microphysics large-eddy simulation of clouds. In the original approach, an additional equation for the mean spatial scale of cloudy filaments was introduced to represent the progress toward microscale homogenization of a volume undergoing turbulent cloud–environment mixing, with the evaporation of cloud water allowed only when the filament scale approached the Kolmogorov microscale. Here, it is shown through a posteriori analysis of model simulations that one should also predict the volume fraction of the cloudy air that was diagnosed in the original approach. The resulting model of turbulent mixing and homogenization, referred to as the λ–β model, is applied in a series of shallow convection simulations using various spatial resolutions and compared to the traditional bulk model. This work represents an intermediate step in the development of a modeling framework to simulate characteristics of microphysical transformations during entrainment and subgrid-scale turbulent mixing.

Representation of Turbulent Mixing and Buoyancy Reversal in Bulk Cloud Models

Abstract This paper discusses the representation of subgrid-scale turbulent mixing in bulk models of warm (ice free) clouds, which assume instantaneous adjustment to grid-scale saturation. This is a reasonable assumption for condensation of water vapor because supersaturations inside clouds are typically small (∼0.1% or smaller), except near cloud bases where about an order of magnitude larger supersaturations are anticipated. For the cloud evaporation, however, instantaneous adjustment to grid-scale saturation is questionable, especially when evaporation occurs as a result of turbulent mixing between a cloud and its unsaturated environment. This is because turbulent mixing between initially separated volumes of cloudy and cloud-free environmental air proceeds through a gradual filamentation of these volumes, with progressively increasing evaporation of cloud water during the approach to final homogenization. A relatively simple model of this chain of events is included in a bulk model of moist nonprecipitating thermodynamics. The model delays adjustment to saturation for cloud evaporation following the turbulent mixing until the volume can be assumed homogeneous. An additional prognostic variable, the width of a cloudy filament, is added to represent the progress of turbulent mixing and the approach to homogenization. Theoretical developments are illustrated by idealized 2D simulations of moist thermals rising from rest and realistic large-eddy simulations of a cloud field.