Turbulent Mixing Model Research Articles

Effects of Turbulence on Upper-Tropospheric Ice Supersaturation

Abstract Effects of turbulence on ice supersaturation at cirrus heights (>8 km) remain unexplored. Small-scale mixing processes become important for high Reynolds number flows, which may develop below the buoyancy length scale (10–100 m). The current study couples a stochastic turbulent mixing model with reduced dimensionality to an entraining parcel model to investigate, in large-ensemble simulations, how supersaturation evolves due to homogeneous turbulence in the stably stratified, cloud-free upper troposphere. The rising parcel is forced by a mesoscale updraft. The perturbation of an initially homogeneous vertical distribution of supersaturation is studied after a 36-m ascent in a baseline case and several sensitivity scenarios. Turbulent mixing and associated temperature fluctuations alone lead to changes in ensemble-mean distributions with standard deviations in the range 0.001–0.006, while mean values are hardly affected. Large case-to-case variability in the supersaturation field is predicted with fluctuation amplitudes of up to 0.03, although such large values are rare. A vertical gradient of supersaturation (≈10−3 m−1) is generated for high turbulence intensities due to the development of a dry-adiabatic lapse rate. Entrainment of slightly warmer (less than 0.1 K) environmental air into the parcel decreases the mean supersaturation by less than 0.01. Supersaturation fluctuations are substantially larger after entrainment events with an additional small offset in absolute humidity (by ±3.5%) between the parcel and environmental air. The predicted perturbations of ice supersaturation are significant enough to motivate studies of turbulence–ice nucleation interactions during cirrus formation that abandon the assumption of instantaneous mixing inherent to traditional parcel models. Significance Statement The purpose of our study is to investigate the effects of microscale turbulence on ice supersaturation in the upper troposphere. The associated variability in temperature and moisture fields is not resolved in cloud models and cannot easily be represented in terms of large-scale flow variables. We specify the conditions in which turbulent mixing and entrainment cause substantial variations in distributions of supersaturation. These include high turbulence intensity, strong atmospheric stability, and large moisture gradients. Our results suggest that turbulence may affect the strongly supersaturation-dependent ice formation processes in high-altitude clouds, pointing to the need to investigate cirrus formation in the presence of turbulence.

Eddy‐Mediated Turbulent Mixing of Oxygen in the Equatorial Pacific

AbstractIn the tropical Pacific, weak ventilation and intense microbial respiration at depth give rise to a low dissolved oxygen (O2) environment that is thought to be ventilated primarily by the equatorial current system (ECS). The role of mesoscale eddies and vertical mixing as potential pathways of O2 supply in this region, however, remains poorly known due to sparse observations and coarse model resolution. Using an eddy resolving simulation of ocean circulation and biogeochemistry, we assess the contribution of these processes to the O2 budget balance and find that vertical mixing of O2, which is modulated by the surface wind speed and the vertical shear of the eddying currents, contributes substantially to the replenishment of O2 in the upper equatorial Pacific thermocline, complementing the advective supply of O2 by the ECS and meridional circulation at depth. These transport processes vary seasonally in conjunction with the wind: mixing of O2 into the upper thermocline is strongest during boreal summer and fall when the vertical shear and eddy kinetic energy are intensified. The relationship between eddy activity and the downward mixing of O2 arises from the modulation of equatorial turbulence by Tropical Instability Waves via their impacts on the vertical shear. This interaction of processes across scales sustains a local pathway of O2 delivery into the equatorial Pacific interior and highlights the need for adequate observations and models of turbulent mixing and mesoscale processes for understanding and predicting the fate of the tropical Pacific O2 content in a warmer and more stratified ocean.

Numerical study of mixing vane spacer grid effect on subchannel mixing in a 5 × 5 rod bundle

Turbulent flow in rod bundle with spacer grid without mixing vanes and with mixing vanes of inclination angles from 10° to 30° was investigated by Reynolds Stress Transportation (RST) model under Reynolds numbers (Re) from 3.96 × 103 to 3.96 × 105. The predicted results were validated by experimental data of lateral velocity field in 5 × 5 rod bundle. The cross-flow velocity was relatively well predicted against experimental data, while lateral Reynolds normal stress was underpredicted near spacer grid and overpredicted far from spacer grid. The mixing vanes in one sub-channel generate high pressure region at the upstream side of mixing vane and low-pressure region at the downstream side of mixing vane, forming secondary flow structures. The lateral velocity increases with inclination angle and Re increasing. The lateral Reynolds stress increases with inclination angle increasing and decreases with Re increasing. The anisotropic turbulent states were studied by Lumley triangle method. The mixing vanes are the main factor dominating the turbulent states in rod bundle. The space grid resistance follows decreasing power function of Re and increases with inclination angle increasing. The secondary flow intensity follows an exponentially decaying function of distance from spacer grid and increases with inclination angle and Re increasing. The turbulent mixing coefficient model is an exponentially decreasing function of the distance from spacer grid, and it increases with inclination angle increasing and decreases with Re increasing. This paper studied the inclination angle and Re effect on the sub-channel mixing in a relatively large range of inclination angle and Re, improving the understandings of the sub-channel mixing phenomena.

Mathematical modeling of turbulent mixing in gas systems with a chevron contact boundary using NUT3D, BIC3D, EGAK, and MIMOSA numerical codes

The paper presents computational and experimental studies of the evolution of turbulent mixing in three-layer gas systems with the development of hydrodynamic instabilities, in particular Richtmyer-Meshkov and Kelvin-Helmholtz, under the action of shock waves. One of the contact boundaries of the gases was flat, the other with a break in the form of a chevron. Numerical calculations are performed both without initial perturbations of the contact boundaries, and in the presence of perturbations. It is shown that the roughness of the contact boundary significantly affects the width of the mixing zone.

Mathematical Modeling of Turbulent Mixing in Gas Systems with a Chevron Contact Boundary using NUT3D, BIC3D, EGAK, and MIMOSA Numerical Codes

Mathematical Modeling of Turbulent Mixing in Gas Systems with a Chevron Contact Boundary using NUT3D, BIC3D, EGAK, and MIMOSA Numerical Codes

Stochastic modeling of turbulent mixing based on a hierarchical swapping of fluid parcels

AbstractTurbulent mixing is an omnipresent phenomenon that constantly affects our everyday life and plays an important role in a variety of industrial applications. The simulation of turbulent mixing poses great challenges, since the full resolution of all relevant length and time scales is associated with an immense computational effort. This limitation can be overcome by only resolving the large‐scale effects and completely model the sub‐grid scales. The development of an accurate sub‐grid mixing model is therefore a key challenge to capture all interactions in the sub‐grid scales. At this place, the hierarchical parcel‐swapping (HiPS) model formulated by A.R. Kerstein [J. Stat. Phys. 153, 142–161 (2013)] represents a computationally efficient and scale‐resolving turbulent mixing model. HiPS mimics the effects of turbulence on time‐evolving, diffusive scalar fields. In HiPS, the diffusive scalar fields or a state space is interpreted as a binary tree structure, which is an alternative approach compared to the most common mixing models. Every level of the tree represents a specific length and time scale, which is based on turbulence inertial range scaling. The state variables are only located at the base of the tree and are treated as fluid parcels. The effects of turbulent advection are represented by stochastic swaps of sub‐trees at rates determined by turbulent time scales associated with the sub‐trees. The mixing only takes places between adjacent fluid parcels and at rates consistent with the prevailing diffusion time scales. In this work, the HiPS model formulation for the simulation of passive scalar mixing is detailed first. Preliminary results for the mean square displacement, passive scalar probability density function (PDF) and scalar dissipation rate are given and reveal the strengths of the HiPS model considering the reduced order and computational efficiency. These model investigations are an important step of further HiPS advancements. The integrated auxiliary binary tree structure allows HiPS to satisfy a large number of criteria for a good mixing model. From this point of view, HiPS is an attractive candidate for modeling the mixing in transported PDF methods.

Radiative–Convective Heating of the Surface of the Martian Descent Vehicle MSL with Taking into Account the Turbulent Nature of Flow

The three-dimensional computer model based on the Reynolds-averaged Navier–Stokes equations together with the Baldwin–Lomax and Prandtl algebraic models of turbulent mixing is used to calculate radiative–convective heat transfer on the surface of the MSL descent space vehicle. The intensification of convective heat transfer on the leeward side of the frontal aerodynamic shield and the superiority of the radiative heat flux density over the convective one on the rear surface are demonstrated. The calculations are performed using the physically and chemically nonequilibrium gas model. The results are compared with the calculations based on other computational models and the flight data on the heat load to the descent vehicle obtained during MSL descent in the dense layers of the Martian atmosphere.

Sub-channel analysis for LBE cooled fuel assembly with grid type spacers of China initiative accelerator driven system

The present study focuses on the thermal hydraulic characteristics of fuel assemblies in the China Initiative Accelerator Driven subcritical System (CiADS), which utilizes grid-type spacers to support lead bismuth eutectic (LBE) cooled fast reactors. While the structural design and mechanical analysis of CiADS triangular fuel assemblies with grid-type spacers have been preliminarily investigated, there is a pressing need to study the thermal hydraulic behavior of liquid LBE within these fuel assemblies. This analysis is crucial for assessing the safety and economy of the CiADS subcritical reactor. The sub-channel analysis code, based on the lumped parameter method, plays a vital role in rapidly evaluating the safety features of LBE-cooled fast reactor fuel assemblies. To comprehensively evaluate the thermal hydraulic performance of fuel assemblies with grid-type spacers in the CiADS LBE cooling system, the flow pressure drop model, turbulent mixing model, and convective heat transfer model for the fuel assembly structure with grid-type spacers were incorporated into the existing CiADS sub-channel analysis code. This enhanced code has been successfully employed in the thermal hydraulic analysis of fuel assemblies utilizing wire-type spacers in the CiADS system. To verify the validity and accuracy of the modified CiADS sub-channel analysis code in calculating triangular fuel assemblies with grid-type spacers, the code was first utilized to replicate a 19-rods flow heat transfer experiment with grid-type spacers cooling liquid LBE. A comparison between the simulation and experimental results confirms that the CiADS sub-channel analysis code can predict the coolant temperature and fuel rod surface temperature in fuel assemblies with grid-type spacers. Subsequently, the structure and thermal hydraulic design of the latest CiADS fuel assembly with grid-type spacers were reviewed. Finally, taking into account the aforementioned enhancements to the CiADS sub-channel analysis code, a comprehensive thermo-hydraulic calculation of the CiADS fuel assembly with grid-type spacers was conducted. The results demonstrate that the coolant outlet temperature, maximum cladding temperature, and maximum fuel pellet temperature all fall within the design parameters of CiADS. Furthermore, the impact of the number of rods in different rod bundles (91, 61, 37, and 7 rods) on thermal hydraulic performance was analyzed. The findings indicate that, while ensuring calculation accuracy and efficiency, the results obtained from the 37-rod bundle can effectively reflect the thermal hydraulic behavior of the reactor core.

Validation of a Human Upper Airway Computational Fluid Dynamics Model for Turbulent Mixing

Abstract Validation of a computational fluid dynamics (CFD) model used to simulate turbulent exchange in an anatomically detailed human upper airway with realistic breathing states is provided. Proper model validation is vital in confirming that temporal mixing and species distribution are accurate, therefore making the model useful in generalized turbulent mixing studies of the upper airway. Numerous levels of refinement were tested for time-step and mesh independence. Higher and lower rigor groups of modeling methodologies involved spatial discretization schemes, gradient reconstruction methods, transient formulations, and turbulence frameworks. A dual mesh independence study revealed that the rate of approach to mesh independence is a function of computational rigor and that multiple mesh independence studies should be carried out in parallel. The final validated model consisted of the finest mesh used in this study (8 × 106 cells), a time-step equating to 4000 timesteps per breath cycle, and higher rigor modeling methodologies. While its results were within the acceptable deviation from the experimental data, it was not as close as the model that utilized the coarsest mesh (∼2 × 106 cells), the fewest timesteps per breath cycle (128 timesteps per breath cycle), and lower rigor methodologies. Though the latter model was closer to the experimental data, it was proven to not be numerically independent, highlighting the importance of utilizing a myriad of metrics to prove numerical independence. Restricting independence studies to only using metrics from experimental comparisons is insufficient for proper validation.

Radiative-convective heating of the surface of the Martian descent vehicle MSL with allowance for the turbulent nature of the flow

A spatial computer model based on the Reynolds-averaged Navier-Stokes equations together with the Baldwin-Lomax and Prandtl algebraic models of turbulent mixing was used to calculate the radiative-convective heat transfer on the surface of the MSL descent vehicle. The intensification of convective heat transfer on the leeward side of the frontal aerodynamic shield and the superiority of the radiative heat flux density over the convective one on the rear surface are shown. The calculations were performed using the model of a physically and chemically nonequilibrium gas. A comparison is made with the results of calculations using other computational models and with flight data on the heat load on the descent vehicle obtained during the MSL descent in the dense layers of the Martian atmosphere.

Efficacy of green infrastructure in reducing exposure to local, traffic-related sources of airborne particulate matter (PM)

One aim of roadside green infrastructure (GI) is to mitigate exposure to local, traffic-generated pollutants. Here, we determine the efficacy of roadside GI in improving local air quality through the deposition and/or dispersion of airborne particulate matter (PM). PM was collected on both pumped air filters and on the leaves of a recently installed ‘tredge’ (trees managed as a head-high hedge) at an open road environment next to a primary school in Manchester, U.K. The magnetic properties of PM deposited on leaves and filters (size fractions PM10 and PM2.5) were deduced from hysteresis loops, first-order reversal curves (FORCs), and low-temperature remanence measurements. These were complemented with electron microscopy to identify changes in magnetic PM concentration downwind of the tredge/GI. We show that the tredge is permeable to airflow using a simple CO2 tracer experiment; hence, it allows interception and subsequent deposition of PM on its leaves. Magnetic loadings per m3 of air from filters (PM10 saturation magnetisation, Ms, at 5 K) were reduced by 40 % behind the tredge and a further 63 % in the playground; a total reduction of 78 % compared to roadside air. For the PM2.5 fraction, the reduction in magnetic loading behind the tredge was remarkable (82 %), reflecting efficient diffusional capture of sub-5 nm Fe-oxide particles by the tredge. Some direct mixing of roadside and playground air occurs at the back of the playground, caused by air flow over, and/or through gaps in, the slowly-permeable tredge. The magnetic loading on tredge leaves increased over successive days, capturing ~23 % of local, traffic-derived PM10. Using a heuristic two-dimensional turbulent mixing model, we assess the limited dispersion of PM < 22.5 μm induced by eddies in the tredge wake. This study demonstrates that PM deposition on leaves reduces exposure significantly in this school playground setting; hence, providing a cost-effective mitigation strategy.

Study of gas-liquid two-phase flow redistribution characteristics in the rod bundle channel using wire-mesh sensor

In subchannel analysis, the gas and liquid flow distribution phenomenon plays an important role in understanding rod bundle channels’ two-phase turbulent mixing mechanism. This paper obtained gas-liquid flow distribution data inside a vertical coupled subchannel rod bundle channel by utilizing a double-set wire-mesh sensor (WMS). To achieve evolutions of two-phase flow distributions, one subchannel was injected with gas and water called the donor channel, and the other injected with water is called the receptor channel. Four axial locations (Z/Dh = 28.95, 57.90, 86.86, and 115.81) were measured for each flow condition to obtain the evolution of the flow distribution. 36 flow conditions were acquired with 〈jg〉 from 0.073 to 1.02 m·s−1 and 〈jl〉 from 0.93 to 1.86 m·s−1 at Z/Dh = 115.81, including bubbly, cap-bubbly, and slug flow. The gas flow distributions were obtained by the cross-correlation calculation of the phase distribution data measured by a double-set WMS. The gas-phase flow rate relative errors acquired by WMS and rotameters are within ± 10%. To obtain the liquid flow distribution, the inter-subchannel equal-slip ratio assumption was introduced, which is according to the truth that two-phase flow characteristics between the adjacent subchannel are similar for most cases in this study. Further, obtained two-phase flow distribution data were verified and evaluated by Han et al.’s drift-flux model, and the relative errors for most cases are less than ± 20%. Results show that, under bubbly flow, the two-phase flow redistribution is weak. 90% of the gas was restricted in the donor channel, and the liquid flow was approximately distributed in both channels. With the increment of void fraction, two-phase flow redistributions are more severe. The liquid-phase recirculation flow was found in the receptor channel, under cap-bubbly and slug flow, which results in a higher gas-liquid flow in the donor channel than in the receptor channel. The rules of two-phase flow distributions indicate that the liquid-phase flow redistribution is more moderate than the gas phase. The drastic change in the gas-phase flow redistribution starts with the cap-bubbly flow. In addition, the current two-phase flow data indicates that the two-phase flow redistribution between the donor and the receptor channels does not follow the equal-volume principle postulated in the existing two-phase turbulent mixing model. Furthermore, current data also imply the relationship between void and mass flux distribution is not linear as assumed in the existing two-phase turbulent mixing model.

Asteroseismic Investigation on KIC 10526294 to Probe Convective Core Overshoot Mixing

In the overshoot mixing model with an exponentially decreasing diffusion coefficient, the initial value of the diffusion coefficient plays a crucial role. According to the turbulent convective mixing model, the characteristic length of convection in the convection zone differs from that in the overshoot region, resulting in a rapid decrease of the diffusion coefficient near the convective boundary. To investigate this quick decrease, we conducted an asteroseismic study on the intermediate-mass slowly pulsating B-type star KIC 10526294. We generated stellar models with varied input parameters, including the overshoot parameters, and compared the resulting stellar oscillation periods with observations. To mitigate the potential issue arising from large steps in the stellar parameters and stellar age, we employed a comprehensive interpolation scheme for the stellar oscillatory frequencies, considering all stellar parameters and stellar age. Our analysis revealed that the quick decreasing of the diffusion coefficient has discernible effects on the stellar oscillations, and a quick decrease with 4 orders of magnitude shows the best oscillatory frequencies compared with the observations. This provides weak evidence in support of the prediction made by the turbulent convective mixing model. Furthermore, we examined the residuals of the oscillation periods and discovered a potential association between abundance anomalies in the buoyancy frequency profile and the oscillation-like patterns observed in the residuals.

Spiral arms are metal freeways: azimuthal gas-phase metallicity variations in flocculent discs in the FIRE-2 cosmological zoom-in simulations

ABSTRACT We examine the azimuthal variations in gas-phase metallicity profiles in simulated Milky Way-mass disc galaxies from the Feedback in Realistic Environments (FIRE-2) cosmological zoom-in simulation suite, which includes a sub-grid turbulent metal mixing model. We produce spatially resolved maps of the discs at z ≈ 0 with pixel sizes ranging from 250 to 750 pc, analogous to modern integral field unit galaxy surveys, mapping the gas-phase metallicities in both the cold and dense gas and the ionized gas correlated with H ii regions. We report that the spiral arms alternate in a pattern of metal rich and metal poor relative to the median metallicity of the order of ≲0.1 dex, appearing generally in this sample of flocculent spirals. The pattern persists even in a simulation with different strengths of metal mixing, indicating that the pattern emerges from physics above the sub-grid scale. Local enrichment does not appear to be the dominant source of the azimuthal metallicity variations at z ≈ 0: there is no correlation with local star formation on these spatial scales. Rather, the arms are moving radially inwards and outwards relative to each other, carrying their local metallicity gradients with them radially before mixing into the larger-scale interstellar medium. We propose that the arms act as freeways channeling relatively metal poor gas radially inwards, and relatively enriched gas radially outwards.

Multifidelity validation of digital surrogates using variable-density turbulent mixing models

High-speed experiments studying the Blast Driven Instability are used to validate Reynolds-Averaged Navier-Stokes (RANS) and Large eddy simulation (LES) turbulent mixing models. The work helps to elucidate the three mixing regimes of the instability and shows that the LES can successfully capture, at lease to the first order, the complex physics therein. The work also highlights the limitations of RANS models for transitioning instabilities and how LES results remain highly sensitive to the characterization of initial conditions.

Data-driven nonlinear K-L turbulent mixing model via gene expression programming method

Data-driven nonlinear K-L turbulent mixing model via gene expression programming method

The Effects of Radiative Feedback and Supernova-induced Turbulence on Early Galaxies

The recently launched James Webb Space Telescope promises unparalleled advances in our understanding of the first stars and galaxies, but realizing this potential requires cosmological simulations that capture the key physical processes that affected these objects. Here, we show that radiative transfer and subgrid turbulent mixing are two such processes. By comparing simulations with and without radiative transfer but with exactly the same physical parameters and subgrid turbulent mixing model, we show that tracking radiative transfer suppresses the Population III star formation density by a factor ≈4. In both simulations, ≳90% of Population III stars are found in the unresolved pristine regions tracked by our subgrid model, which does a better job at modeling the regions surrounding proto-galaxy cores where metals from supernovae take tens of megayears to mix thoroughly. At the same time, radiative transfer suppresses Population III star formation, via the development of ionized bubbles that slow gas accretion in these regions, and it results in compact high-redshift galaxies that are surrounded by isolated low-mass satellites. Thus, turbulent mixing and radiative transfer are both essential processes that must be included to accurately model the morphology, composition, and growth of primordial galaxies.

Development of a Single-Phase, Transient, Subchannel Code, within the MOOSE Multi-Physics Computational Framework

Subchannel codes have been widely used for thermal-hydraulics analyses in nuclear reactors. This paper details the development of a novel subchannel code within the Idaho National Laboratory’s (INL) Multi-physics Object Oriented Simulation Environment (MOOSE). MOOSE is a parallel computational framework targeted at the solution of systems of coupled, nonlinear partial differential equations, that often arise in the simulation of nuclear processes. As such, it includes codes/modules able to solve the multiple linear and nonlinear physics that describe a nuclear reactor, under normal operation conditions or accidents. This includes thermal-hydraulics, fuel performance, and neutronics codes, between others. A MOOSE-based subchannel code is a new addition to the fleet of INL-developed codes, based on the MOOSE framework. In this work, we present the derivation of the subchannel equations for a single-phase fluid, we proceed with the description of the algorithm that is used to solve these equations and describe how this algorithm was implemented within MOOSE. We also present how this code can be coupled to the BISON fuel performance code. Next, we verify the friction model and the turbulent mixing model. We calibrate the turbulent modeling parameters for momentum mixing and enthalpy mixing, CT,β. We validate the code using experimental results and last demonstrate the coupling capabilities using a simple example.

Sub-channel analysis of lead–bismuth fast reactor fuel assembly with wire spacers for China initiative accelerator driven system

The lead bismuth eutectic (LBE) cooled fast reactor fuel assemblies in China Initiative Accelerator Driven subcritical System (CiADS) are supported by wire spacers, and the sub-channel code is a significant analysis method to evaluate the thermal–hydraulic behavior of fuel assemblies. In this study, a sub-channel analysis code for LBE coolant is developed, in which the pressure drop model, turbulent mixing model, and heat transfer model based on LBE are added and applied. Besides, the heat transfer experience of the 61-pin fuel assembly and other sub-channel codes are chosen to verify. Finally, the full-scale simulation of CiADS fuel assembly is calculated. The results show that the thermal–hydraulic parameters of CiADS meet the design criterion. The optimized range of pitch to diameter ratio is 1.133–1.145 according to the thermal–hydraulic analysis. It is recommended to use 37-pin bundle for the numerical simulation simplification of full-scale rod bundles.

Sensitivity of large eddy simulations of tropical cyclone to sub-grid scale mixing parameterization

The surface wind structure and vertical turbulent transport processes in the eyewall of hurricane Isabel (2003) are investigated using six large-eddy simulations (LESs) with different horizontal grid spacing and three-dimensional (3D) sub-grid scale (SGS) turbulent mixing models and a convection permitting simulation that uses a coarser grid spacing and one-dimensional vertical turbulent mixing scheme. The mean radius-height distribution of storm tangential wind and radial flow, vertical velocity structure, and turbulent kinetic energy and momentum fluxes in the boundary layer generated by LESs are consistent with those derived from historical dropsonde composites, Doppler radar, and aircraft measurements. Unlike the convection permitting simulation that produces storm wind fields lacking small-scale disturbances, all LESs are able to produce sub-kilometer and kilometer scale eddy circulations in the eyewall. The inter-LES differences generally reduce with the decrease of model grid spacing. At 100-m horizontal grid spacing, the vertical momentum fluxes induced by the model-resolved eddies and the associated eddy exchange coefficients in the eyewall simulated by the LESs with different 3D SGS mixing schemes are fairly consistent. Although with uncertainties, the decomposition in terms of eddy scales suggests that sub-kilometer eddies are mainly responsible for the vertical turbulent transport within the boundary layer (~1 km depth following the conventional definition) whereas eddies greater than 1 km become the dominant contributors to the vertical momentum transport above the boundary layer in the eyewall. The strong dependence of vertical turbulent transport on eddy scales suggests that the vertical turbulent mixing parameterization in mesoscale simulations of tropical cyclones is ultimately a scale-sensitive problem.