Turbulent Velocity Scale Research Articles

The K‐Profile Parameterization Augmented by Deep Neural Networks (KPP_DNN) in the General Ocean Turbulence Model (GOTM)

AbstractThis study utilizes Deep Neural Networks (DNN) to improve the K‐Profile Parameterization (KPP) for the vertical mixing effects in the ocean's surface boundary layer turbulence. The deep neural networks were trained using 11‐year turbulence‐resolving solutions, obtained by running a large eddy simulation model for Ocean Station Papa, to predict the turbulence velocity scale coefficient and unresolved shear coefficient in the KPP. The DNN‐augmented KPP schemes (KPP_DNN) have been implemented in the General Ocean Turbulence Model (GOTM). The KPP_DNN is stable for long‐term integration and more efficient than existing variants of KPP schemes with wave effects. Three different KPP_DNN schemes, each differing in their input and output variables, have been developed and trained. The performance of models utilizing the KPP_DNN schemes is compared to those employing traditional deterministic first‐order and second‐moment closure turbulent mixing parameterizations. Solution comparisons indicate that the simulated mixed layer becomes cooler and deeper when wave effects are included in parameterizations, aligning closer with observations. In the KPP framework, the velocity scale of unresolved shear, which is used to calculate ocean surface boundary layer depth, has a greater impact on the simulated mixed layer than the magnitude of diffusivity does. In the KPP_DNN, unresolved shear depends not only on wave forcing, but also on the mixed layer depth and buoyancy forcing.

Reinterpretation of the Thorpe Length Scale

Abstract In 1977, S. A. Thorpe proposed a method to estimate the dissipation rate ε of turbulence kinetic energy (TKE) in an overturning turbulent layer in a lake, by sorting the observed (unstable) density profile to render it stable and thus deriving a length scale LT named after him, from the resulting vertical displacements of water parcels. By further proposing that this purely empirical scale (with no a priori physical basis, unlike many other turbulence length scales) is proportional to the Ozmidov scale LO, definable only for stably (not unstably or neutrally) stratified flows, he was able to extract ε. The simplicity of the approach that requires nothing but CTD (Conductivity, Temperature and Depth) casts in water bodies, including lakes and oceans, made it attractive, until microstructure profilers were developed and perfected in later decades to actually make in-situ measurements of ε. Since equivalent microstructure devices are not available for the atmosphere, Thorpe technique has been resurrected in recent years for application to the atmosphere, using potential temperature profiles obtained from high vertical resolution radiosondes. Its popularity and utility have increased lately, in spite of unresolved issues related to the validity of assuming LT is proportional to LO. In this study, we touch upon these issues and offer an alternative interpretation of the Thorpe length scale as indicative of the turbulence velocity scale σK, which allows Thorpe sorting technique to be applied to all turbulent flows, including those generated by convection.

Numerical study of shock wave boundary layer interaction flows using a novel turbulence model

This study proposes a novel partial average fluctuation velocity (PAFV) turbulence based on the PAFV and the average strain rate tensor, which is used to calculate the shock wave boundary layer interaction flows, including cascade flow and transonic compressor flow. In order to illustrate the adequacy, the calculation results of several other turbulence models were also compared with PAFV, including k-ω, shear stress transport, SA-neg (negative Spalart-Allmaras), and stress-BSL (ω-based Reynolds stress model). The suitability of the PAFV turbulence model was initially tested by calculating the transonic flow in the L030-4 cascade. Subsequently, numerical computations were performed for the 3D (three-dimensional) National Aeronautics and Space Administration Rotor 67 transonic compressor rotor. In the numerical simulation, the flow control equations were transformed in a general curvilinear coordinate system for precision enhancement, and the spatial discretization of control equations was executed using the finite difference method. The convection term was processed using the Steger–Warming flux vector splitting method, the diffusion term was discretized using a second-order central difference scheme, and the time derivative term was discretized using the third-order Runge–Kutta method. A parallel computing strategy with multi-block partitioning was employed to speed up the calculations and facilitate faster convergence alongside a local time step method. All numerical computation procedures were written in Python, revealing the following: (1) The PAFV turbulence model aptly simulates the transonic flow within the cascade channel. The shock wave pattern in the cascade channel aligns well with the experimental schlieren images. (2) During the Rotor 67 transonic compressor rotor calculation, the flow–pressure ratio, flow efficiency, and inlet and outlet total temperatures and pressures align well with the experimental data. Furthermore, the resolution of the flow field structure related to the interaction between the tip leakage vortex and channel shock wave is high. (3) The turbulence model uses PAFV as the turbulence velocity scale, thereby suppressing the fluctuation velocity and turbulence viscosity near shock wave areas, preventing excessive turbulence viscosity. Moreover, PAFV inherently exhibits transport properties and anisotropic characteristics, making it well-suited for handling transonic compressor flows.

Effect of Small-Scale Topographical Variations and Fetch from Roughness Elements on the Stable Boundary Layer Turbulence Statistics

Understanding the influence of roughness and terrain slope on stable boundary layer turbulence is challenging. This is investigated using observations collected from October to November of 2018 during the Stable Atmospheric Variability ANd Transport (SAVANT) field campaign conducted in a shallow sloping Midwestern field. We analyze the turbulence velocity scale and its variation with the mean wind speed using observations up to 10–20 m on four meteorological towers located along a shallow gully. The roughness length for momentum over this complex terrain varied with wind direction from 0.0049 m to a maximum of 0.12 m for winds coming through deciduous trees present in the field. The variation of the turbulence velocity with wind speed shows a transition from a weak wind regime to a stronger wind regime, as reported by past studies. This transition is not observed for winds coming from the tree area, where turbulence is enhanced even for weak wind speeds. For weak stratification and stronger winds, the turbulent velocity scale increased with an increase in roughness while the terrain slope is seen to have a weak influence. The sizes of the dominant turbulent eddies seen from the vertical velocity power spectra are observed to be larger for winds coming through the tree area. The turbulence enhancement by the trees is found to be strong within a fetch distance of 7 times the tree height and not observable at 16 times of the tree height.

Numerical Simulation of Transonic Compressors with Different Turbulence Models

One of the most commonly used techniques in aerospace engineering is the RANS (Reynolds average Navier–Stokes) approach for calculating the transonic compressor flow field, where the accuracy of the computation is significantly affected by the turbulence model used. In this work, we use SA, SST, k-ɛ, and the PAFV turbulence model developed based on the side-biased mean fluctuations velocity and the mean strain rate tensor to numerically simulate the transonic compressor NASA Rotor 67 to evaluate the accuracy of turbulence modeling in numerical calculations of transonic compressors. The simulation results demonstrate that the four turbulence models are generally superior in the numerical computation of NASA Rotor 67, which essentially satisfies the requirements of the accuracy of engineering calculations; by comparing and analyzing the ability of the four turbulence models to predict the aerodynamic performance of transonic compressors and to capture the details of the flow inside the rotor. The errors of the Rotor 67 clogging flow rate calculated by the SA, SST, k-ɛ, and PAFV turbulence models with the experimental data are 0.9%, 0.8%, 0.7%, and 0.6%, respectively. The errors of the calculated peak efficiencies are 2.2%, 1.6%, 0.9%, and 4.9%. The SA and SST turbulence models were developed for the computational characteristics of the aerospace industry. Their computational stability is better and their outputs for Rotor 67 are comparable. The k-ɛ turbulence model calculates the pressure ratio and efficiency that are closest to the experimental data, but the computation of its details of the flow field near the wall surface is not ideal because the k-ɛ turbulence model cannot accurately capture the flow characteristics of the region of high shear stresses. The PAFV turbulence model has a better prediction of complex phenomena such as rotor internal shock wave location, shock–boundary layer interaction, etc., due to the use of a turbulent velocity scale in vector form, but the calculated rotor efficiency is small.

Microplastics segregation by rise velocity at the ocean surface

Predicting the vertical distribution of microplastics in the ocean surface mixed layer is necessary for extrapolating surface measurements and comparing observations across conditions. The competing mechanisms that control the vertical distribution are particle buoyancy, which is primarily a function of particle properties and drives microplastics to accumulate at the ocean surface, and turbulent mixing, which disperses microplastics throughout the mixed layer and depends on local hydrodynamics. In this study, we focused on the physical properties of microplastics collected within one vertical profile in the North Pacific. We measured the size, shape, and rise velocity of all microplastics collected, finding that average size and rise velocity decay with depth. In addition, we demonstrate how the vertical distribution of the microplastics depends on the rise velocity of the microplastics by segregating the data into three regimes based on a ratio of microplastic rise velocity and a characteristic turbulence velocity scale. Using an individual model for each regime, we can extrapolate the vertical distribution of microplastics to the bottom of the mixed layer and find the total concentration of microplastics. The total extrapolated concentration using the combined model results in 10× the concentration of the surface net alone and 47% more than a model which does not consider the different microplastic regimes. Finally, we discuss how the vertical distribution also depends on microplastic form, finding that lines are approximately well-mixed whereas the concentration of fragments decays with depth. These observations indicate the importance of considering the appropriate rise velocity regime when predicting the vertical distribution of microplastics.

Dry Deposition Methods Based on Turbulence Kinetic Energy: Part 1. Evaluation of Various Resistances and Sensitivity Studies Using a Single-Point Model.

Different functions are used to account for turbulence strength in the atmospheric boundary layer for different stability regimes. These functions are one of the sources for differences among different atmospheric models' predictions and associated biases. Also, turbulence strength is underrepresented in some of the resistance formulations. To address these issues with dry deposition, firstly we take advantage of three-dimensional (3-D) turbulence information in estimating resistances by proposing and validating a 3-D turbulence velocity scale that is relevant for different stability regimes of boundary layer. Secondly, we hypothesize and validate that friction velocity measured by 3-D sonic anemometer can be effectively replaced by the new turbulence velocity scale multiplied by the von Karman constant. Finally, we (1) present a set of resistance formulations for ozone (O3) based on the 3-D turbulence velocity scale; (2) intercompare estimations of such resistances with those obtained using existing formulations; and, (3) evaluate simulated O3 fluxes using a single-point dry deposition model against long-term observations of O3 fluxes at the Harvard Forest (MA) site. Results indicate that the new resistance formulations work very well in simulating surface latent heat and O3 fluxes when compared to respective existing formulations and measurements at a decadal time scale. Findings from this research may help to improve the capability of dry deposition schemes for better estimation of dry deposition fluxes and create opportunities for the development of a community dry deposition model for use in regional/global air quality models.

Dry Deposition Methods Based on Turbulence Kinetic Energy: Part 2. Extension to Particle Deposition Using a Single-Point Model.

Magnitude of atmospheric turbulence, a key driver of several processes that contribute to aerosol (i.e., particle) deposition, is underrepresented in current models. Various formulations have been developed to model particle dry deposition; all these formulations typically rely on friction velocity and some use additional ad hoc factors to represent enhanced impacts of turbulence. However, none were formally linked with the three-dimensional (3-D) turbulence. Here, we propose a set of 3-D turbulence-dependent resistance formulations for particle dry deposition simulation and intercompare the performance of new resistance formulations with that obtained from using the existing formulations and measured dry deposition velocity. Turbulence parameters such as turbulence velocity scale, turbulence factor, intensity of turbulence, effective sedimentation velocity, and effective Stokes number are newly introduced into two different particle deposition schemes to improve turbulence strength representation. For an assumed particle size distribution, the newly proposed schemes predict stronger diurnal variation of particle dry deposition velocity and are comparable to corresponding measurements while existing formulations indicate large underpredictions. We also find that the incorporation of new turbulence parameters either introduced or added stronger diurnal variability to sedimentation velocity and collection efficiencies values, making the new schemes predict higher deposition values during daytime and nighttime when compared to existing schemes. The findings from this research may help improve the capability of dry deposition schemes in regional and global models.

Some new insights for inferring diapycnal (irreversible) diffusivity in stably stratified turbulence

New insight for inferring diapycnal diffusivity in stably stratified turbulent flows is obtained based on physical scaling arguments and tested using high-resolution direct numerical simulation data. It is shown that the irreversible diapycnal diffusivity can be decomposed into a diapycnal length scale that represents an inner scale of turbulence and a diapycnal velocity scale. Furthermore, it is shown that the diapycnal length scale and velocity scale can be related to the measurable Ellison length scale (LE) that represents outer scale of turbulence and vertical turbulent velocity scale (w′) through a turbulent Froude number scaling analysis. The turbulent Froude number is defined as Fr=ε/Nk, where ε is the rate of dissipation of turbulent kinetic energy, N is the buoyancy frequency, and k is the turbulent kinetic energy. The scaling analysis suggests that the diapycnal diffusivity Kρ∼w′LE in the weakly stratified regime (Fr >1) and Kρ∼(w′LE)×Fr for the strongly stratified regime (Fr <1).

Influence of Stability and Surface Roughness on Turbulence during the Stable Atmospheric Variability and Transport (SAVANT) Field Campaign

Abstract Harvesting of crops in a weakly sloping Midwestern field during the Stable Atmospheric Variability and Transport (SAVANT) observation campaign allowed for a systematic investigation of the influence of surface roughness and static stability magnitude on the applicability of the Monin–Obukhov similarity (MOST) and hockey-stick transition (HOST) theories during stable boundary layer periods. We analyze momentum flux and turbulent velocity scale VTKE in three regimes, defined using the gradient Richardson number Ri and flux Richardson number Rif as regime 1 (0 < Ri ≤ 0.1 and 0 < Rif ≤ 0.1), regime 2 (0.1 < Ri ≤ 0.23 and 0.1 < Rif ≤ 0.23), and regime 3 (both Ri and Rif > 0.23). After harvest, in regime 1, stability varied from near-neutral to weakly stable and both MOST and HOST were applicable to estimate the momentum fluxes and VTKE as a function of mean wind speed. In regime 2, the momentum flux deviated from the MOST linear relationship as stability increased. In regimes 1 and 2, a HOST-defined threshold wind speed Vs was identified beyond which VTKE increased linearly with wind speed at a rate of 0.26 for all observation heights. Below this threshold wind speed, VTKE behaved independent of mean wind and observation heights. Alternatively, for preharvest periods, MOST was applicable in regimes 1 and 2 for all heights and HOST was applicable with reduced Vs for heights above the crop layer. Regime 3 during pre- and postharvest consisted of strongly stable periods and very weak to weak winds, where MOST was found to be invalid and VTKE remained low and independent of wind speed. The results suggest that roughness due to crops enhances the turbulence generation at lower wind speeds.

A multispecies 1D concentration distribution model for coarse‐particle slurries

AbstractCoarse‐particle (settling) slurry pipelines are key process units in many industries. In Canada's oil sands operations, such pipelines represent hundreds of millions of dollars of infrastructure investment and transport thousands of tonnes of solids every hour. The ability to determine key design/operating parameters of a settling slurry, such as frictional pressure gradient and deposition velocity, is dependent on the accuracy of the concentration distribution model used to determine the local concentration of coarse solids as a function of vertical position within the pipe. Accurate predictions of the concentration profile are also required for physics‐based models of particle‐impact erosion in slurry pipelines. In this study, an improved concentration distribution model was developed. The classic Schmidt‐Rouse turbulent diffusion equation forms the basis for the model. The improvements made here include the use of a more suitable, high‐concentration hindered settling velocity correlation, and a simple semi‐empirical correlation for the particle diffusivity, which is shown to be dependent only upon the terminal particle settling velocity and the Kolmogorov turbulent velocity scale. The model is applicable to slurries with broad size distributions and/or species with different densities. The performance of the model is tested against numerous slurry flow conditions, including particles from 70 μm to 8 mm in diameter, pipe diameters of 76 mm ≤ D ≤ 500 mm, and in situ solids volume concentrations from 0.10 to 0.45. The concentration distribution predictions are shown to be in excellent agreement with the measurements.

Novel scaling laws in the nonequilibrium turbulent wake of a rotor and a fractal plate

This paper describes an experimental study in which a novel nonequilibrium self-similarity/self-preservation region is found to exist in the wakes of both a rotor and a fractal plate. In this novel nonequilibrium self-similarity region, the ratio of the mean flow length scale to the turbulence length scale and the ratio of the mean flow velocity scale to the turbulence velocity scale are not constant in the streamwise direction. However, in this region, the ratio of the mean flow time scale to the turbulence time scale is approximately constant in the streamwise direction. Using the simplified Reynolds-averaged equation of motion, new scaling laws are derived for this novel nonequilibrium self-similarity region, and these are confirmed by experimental measurements. Significant differences are observed between the rotor wake and fractal plate wake. The rotor wake reaches a self-similarity state much earlier than the fractal plate wake. A transition in the self-similarity state and scaling laws is found to occur in the rotor wake within the measurement region considered in the present study (3D–20D, where D is the effective diameter of the wake generator).

Improving stratocumulus cloud turbulence and entrainment parametrizations in OpenIFS

AbstractA series of modifications to the stratocumulus cloud turbulence and entrainment parametrizations in the Open Integrated Forecasting System (OpenIFS) model are performed in a Lagrangian single‐column model framework to determine whether they are able to improve the representation of the stratocumulus‐topped boundary layer and its transition to cloud break‐up. Two very different regimes are studied and compared with large‐eddy simulations: a subtropical marine stratocumulus‐to‐cumulus transition case driven by a warming sea‐surface temperature, and an Arctic air‐mass transformation case where warm and moist air is advected over sea ice during wintertime. The addition of nonlocal mixing driven by stratocumulus cloud‐top cooling for stable and dry convective boundary‐layer types is found to sustain the cloud deck for longer in the Arctic case, while it dissipates around one day earlier in the original OpenIFS. The assumption that cloud‐top‐driven mixing reaches the surface, forming a coupled boundary layer, is relaxed. The resulting eddy diffusivity profile is altered such that mixing at cloud top may be enhanced relative to cloud base, promoting decoupling. Decoupling in the subtropical boundary layer is further promoted when the cloud‐top turbulent velocity scale is based on the integral of the in‐cloud buoyancy flux, accounting for the turbulence generated by latent heat release within the cloud, which increases cloud‐top entrainment further relative to cloud base. Some long‐standing model issues persist, such as underestimation of the subtropical boundary‐layer deepening rate, which leads to a cold and moist bias in the boundary layer. In the Arctic, the boundary layer is generally too well mixed and warm at the surface. The degree of decoupling is also underestimated in both cases. However, the modifications discussed here lead to some improvement in OpenIFS.

Stress equation based scaling framework for adverse pressure gradient turbulent boundary layers

This paper provides a framework for estimating appropriate turbulent velocity scales in adverse pressure gradient turbulent boundary layers (APG TBLs) via a study of the mean stress balance. We examine the velocity scales of APG TBLs using the relationship between the Reynolds shear stress and pressure stress. It is reasoned that as distance from the wall increases the velocity scaling transitions from one dominated by the wall-shear-stress velocity scale, uτ, to a scaling dominated by the pressure stress. A velocity scale, uhyb, is proposed that varies with distance from the wall and combines the wall-shear-stress velocity with a pressure-stress-based velocity. This investigation uses new high Reynolds number (7000≲Reτ≲7800) experimental measurements, existing lower Reynolds number experimental (600≲Reτ≲2000) and computational (Reτ<700) data sets. The proposed velocity scale realizes similarity in the turbulent stress profiles to a degree that is superior to that achievable via any wall-distance-independent velocity scale when considering the full extent of the flow domain.

Scaling of Shear‐Generated Turbulence: The Equatorial Thermocline, a Case Study

AbstractWe formulate an expression for the turbulent kinetic energy dissipation rate, ϵ, associated with shear‐generated turbulence in terms of quantities in the ocean or atmosphere that, depending on the situation, may be measurable or resolved in models. The expression depends on the turbulent vertical length scale, ℓv, the inverse time scale N, and the Richardson number Ri = N2/S2, where S is the vertical shear, with ℓv scaled in a way consistent with theories and observations of stratified turbulence. Unlike previous studies, the focus is not so much on the functional form of Ri, but the vertical variation of the length scale ℓv. Using data from two ∼7‐day time series in the western equatorial Pacific, the scaling is compared with the observed ϵ. The scaling works well with the estimated ϵ capturing the differences in amplitude and vertical distribution of the observed ϵ between the two times series. Much of those differences are attributable to changes in the vertical distribution of the length scale ℓv, and in particular the associated turbulent velocity scale, ut. We relate ut to a measure of the fine‐scale variations in velocity, . Our study highlights the need to consider the length scale and its estimation in environmental flows. The implications for the vertical variation of the associated turbulent diffusivity are discussed.

External controls on the transition between stable boundary‐layer turbulence regimes

AbstractThe mean wind speed at which the stable boundary layer (SBL) experiences a turbulence regime transition (Vr) depends on other flow characteristics, such as its thermal stability. Here, Vr variability is examined both at a single site and across sites using three multiple‐level datasets: Santa Maria, Cooperative Atmosphere–Surface Exchange Study–1999 (CASES‐99), and Fluxes over Snow Surfaces (FLOSS II). A method to determine Vr is introduced and validated. It is taken as the mean wind speed at which the vertical gradient of the turbulence velocity scale switches sign. Emphasis is given to the control exerted on Vr by quantities that are external to the SBL, such as radiation, roughness, and soil properties. In each of the experiments, Vr increases with net radiative loss at the surface (Rn) at a rate that is site‐dependent. It also increases for smaller roughness lengths, as indicated by its wind direction dependence. No conclusive relationship has been found between Vr and downward longwave radiation observed at the surface. The across‐site comparison indicates that soil heat capacity influences the rate at which Vr increases with Rn.

Spectral proper orthogonal decomposition analysis of the turbulent wake of a disk at Re = 50 000

The coherent structures in the turbulent wake of a disk at a moderately high Reynolds number ($\Rey$) of $50,000$ are examined using spectral proper orthogonal decomposition (SPOD) which considers all three velocity components in a numerical database. The SPOD eigenvalues at a given streamwise ($x$) location are functions of azimuthal wavenumber ($m$), frequency ($\Str$), and SPOD index ($n$). By $x/D =10$, two specific modes dominate the fluctuation energy: (i) the vortex shedding (VS) mode with $m=1, \Str =0.135, n=1$, and (ii) the double helix (DH) mode with $m=2, \Str \rightarrow 0, n=1$. The VS mode is more energetic than the DH mode in the near wake but, in the far wake, it is the DH mode which is dominant. The DH mode, when scaled with local turbulent velocity and length scales, shows self-similarity in eigenvalues and eigenmodes while the VS mode, which is a global mode, does not exhibit strict self-similarity. Modes $m = 0$, 3 and 4, although subdominant, also make a significant net contribution to the fluctuation energy, and their eigenspectra are evaluated. The reconstruction of TKE and Reynolds shear stress, $\langle u'_{x} u'_{r} \rangle$, is evaluated by varying $(m,\Str,n)$ combinations. Higher SPOD modes contribute significantly to the TKE, especially near the centerline. In contrast, reconstruction of $\langle u'_{x}u'_{r}\rangle $ requires far fewer modes: $|m| \leq 4 $, $|\Str| \leq 1$ and $n \leq 3$. Among azimuthal modes, $m=1$ and $2$ are the leading contributors to both TKE and $\langle u'_{x}u'_{r} \rangle $. While $m=1$ captures the slope of the shear-stress profile near the centerline, $m=2$ is important to capture $\langle u'_{x}u'_{r} \rangle $ at and near its peak. SPOD is also performed in the vicinity of the disk to describe the modal transition to the principal contributors in the wake.

How is the Two-Regime Stable Boundary Layer Reproduced by the Different Turbulence Parametrizations in the Weather Research and Forecasting Model?

Five planetary-boundary-layer parametrizations of the Weather Research and Forecasting model are compared with respect to their ability to simulate the very stable and the weakly stable regimes of the stable boundary layer. This is performed for single column models where the large-scale mechanical forcing is represented by geostrophic wind speeds ranging from 0.5 to 12 m $$\hbox {s}^{-1}$$ . The performance of the models is assessed by contrasting the relationships they produce between the turbulence velocity scale and the mean wind speed, between potential temperature gradient and the mean wind speed, and between the flux and gradient Richardson numbers. The level-2.5 Mellor–Yamada–Nakanishi–Niino parametrization simulates the very stable regime the best, mainly because its heat eddy diffusivity decreases with respect to the momentum eddy diffusivity as the stability increases, while the same is not true for the other parametrizations considered.

Impact of Increased Vertical Resolution on Medium-Range Forecasts in a Global Atmospheric Model

Abstract This study aims to investigate the impact of increased vertical resolution on global medium-range forecasts. For this purpose, the dependencies of simulated atmospheric temperature and specific humidity on the lowest model level height and vertical grid spacing are investigated. The reduced first model level increases vertical turbulent mixing by determining a higher planetary boundary layer (PBL) height and associated turbulent diffusivities and velocity scales. This contributes to warming/drying within the PBL and cooling/moistening above the PBL. Resulting dryness near the surface enhances an increase in surface moisture flux from the ocean, which results in the apparent moistening of the troposphere. Consequently, large-scale precipitation increases due to more humid atmospheric conditions, while convective precipitation decreases because of drier conditions near the starting level of convection. Meanwhile, the reduced vertical grid spacing resolves the overshooting layer well in the cumulus convection process, which decreases the detrained moisture at the convective cloud top. This leads to a noticeable downward shift of ice clouds in the upper troposphere, and further contributes to the enhancement of longwave cooling via cloud–radiation processes. In medium-range forecasts, the increased vertical resolution exerts a significant impact on the simulated features of tropospheric temperature and humidity, while changes in the prediction accuracy precipitation are negligible owing to compensation between convective and large-scale precipitation. Finally, the discussion of possible methods to minimize the sensitivities of model’s physics to vertical resolution is presented.

Similarity Theory in the Surface Layer of Large-Eddy Simulations of the Wind-, Wave-, and Buoyancy-Forced Southern Ocean

AbstractMonin–Obukhov similarity theory is applied to the surface layer of large-eddy simulations (LES) of deep Southern Ocean boundary layers. Observations from the Southern Ocean Flux Station provide a wide range of wind, buoyancy, and wave (Stokes drift) forcing. Two No-Stokes LES are used to determine the extent of the ocean surface layer and to adapt the nondimensional momentum and buoyancy gradients, as functions of the stability parameter. Stokes-forced LES are used to modify this parameter for wave effects, then to formulate dependencies of Stokes similarity functions on a Stokes parameter ξ. To account for wind-wave misalignment, the dimensional analysis is extended with two independent variables, namely, the production of turbulent kinetic energy in the surface layer due to Stokes shear and the total production, so that their ratio gives ξ. Stokes forcing is shown to reduce vertical shear more than stratification, and to enhance viscosity and diffusivity by factors up to 5.8 and 4.0, respectively, such that the Prandtl number can exceed unity. A practical parameterization is developed for ξ in terms of the meteorological forcing plus a Stokes drift profile, so that the Stokes and stability similarity functions can be combined to give turbulent velocity scales. These scales for both viscosity and diffusivity are evaluated against the LES, and the correlations are nearly 0.97. The benefit of calculating Stokes drift profiles from directional wave spectra is demonstrated by similarly evaluating three alternatives.