Eddy Diffusivities Of Momentum Research Articles

Flux‐gradient relations and their dependence on turbulence anisotropy

AbstractMonin–Obukhov similarity theory (MOST) is used in virtually all Earth System Models to parametrize the near‐surface turbulent exchanges and mean variable profiles. Despite its widespread use, there is high uncertainty in the literature about the appropriate parametrizations to use. In addition, MOST has limitations in very stable and unstable regimes, over heterogeneous terrain and complex orography, and has been found to represent the surface fluxes incorrectly. A new approach including turbulence anisotropy as a non‐dimensional scaling parameter has recently been developed and has been shown to overcome these limitations and generalize the flux‐variance relations to complex terrain. In this article, we analyze the flux‐gradient relations for five well‐known datasets, ranging from flat and homogeneous to slightly complex terrain. The scaling relations show substantial scatter and highlight the uncertainty in the choice of parametrization even over canonical conditions. We show that, by including information on turbulence anisotropy as an additional scaling parameter, the original scatter becomes well bounded and new formulations can be developed that drastically improve the accuracy of the flux‐gradient relations for wind shear () in unstable conditions and for temperature gradient () in both unstable and stable regimes. This analysis shows that both and are strongly dependent on turbulence anisotropy and allows us finally to settle the extensively discussed free convection regime for , which clearly exhibits a power law when anisotropy is accounted for. Furthermore, we show that the eddy diffusivities for momentum and heat and the turbulent Prandtl number are strongly dependent on anisotropy and that the latter goes to zero in the free convection limit. These results highlight the necessity to include anisotropy in the study of near‐surface atmospheric turbulence and lead the way for theoretically more robust simulations of the boundary layer over complex terrain.

Vertical Eddy Diffusivity in the Tropical Cyclone Boundary Layer during Landfall

This study investigated surface layer turbulence characteristics and parameters using 20 Hz eddy covariance data collected from five heights with winds up to 42.27 m s−1 when Super Typhoon Maria (2018) made landfall. The dependence of these parameters including eddy diffusivities for momentum (Km) and heat (Kt), vertical mixing length (Lm), and strain rate (S) on wind speed (un), height, and radii was examined. The results show that momentum fluxes (τ), turbulent kinetic energy (TKE), and Km had a parabolic dependence on un at all five heights outside three times the RMW, the maximum of Km and S increased from the surface to a maximum value at a height of 50 m, and then decreased with greater heights. However, Km and S were nearly constant with wind and height within two to three times the RMW from the TC center before landfall. Our results also found the |τ|, TKE, and Km were larger than over oceanic areas at any given wind, and Km was about one to two orders of magnitude bigger than Kt. The turbulence characteristic and parameters’ change with height and radii from the TC center should be accounted for in sub-grid scale physical processes of momentum fluxes in numerical TC models.

Sensitivity of an Idealized Tropical Cyclone to the Configuration of the Global Forecast System–Eddy Diffusivity Mass Flux Planetary Boundary Layer Scheme

The intensity and structure of simulated tropical cyclones (TCs) are known to be sensitive to the planetary boundary layer (PBL) parameterization in numerical weather prediction models. In this paper, we use an idealized version of the Hurricane Weather Research and Forecast system (HWRF) with constant sea-surface temperature (SST) to examine how the configuration of the PBL scheme used in the operational HWRF affects TC intensity change (including rapid intensification) and structure. The configuration changes explored in this study include disabling non-local vertical mixing, changing the coefficients in the stability functions for momentum and heat, and directly modifying the Prandtl number (Pr), which controls the ratio of momentum to heat and moisture exchange in the PBL. Relative to the control simulation, disabling non-local mixing produced a ~15% larger storm that intensified more gradually, while changing the coefficient values used in the stability functions had little effect. Varying Pr within the PBL had the greatest impact, with the largest Pr (~1.6 versus ~0.8) associated with more rapid intensification (~38 versus 29 m s−1 per day) but a 5–10 m s−1 weaker intensity after the initial period of strengthening. This seemingly paradoxical result is likely due to a decrease in the radius of maximum wind (~15 versus 20 km), but smaller enthalpy fluxes, in simulated storms with larger Pr. These results underscore the importance of measuring the vertical eddy diffusivities of momentum, heat, and moisture under high-wind, open-ocean conditions to reduce uncertainty in Pr in the TC PBL.

Eddy mixing of momentum and heat in stably stratified boundary layers: Numerical study

The paper analyzes the features of turbulent momentum and heat transfer in a stably stratified atmospheric boundary layer (ABL), in the upper troposphere and lower stratosphere, and the possibility of taking them into account in RANS (Reynolds Average Navier Stokes) turbulence models. Such features, for example, include the transfer of momentum (but not heat) by internal gravitational waves under conditions of strong stability, the formation of a low-level jet. Models for the coefficients of eddy diffusion of momentum and heat were obtained by writing the differential equations for the Reynolds stresses and the turbulent heat flux vector in the weakly equilibrium approximation, in which the advection and diffusion of some dimensionless quantities are neglected. In the considered version of the algebraic model built on the physical principles of the RANS approximation for stratified turbulence, three prognostic equations are used: for the kinetic energy of turbulence, the rate of its spectral consumption and the dispersion of temperature fluctuations. It is shown that the profile of the vertical diffusivity for momentum, which was calculated using three-parametric turbulent model, is in agreement with data of direct measurements either within a stable stratified atmospheric boundary layer or beyond this layer in free atmosphere.

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.

COEFFICIENTS OF EDDY DIFFUSION OF MOMENTUM AND HEAT IN ATMOSPHERIC BOUNDARY LAYER: NUMERICAL STUDY

The changes in turbulent eddy mixing in the atmospheric boundary layer (ABL) are investigated with the use of the mesoscale RANS turbulence model with account for effects of internal gravitational waves, which support momentum transfer under condition of very stable stratification. A focus was put on analysis of behavior of the coefficients of vertical eddy diffusion of momentum and heat. The behavior of the turbulent eddy mixing parameters was found to be consistent with measurements in the laboratory and atmosphere. In particular, the flow Richardson number () during the transient flow to a strongly stable state can behave nonmonotonically, growing with increasing gradient Richardson number () to the state of saturation at a certain gradient Richardson number ( Ri@ 1 ), which separates two different turbulent regimes: strong mixing and weak mixing.

Energetics and mixing efficiency of lock-exchange gravity currents using simultaneous velocity and density fields

A series of laboratory experiments on energy conserving gravity currents in a lock-exchange facility are conducted for a range of Reynolds numbers, $Re= \frac{U_Fh}{\nu} =$ 485-12270. The velocity and density fields are captured simultaneously using a PIV-PLIF system. A moving average method is employed to compute the mean field and a host of turbulence statistics, namely, turbulent kinetic energy ($K$), shear production ($P$), buoyancy flux ($B$), and energy dissipation ($\epsilon$) during the slumping phase of the current. The subsequent findings are used to ascertain the quantitative values of mixing efficiency, $Ri_{f}$, Ozmidov length-scale ($L_O$), Kolmogorov length-scale ($L_\kappa$), and eddy diffusivities of momentum ($\kappa_m$) and scalar ($\kappa_\rho$). Two different forms of $Ri_{f}$ are characterized in this study, denoted by $Ri_{f}^I=\frac{B}{P}$ and $Ri_{f}^{II}=\frac{B}{B+\epsilon}$. The results cover the entire diffusive regime (3 $<Re_b<$ 10) and a portion of the intermediate regime (10 $<Re_b<$ 50), where $Re_b=\frac{\epsilon}{\nu N^2}$ is the buoyancy Reynolds number that measures the level of turbulence in a shear-stratified flow. The values of $P$, $B$, and $\epsilon$ show a marked increase at the interface of the ambient fluid and the current, owing to the development of a shear-driven mixed layer. Based on the changes in the turbulence statistics and the length scales, it is inferred that the turbulence decays along the length of the current. The mixing efficiency monotonically increases in the diffusive regime ($Re_{b}<$10), and is found to have an upper bound of $Ri_{f}^{I}\approx$ 0.15 and $Ri_{f}^{II}\approx$ 0.2 in the intermediate regime. Using the values of $Ri_{f}$, the normalized eddy diffusivity of momentum is parameterized as $\frac{\kappa_m}{\nu.Ri_{g}}$=1.2$Re_{b}$ and normalized eddy diffusivity of scalar as $\frac{\kappa_{\rho}}{\nu}$=0.2$Re_{b}$

Turbulent Schmidt Number Measurements Over Three-Dimensional Cubic Arrays

We present turbulent Schmidt number Sc_t estimations above three-dimensional urban canopies, where Sc_t is a property of the flow defined as the ratio of the eddy diffusivity of momentum (K_M) to the eddy diffusivity of mass (D_t). Despite the fact that Sc_t modelling is of great interest, inter alia, for pollutant dispersion simulations conducted via computational fluid dynamics, no universal value is known. Simultaneous measurements of fluid velocity and mass concentration are carried out in a water channel for three staggered arrays of cubical obstacles corresponding to isolated flow, wake-interference, and skimming-flow regimes. A passive tracer is released from a continuous point source located at a height z=1.67H, where H is the obstacle height. The results show an increase of Sc_t with height above the canopy for all three arrays, with values at z=2H (Sc_t = 0.6) about double compared to that at z=H. The observed Sc_t agrees well with that modelled by using a simple formulation for Sc_t based on expressions for K_M and D_t published in previous studies. Comparisons with other Sc_t models found in the literature are also presented and discussed.

Numerical investigation for turbulent heat transfer of TiO2–SiO2 nanofluids with wire coil inserts

A numerical model has been developed for turbulent flow of hybrid nanofluids in a tube with wire coil inserts. The model was developed from van Driest eddy diffusivity equation. The model can be implemented with the consideration of new variables in eddy diffusivity of momentum and heat by using the coefficient, K and Prandtl index, ζ, respectively. The numerical analysis are undertaken for wide range of Reynolds number, different volume concentration, ϕ and various pitch ratio, P/D of wire coil. The numerical results were validated with the experimental data of TiO2–SiO2 nanofluids undertaken for wide range of Reynolds number and volume concentration. The final regression models of coefficient K and Prandtl index ζ were developed as a function of Reynolds number, Re or dimensionless radius, R+, volume concentration, ϕ and pitch ratio, P/D. A good agreement between the experimental data and numerical model indicating the validity of the numerical model for hybrid nanofluids with wire coil inserts. The numerical analysis was proved that the hybrid nanofluids contributes to higher Nusselt number and thus have better heat transfer performance compared to single nanofluids.

Large-eddy simulation of thermally stratified forest canopy flow for wind energy studies purposes

A Large Eddy Simulation (LES) code using Lagrangian Dynamic Smagorinsky subgrid models was developed for the simulation of atmospheric stratified flows over topography for wind energy assessment purposes. In this article, the code, which uses separated dynamic procedures for the calculation of eddy diffusivities of momentum and heat, was used to simulate horizontally homogeneous flow in forest canopies, for both unstable and stable regimes. The results were in good agreement with both numerical and experimental results for stable stratified wind regimes but, as far as unstable regimes are concerned, there are still unresolved issues to be addressed.

Water-Channel Estimation of Eulerian and Lagrangian Time Scales of the Turbulence in Idealized Two-Dimensional Urban Canopies

Lagrangian and Eulerian statistics are obtained from a water-channel experiment of an idealized two-dimensional urban canopy flow in neutral conditions. The objective is to quantify the Eulerian $$(T^{\mathrm{E}})$$ and Lagrangian $$(T^{\mathrm{L}})$$ time scales of the turbulence above the canopy layer as well as to investigate their dependence on the aspect ratio of the canopy, AR, as the latter is the ratio of the width (W) to the height (H) of the canyon. Experiments are also conducted for the case of flat terrain, which can be thought of as equivalent to a classical one-directional shear flow. The values found for the Eulerian time scales on flat terrain are in agreement with previous numerical results found in the literature. It is found that both the streamwise and vertical components of the Lagrangian time scale, $$T_\mathrm{u}^\mathrm{L} $$ and $$T_\mathrm{w}^\mathrm{L} $$ , follow Raupach’s linear law within the constant-flux layer. The same holds true for $$T_\mathrm{w}^\mathrm{L} $$ in both the canopies analyzed $$(AR= 1$$ and $$AR= 2$$ ) and also for $$T_\mathrm{u}^\mathrm{L} $$ when $$AR = 1$$ . In contrast, for $$AR = 2$$ , $$T_\mathrm{u}^\mathrm{L} $$ follows Raupach’s law only above $$z=2H$$ . Below that level, $$T_\mathrm{u}^\mathrm{L} $$ is nearly constant with height, showing at $$z=H$$ a value approximately one order of magnitude greater than that found for $$AR = 1$$ . It is shown that the assumption usually adopted for flat terrain, that $$\beta =T^{\mathrm{L}}/T^{\mathrm{E}}$$ is proportional to the inverse of the turbulence intensity, also holds true even for the canopy flow in the constant-flux layer. In particular, $$\gamma /i_\mathrm{u} $$ fits well $$\beta _\mathrm{u} =T_\mathrm{u}^\mathrm{L} /T_\mathrm{u}^\mathrm{E} $$ in both the configurations by choosing $$\gamma $$ to be 0.35 (here, $$i_\mathrm{u} =\sigma _\mathrm{u} / \bar{u} $$ , where $$\bar{u} $$ and $$\sigma _\mathrm{u} $$ are the mean and the root-mean-square of the streamwise velocity component, respectively). On the other hand, $$\beta _\mathrm{w} =T_\mathrm{w}^\mathrm{L} /T_\mathrm{w}^\mathrm{E} $$ follows approximately $$\gamma /i_\mathrm{w} =0.65/\left( {\sigma _\mathrm{w} /\bar{u} } \right) $$ for $$z > 2H$$ , irrespective of the AR value. The second main objective is to estimate other parameters of interest in dispersion studies, such as the eddy diffusivity of momentum $$(K_\mathrm{{T}})$$ and the Kolmogorov constant $$(C_0)$$ . It is found that $$C_0$$ depends appreciably on the velocity component both for the flat terrain and canopy flow, even though for the latter case it is insensitive to AR values. In all the three experimental configurations analyzed here, $$K_\mathrm{{T}}$$ shows an overall linear growth with height in agreement with the linear trend predicted by Prandtl’s theory.

Influence of texture on thermal transport in streamwise-aligned superhydrophobic turbulent channels

A series of Direct Numerical Simulations (DNS) is performed for a systematic study of thermal transport in a periodic turbulent channel bounded by superhydrophobic surface (SHS) walls at a friction Reynolds number of Reτ=180. The SHS examined here is comprised of interspersed ridges and cavities aligned along the mean streamwise flow direction. The SHS is modelled as a planar surface consisting of spanwise-alternating regions of free-shear and no-slip boundary conditions. Water is considered as the bulk fluid where the SHS surface is assumed to be in a Cassie-Baxter state with non-wetting cavities containing air. The ridges are maintained at a constant temperature while heat transfer through the air/water interface supported by the ridges is assumed negligible and is modelled as adiabatic. Phase averaged statistics were obtained for a range of relative periodicity widths. Reorganisation of secondary flow structures owing to an increase in SHS feature width and its effect on thermal transport are analyzed with a particular focus on phase-averaged statistics. The relative feature width or periodicity length is found to influence strongly on thermal performance, or the average Nusselt number. A reduction in the turbulent Prandtl number is observed in the buffer region due to an increase in thermal eddy diffusivity relative to the momentum eddy diffusivity. The amount of heat transfer and mixing depend upon the periodicity length, and there is a reduction in the heat transfer along with the drag-reduction. A substantial decrease in the temperature fluctuations is observed in the vicinity of the wall as the production of temperature variance is diminished with an increase in the periodicity length, primarily due to a reduction in the mean temperature gradient in the wall-normal direction.

A Shear-Based Parameterization of Turbulent Mixing in the Stable Atmospheric Boundary Layer

AbstractIn this study, shear-based parameterizations of turbulent mixing in the stable atmospheric boundary layer (SABL) are proposed. A relevant length-scale estimate for the mixing length of the turbulent momentum field is constructed from the turbulent kinetic energy and the mean shear rate S as . Using observational data from two field campaigns—the Surface Heat Budget of the Arctic Ocean (SHEBA) experiment and the 1999 Cooperative Atmosphere–Surface Exchange Study (CASES-99)— is shown to have a strong correlation with . The relationship between and corresponds to the ratio of the magnitude of the tangential components of the turbulent momentum flux tensor to , known as stress intensity ratio, . The field data clearly show that is linked to stability. The stress intensity ratio also depends on the flow energetics that can be assessed using a shear-production Reynolds number, , where P is shear production of turbulent kinetic energy and is the kinematic viscosity. This analysis shows that high mixing rates can indeed persist at strong stability. On this basis, shear-based parameterizations are proposed for the eddy diffusivity for momentum, , and eddy diffusivity for heat, , showing remarkable agreement with the exact quantities. Furthermore, a broader assessment of the proposed parameterizations is given through an a priori evaluation of large-eddy simulation (LES) data from the first GEWEX Atmospheric Boundary Layer Study (GABLS). The shear-based parameterizations outperform many existing models in predicting turbulent mixing in the SABL. The results of this study provide a framework for improved representation of the SABL in operational models.

Features of eddy diffusion of momentum and heat in stably stratified flows of environment

The study was performed on features of eddy transport of momentum and heat in the lower atmosphere, which includes the planetary boundary layer as well as upper troposphere and lower stratosphere; the study used a three-parametric method for modeling of stratified turbulent flows. A focus was put on analysis of behavior of vertical diffusivities of momentum and heat: data were obtained through direct measurements and through simulation with three-parametric turbulence model with account for effects of internal gravitational waves which support momentum transfer under condition of very stable stratification (while possessing considerable wavy dynamics). It was demonstrated that the profile of vertical diffusivity for momentum, which was calculated using three-parametric turbulence model, is in agreement with data on direct measurements when measured either within a stable stratified planetary boundary layer or beyond this layer, in free atmosphere.

Numerical Analysis of Flow Structure Above Dimpled Surfaces with Different Depths in a Channel

Turbulent air flow characteristics in channels of three different dimple depth (δ/D = 0.1, 0.2, and 0.3) placed on the bottom wall are numerically predicted using FLUENT for Reynolds number based on the channel height, Re H = 20,000, and the ratio of channel height to dimple print diameter, H/D = 1.0. The turbulence model employed is a realizable k − ϵ model with no wall function. Steady-state analyses of fluid within and near different dimple depths demonstrate the existence of different vortex pairs. These vortex pairs are investigated at the central position of dimples as well as near the spanwise edge of individual dimples, and become stronger as dimple depth increases. In addition, steady-state results show that the streamwise vorticity distributions, which are associated with the flow recirculation zones positioned within the upstream halves of each dimple, are higher in magnitude and cover larger spatial extents as the dimple depth increases. Magnitudes of eddy diffusivity for momentum and eddy diffusivity for heat are also augmented by the vorticity concentrations within and downstream of individual dimples as the dimple depth increases. Such characteristics are due to the advection of reattaching and recirculating flow within the dimple cavities, as well as to the strong instantaneous secondary flows and mixing within the vortex pairs.

Experimental investigation of polymer diffusion in the drag-reduced turbulent channel flow of inhomogeneous solution

Spatial polymer diffusion in the drag-reduced turbulent channel flow of an inhomogeneous polymer solution was investigated by simultaneously measuring velocity and concentration fields using particle imaging velocimetry and planar laser-induced fluorescence techniques. The polymer solution was dosed into the turbulent channel flow from the surface of one-side of the channel wall. The Reynolds number (based on channel height, bulk velocity and solvent viscosity) was set as 4.0×104 and the weight concentrations of dosed polymer solution were set to 25, 50 and 100ppm. The measurements were obtained in the streamwise wall-normal (x–y) plane at three streamwise positions along the dosing wall. The detailed statistical analyses consisting of concentration distribution, turbulence modification, turbulent mass flux, and eddy diffusivities of momentum and of mass are presented. The results show that the polymer diffusion, which has a close relationship with the local polymer concentration and drag reduction in the drag-reduced turbulent channel flow, is suppressed due to the inhibited turbulence other than the diffusion of passive scalar in ordinary turbulence. Two characteristic regions exist in the near-wall region according to the diffusion characteristics and altered motions in the wall-normal direction. The wall-normal turbulent fluxes that control the transport of mass are reduced significantly in the near-wall region for the drag-reduced flow when compared with the case of dosing water. With the increase of local polymer concentration in the “effective position”, the corresponding drag reduction rate (DR) increases. The turbulent Schmidt number (ScT), which represents the relative intensities of the eddy diffusivities of momentum and of mass, is also found to increase with increasing DR. The mean value of ScT for the drag-reduced flow can rise to 2.9, while it is 1.2 for the case of dosing water in the present measurements.

Combined Laminar And Turbulent Flow Over Rotating Cones

An analysis has been carried out for the combined laminar and turbulent flow over rotating cones in an otherwise undisturbed fluid. The momentum integral equations in meridianal and circumferential directions, which govern the turbulent fluid flow over a rotating cone, have been solved in their dimensionless forms. A continuous eddy diffusivity of momentum, suggested by Van Driest, has been adopted to obtain the velocity components. Taking the central laminar core into account, friction moment coefficients are calculated as functions of cone Reynolds number Re/sub 0/. The theoretical are compared with other theories and the available experimental data.

Waves and turbulence in katabatic winds

The measurements taken during the Vertical Transport and Mixing Experiment (VTMX, October, 2000) on a northeastern slope of Salt Lake Valley, Utah, were used to calculate the statistics of velocity fluctuations in a katabatic gravity current in the absence of synoptic forcing. The data from ultrasonic anemometer-thermometers placed at elevations 4.5 and 13.9 m were used. The contributions of small-scale turbulence and waves were isolated by applying a high-pass digital (Elliptical) filter, whereupon the filtered quantities were identified as small-scale turbulence and the rest as internal gravity waves. Internal waves were found to play a role not only at canonical large gradient Richardson numbers $$(\overline{\hbox {Ri}_\mathrm{g} } >1)$$ , but sometimes at smaller values $$(0.1 < \overline{\hbox {Ri}_\mathrm{g}}<1)$$ , in contrast to typical observations in flat-terrain stable boundary layers. This may be attributed, at least partly, to (critical) internal waves on the slope, identified by Princevac et al. [1], which degenerate into turbulence and help maintain an active internal wave field. The applicability of both Monin-Obukhov (MO) similarity theory and local scaling to filtered and unfiltered data was tested by analyzing rms velocity fluctuations as a function of the stability parameter z/L, where L is the Obukhov length and z the height above the ground. For weaker stabilities, $$\hbox {z/L}<1$$ , the MO similarity and local scaling were valid for both filtered and unfiltered data. Conversely, when $$\hbox {z/L}>1$$ , the use of both scaling types is questionable, although filtered data showed a tendency to follow local scaling. A relationship between z/L and $$\overline{\hbox {Ri}_\mathrm{g} }$$ was identified. Eddy diffusivities of momentum $$\hbox {K}_\mathrm{M}$$ and heat $$\hbox {K}_\mathrm{H}$$ were dependent on wave activities, notably when $$\overline{\hbox {Ri}_\mathrm{g} } > 1$$ . The ratio $$\hbox {K}_{\mathrm{H}}/\hbox {K}_{\mathrm{M}}$$ dropped well below unity at high $$\overline{\hbox {Ri}_\mathrm{g} }$$ , in consonance with previous laboratory stratified shear layer measurements as well as other field observations.

Investigation of the Stable Atmospheric Boundary Layer at Halley Antarctica

Boundary-layer measurements from the Brunt Ice Shelf, Antarctica are analyzed to determine flux–profile relationships. Dimensionless quantities are derived in the standard approach from estimates of wind shear, potential temperature gradient, Richardson number, eddy diffusivities for momentum and heat, Prandtl number, mixing length and turbulent kinetic energy. Nieuwstadt local scaling theory for the stable atmospheric boundary-layer appears to work well departing only slightly from expressions found in mid-latitudes. An \(E\)–\(l_{\mathrm{m}}\) single-column model of the stable boundary layer is implemented based on local scaling arguments. Simulations based on the first GEWEX Atmospheric Boundary-Layer Study case study are validated against ensemble-averaged profiles for various stability classes. A stability-dependent function of the dimensionless turbulent kinetic energy allows a better fit to the ensemble profiles.

An Observational Study of Vertical Eddy Diffusivity in the Hurricane Boundary Layer

Abstract Although vertical eddy diffusivity or viscosity has been extensively used in theoretical and numerical models simulating tropical cyclones, little observational study has documented the magnitude of the eddy diffusivity in high-wind conditions (&amp;gt;20 m s−1) until now. Through analyzing in situ aircraft data that were collected in the atmospheric boundary layer of four intense hurricanes, this study provides the first estimates of vertical distributions of the vertical eddy diffusivities for momentum, sensible heat, and latent heat fluxes in the surface wind speed range between 18 and 30 m s−1. In this work, eddy diffusivity is determined from directly measured turbulent fluxes and vertical gradients of the mean variable, such as wind speed, temperature, and humidity. The analyses show that the magnitudes of vertical eddy diffusivities for momentum and latent heat fluxes are comparable to each other, but the eddy diffusivity for sensible heat flux is much smaller than that for the latent heat flux. The vertical distributions of the eddy diffusivities are generally alike, increasing from the surface to a maximum value within the thermodynamic mixed layer and then deceasing with height. The results indicate also that momentum and latent heat are mainly transferred downgradient of the mean flow and that countergradient transport of the sensible heat may exist. The observational estimates are compared with the eddy diffusivities derived from different methods as used in planetary boundary layer (PBL) parameterization schemes in numerical models as well as ones used in previous observational studies.