Eddy Diffusivity Profiles Research Articles

Canopy-Mediated Hydrodynamics Contributes to Greater Allelic Richness in Seeds Produced Higher in Meadows of the Coastal Eelgrass Zostera marina

Seagrass meadows, which mediate ocean acidity and turbidity, sequester carbon, and increase biodiversity by providing shelter for larvae and small fish, are among the fastest disappearing ecosystems worldwide. Seagrasses are ecosystem engineers, creating distinct regions of enhanced and diminished flow and turbulent mixing, dependent upon canopy physical parameters, such as canopy density and blade morphology, which in turn impact the transport of pollen, sediment, and nutrients. The health and resilience of seagrass meadows increase with intraspecies genetic diversity, which depends on successful sexual reproduction and the transport of pollen particles between reproductive shoots, which in turn depends on the hydrodynamic conditions created by the meadow. This paper explored the transport of pollen grains in seagrass meadows using a random walk model. The model was parameterized with profiles of mean velocity and eddy diffusivity derived as functions of shoot density, canopy height, canopy shear velocity, canopy drag coefficient, and blade width, and validated with experimental measurements of a tracer plume evolving in a submerged model canopy. Model results showed that release at the top of the canopy led to significantly greater dispersal than release within the canopy, which was consistent with observed patterns of genetic diversity in Zostera marina seeds collected from coastal Massachusetts meadows. Specifically, seeds produced from upper inflorescences had greater allelic richness than seeds from lower inflorescences on the same reproductive shoot, and were the product of a greater number of fathers, reflecting the greater in-canopy pollen movement farther from the bed. Pollen grains modeled with a realistic elongated shape experienced significantly higher rates of capture by the canopy relative to spherical grains of the same volume. The effect of submergence depth (the ratio of water depth to canopy height) on pollen dispersal depended on the nature of the surface boundary: when pollen reflected off the water surface, the mean travel distance before pollen capture decreased with decreasing submergence depth. In contrast, when pollen accumulated at the water surface, surface transport increased pollen dispersal distances, especially at low submergence depths.

Global-mean Vertical Tracer Mixing in Planetary Atmospheres. I. Theory and Fast-rotating Planets

Abstract Most chemistry and cloud formation models for planetary atmospheres adopt a one-dimensional (1D) diffusion approach to approximate the global-mean vertical tracer transport. The physical underpinning of the key parameter in this framework, eddy diffusivity K zz , is usually obscure. Here we analytically and numerically investigate vertical tracer transport in a 3D stratified atmosphere and predict K zz as a function of the large-scale circulation strength, horizontal mixing due to eddies and waves and local tracer sources and sinks. We find that K zz increases with tracer chemical lifetime and circulation strength but decreases with horizontal eddy mixing efficiency. We demarcated three K zz regimes in planetary atmospheres. In the first regime where the tracer lifetime is short compared with the transport timescale and horizontal tracer distribution under chemical equilibrium ( ) is uniformly distributed across the globe, global-mean vertical tracer mixing behaves diffusively. But the traditional assumption in current 1D models that all chemical species are transported via the same eddy diffusivity generally breaks down. We show that different chemical species in a single atmosphere should in principle have different eddy diffusion profiles. In the second regime where the tracer is short-lived but is non-uniformly distributed, a significant non-diffusive component might lead to a negative K zz under the diffusive assumption. In the third regime where the tracer is long-lived, global-mean vertical tracer transport is also largely influenced by non-diffusive effects. Numerical simulations of 2D tracer transport on fast-rotating zonally symmetric planets validate our analytical K zz theory over a wide parameter space.

Improving NCEP HWRF Simulations of Surface Wind and Inflow Angle in the Eyewall Area

Abstract This note describes a modification of the boundary layer parameterization scheme in the Hurricane Weather Research and Forecasting (HWRF) Model, which improves the simulations of low-level wind and surface inflow angle in the eyewall area and has been implemented in the HWRF system and used in the operational system since 2016. The modification is on an observation-based adjustment of eddy diffusivity previously implemented in the model. It is needed because the previous adjustment resulted in a discontinuity in the vertical distribution of eddy diffusivity near the surface-layer top, which increases the friction within the surface layer and compromises the surface-layer constant-flux assumption. The discontinuity affects the simulation of storm intensity and intensification, one of the main metrics of model performance, particularly in strong tropical cyclones. This issue is addressed by introducing a height-dependent adjustment so that the vertical profile of eddy diffusivity is continuous throughout the boundary layer. It is shown that the implementation of the modification results in low-level winds and surface inflow angles in the storm’s eyewall region closer to observations.

Different Numerical Inversion Algorithms of the Laplace Transform for the Solution of the Advection-Diffusion Equation with Non-local Closure in Air Pollution Modeling

In this paper, a three-dimensional solution of the steady-state advection-diffusion equation is obtained applying the Generalized Integral Advection Diffusion Multilayer Technique (GIADMT), considering non-local closure for turbulent flow. Two different parameterizations were considering for the countergradient term and different methods of numerical inversion for inverse Laplace transform. The results were compared with the experimental data of Copenhagen experiment by an evaluation of statistical indices to analyse the solution of the equation through the methods of numerical inversion. Differents parameterizations for the vertical turbulent eddy diffusivity and wind profile were utilized. The results show a good agreement with the experiment and the methods of numerical inversion for inverse Laplace transform show same efficacy.

Turbulent mixing and removal of ozone within an Amazon rainforest canopy

AbstractSimultaneous profiles of turbulence statistics and mean ozone mixing ratio are used to establish a relation between eddy diffusivity and ozone mixing within the Amazon forest. A one‐dimensional diffusion model is proposed and used to infer mixing time scales from the eddy diffusivity profiles. Data and model results indicate that during daytime conditions, the upper (lower) half of the canopy is well (partially) mixed most of the time and that most of the vertical extent of the forest can be mixed in less than an hour. During nighttime, most of the canopy is predominantly poorly mixed, except for periods with bursts of intermittent turbulence. Even though turbulence is faster than chemistry during daytime, both processes have comparable time scales in the lower canopy layers during nighttime conditions. Nonchemical loss time scales (associated with stomatal uptake and dry deposition) for the entire forest are comparable to turbulent mixing time scale in the lower canopy during the day and in the entire canopy during the night, indicating a tight coupling between turbulent transport and dry deposition and stomatal uptake processes. Because of the significant time of day and height variability of the turbulent mixing time scale inside the canopy, it is important to take it into account when studying chemical and biophysical processes happening in the forest environment. The method proposed here to estimate turbulent mixing time scales is a reliable alternative to currently used models, especially for situations in which the vertical distribution of the time scale is relevant.

Production and destruction of eddy kinetic energy in forced submesoscale eddy-resolving simulations

We study the production and dissipation of the eddy kinetic energy (EKE) in a submesoscale eddy field forced with downfront winds using the Process Study Ocean Model (PSOM) with a horizontal grid resolution of 0.5 km. We simulate an idealized 100 m deep mixed-layer front initially in geostrophic balance with a jet in a domain that permits eddies within a range of O(1 km–100 km). The vertical eddy viscosities and the dissipation are parameterized using four different subgrid vertical mixing parameterizations: the k−ϵ, the KPP, and two different constant eddy viscosity and diffusivity profiles with a magnitude of O(10−2m2s−1) in the mixed layer. Our study shows that strong vertical eddy viscosities near the surface reduce the parameterized dissipation, whereas strong vertical eddy diffusivities reduce the lateral buoyancy gradients and consequently the rate of restratification by mixed-layer instabilities (MLI).Our simulations show that near the surface, the spatial variability of the dissipation along the periphery of the eddies depends on the relative alignment of the ageostrophic and geostrophic shear. Analysis of the resolved EKE budgets in the frontal region from the simulations show important similarities between the vertical structure of the EKE budget produced by the k−ϵ and KPP parameterizations, and earlier LES studies. Such an agreement is absent in the simulations using constant eddy-viscosity parameterizations.

Evaluation of a random displacement model for predicting particle escape from canopies using a simple eddy diffusivity model

There is a need for more practical tools for estimating spore escape from crop canopies, which is essential in forecasting the propagation of disease to other fields. In this paper, we evaluated whether a random displacement model (RDM) parameterized with an eddy diffusivity Kz(z) could be used to predict spore escape probability. The proposed RDM does not require detailed turbulence measurements for parameterization. Instead, it constructs profiles of velocity and eddy diffusivity from a simple set of parameters [canopy height, canopy density, vegetation length scale, and wind speed]. The RDM was validated using field measurements of spore concentration. On average, the model predictions matched the field measurements within 28% inside the canopy and 42% above it, comparable to LES results over the same canopy. Once validated, the RDM was used to explore particle escape across a range of canopy densities and particle settling velocities, in order to inform estimates of particle escape from crops of varying maturity or area density. Escape fraction as calculated by the RDM increased as canopy density decreased, as the ratio of particle settling velocity to turbulent shear velocity ratio decreased, and as the source height within the canopy increased.

Implementation in the NCEP GFS of a Hybrid Eddy-Diffusivity Mass-Flux (EDMF) Boundary Layer Parameterization with Dissipative Heating and Modified Stable Boundary Layer Mixing

Abstract The current operational eddy-diffusivity countergradient (EDCG) planetary boundary layer (PBL) scheme in the NCEP Global Forecast System (GFS) tends to underestimate the PBL growth in the convective boundary layer (CBL). To improve CBL growth, an eddy-diffusivity mass-flux (EDMF) PBL scheme is developed, where the nonlocal transport by large turbulent eddies is represented by a mass-flux (MF) scheme and the local transport by small eddies is represented by an eddy-diffusivity (ED) scheme. For the vertical momentum mixing, the MF scheme is modified to include the effect of the updraft-induced pressure gradient force. While the EDMF scheme displays better CBL growth than the EDCG scheme, it tends to overproduce the amount of low clouds and degrades wind vector forecasts over the tropical ocean where strongly unstable PBLs are rarely found. In order not to degrade the forecast skill in the tropics, a hybrid scheme is developed, where the EDMF scheme is applied only for the strongly unstable PBL, while the EDCG scheme is used for the weakly unstable PBL. Along with the hybrid EDMF scheme, the heating by turbulent kinetic energy (TKE) dissipation is parameterized to reduce an energy imbalance in the GFS. To enhance a too weak vertical turbulent mixing for weakly and moderately stable conditions, the current local scheme in the stable boundary layer (SBL) is modified to use an eddy-diffusivity profile method. The hybrid EDMF PBL scheme with TKE dissipative heating and modified SBL mixing led to significant improvements in some key medium-range weather forecast metrics and was operationally implemented into the NCEP GFS in January 2015.

On the modeling of atmospheric pollutant dispersion during a diurnal cycle: A finite element study

In this paper, we present a numerical model to study pollutant dispersion in the atmospheric boundary layer (ABL). The model accounts for the mechanisms of advection by the mean wind in the horizontal direction, turbulent diffusion in the vertical direction to ground surface, dry deposition, and radioactive decay. More importantly, the model is capable of accounting for the evolution of the ABL structure over a diurnal cycle by considering parameterizations for the wind-speed and eddy-diffusivity profiles that depend on the atmospheric stability condition, which in turn undergoes dramatic changes throughout the day. To solve the resulting advection–diffusion equation, we propose a numerical method based on a stabilized finite element formulation. After validating the numerical model by simulating classical experiments and comparing its predictions with those available in literature, we study the dispersion of a pollutant during a full diurnal ABL cycle with the meteorological parameters generated by AERMET for a 24-h period on a 1-h basis.

Modeling investigation of asymmetric tidal mixing and residual circulation in a partially stratified estuary

A three-dimensional hydrodynamic model was applied to the Danshuei River estuarine system in northern Taiwan to investigate the influence of flood-ebb, spring-neap tidal cycles, and salinity distribution on tidal mixing, residual circulation, stratification, and tidal asymmetry. The model was validated using observational data collected in 2008. The results from the model agreed well with observations of water surface elevation, tidal currents, and salinity. It was found that the depth-averaged tidal current during flood tide is weaker with a shorter duration than that during ebb tide in the estuary, which was attributed to tidal asymmetry. Vertical profiles of salinity, flow, eddy diffusivity, and Richardson number also showed a marked asymmetry between flood and ebb tides. Bottom boundary stresses were higher during flood tides than during ebb tides, resulting in more mixing occurrence and consequently decreasing the Richardson numbers. The tidally averaged salinity was more stratified during neap tides than during spring tides because the presence of the stronger vertical diffusivity and turbulent kinetic energy during spring tides. The modeling results also confirmed that the residual circulation was stronger during neap tides than during spring tides.

Passive buoyant tracers in the ocean surface boundary layer: 1. Influence of equilibrium wind‐waves on vertical distributions

AbstractThis paper is the first of a two part series that investigates passive buoyant tracers in the ocean surface boundary layer. The first part examines the influence of equilibrium wind‐waves on vertical tracer distributions, based on large eddy simulations (LES) of the wave‐averaged Navier‐Stokes equation. The second part applies the model to investigate observations of buoyant microplastic marine debris, which has emerged as a major ocean pollutant. The LES model captures both Langmuir turbulence (LT) and enhanced turbulent kinetic energy input due to breaking waves (BW) by imposing equilibrium wind‐wave statistics for a range of wind and wave conditions. Concentration profiles of LES agree well with analytic solutions obtained for an eddy diffusivity profile that is constant near the surface and transitions into the K‐Profile Parameterization (KPP) profile shape at greater depth. For a range of wind and wave conditions, the eddy diffusivity normalized by the product of water‐side friction velocity and mixed layer depth, h, mainly depends on a single nondimensional parameter, the peak wavelength (which is related to Stokes drift decay depth) normalized by h. For smaller wave ages, BW critically enhances near‐surface mixing, while LT effects are relatively small. For greater wave ages, both BW and LT contribute to elevated near‐surface mixing, and LT significantly increases turbulent transport at greater depth. We identify a range of realistic wind and wave conditions for which only Langmuir (and not BW or shear driven) turbulence is capable of deeply submerging buoyant tracers.

VERTICAL DISTRIBUTION OF C 3 -HYDROCARBONS IN THE STRATOSPHERE OF TITAN

Motivated by the recent detection of propene (C_3H_6) in the atmosphere of Titan, we use a one-dimensional Titan photochemical model with an updated eddy diffusion profile to systematically study the vertical profiles of the stable species in the C_3-hydrocarbon family. We find that the stratospheric volume mixing ratio of propene (C_3H_6) peaks at 150 km with a value of 5 × 10^(−9), which is in good agreement with recent observations by the Composite Infrared Spectrometer on the Cassini spacecraft. Another important species that is currently missing from the hydrocarbon family in Titan's stratosphere is allene (CH_2CCH_2), an isomer of methylacetylene (CH_3C_2H). We predict that its mixing ratio in the stratosphere is about 10^(−9), which is on the margin of the detection limit. CH_2CCH_2 and CH_3C_2H equilibrate at a constant ratio in the stratosphere by hydrogen-exchanging reactions. Thus, by precisely measuring the ratio of CH_2CCH_2 to CH_3C_2H, the abundance of atomic hydrogen in the atmosphere can be inferred. No direct yield for the production of cyclopropane (c-C_3H_6) is available. From the discharge experiments of Navarro-Gonzalez & Ramirez, the abundance of cyclopropane is estimated to be 100 times less than that of C_3H_6.

Photochemical control of the distribution of Venusian water

We use the JPL/Caltech 1-D photochemical model to solve continuity diffusion equation for atmospheric constituent abundances and total number density as a function of radial distance from the planet Venus. Photochemistry of the Venus atmosphere from 58 to 112km is modeled using an updated and expanded chemical scheme (Zhang et al., 2010, 2012), guided by the results of recent observations and we mainly follow these references in our choice of boundary conditions for 40 species. We model water between 10 and 35ppm at our 58km lower boundary using an SO2 mixing ratio of 25ppm as our nominal reference value. We then vary the SO2 mixing ratio at the lower boundary between 5 and 75ppm holding water mixing ratio of 18ppm at the lower boundary and finding that it can control the water distribution at higher altitudes. SO2 and H2O can regulate each other via formation of H2SO4. In regions of high mixing ratios of SO2 there exists a “runaway effect” such that SO2 gets oxidized to SO3, which quickly soaks up H2O causing a major depletion of water between 70 and 100km. Eddy diffusion sensitivity studies performed characterizing variability due to mixing that show less of an effect than varying the lower boundary mixing ratio value. However, calculations using our nominal eddy diffusion profile multiplied and divided by a factor of four can give an order of magnitude maximum difference in the SO2 mixing ratio and a factor of a few difference in the H2O mixing ratio when compared with the respective nominal mixing ratio for these two species. In addition to explaining some of the observed variability in SO2 and H2O on Venus, our work also sheds light on the observations of dark and bright contrasts at the Venus cloud tops observed in an ultraviolet spectrum. Our calculations produce results in agreement with the SOIR Venus Express results of 1ppm at 70–90km (Bertaux et al., 2007) by using an SO2 mixing ratio of 25ppm SO2 and 18ppm water as our nominal reference values. Timescales for a chemical bifurcation causing a collapse of water concentrations above the cloud tops (>64km) are relatively short and on the order of a less than a few months, decreasing with altitude to less than a few days.

Experimental and computational investigation of vertical downflow condensation

This explores downflow condensation in a circular tube both experimentally and computationally using FC-72 as a working fluid. A highly instrumented condensation module is used to map detailed axial variations of both wall heat flux and wall temperature, which are used to determine axial variations of the condensation heat transfer coefficient. The experimental results are compared to predictions of a two-dimensional axisymmetric computational model using FLUENT. The study provides detailed construction of the model, including choice of interfacial phase change sub-model, numerical methods, and convergence criteria. The model is shown to yield good prediction of the heat transfer coefficient. The computed temperature profiles exhibit unusual shape, with steep gradient near the annular liquid film interface as well as near the wall, and a mild gradient in between. This shape is shown to be closely related to the shape of the eddy diffusivity profile. These findings point to the need for future, more sophisticated measurements of liquid film thickness, and both velocity and temperature profiles, to both validate and refine two-phase computational models.

Computational modeling of turbulent evaporating falling films

Abstract The primary objective of this study is to construct a computational model for turbulent, free-falling liquid films subjected to evaporative heating. The model is developed for two-dimensional axisymmetric flow on a vertical circular tube, with both the computational domain and operating conditions matching those of an experimental database for evaporating water films. Implemented in FLUENT, the model is used to predict variations of the evaporative heat transfer coefficient along the heated length, as well as profiles of eddy diffusivity, flow velocity, and temperature across the film. Energy transfer at the film’s interface is captured successfully with the aid of a prior phase change model. The computational model predicts heat transfer coefficients for a broad range of Reynolds numbers that are in between predictions of two prior experimental correlations. The model predicts eddy diffusivity is fully dampened at the interface. The temperature profile across the liquid film features a steep gradient near the interface, which is attributed to turbulence dampening coupled with energy loss at the film’s interface.

On the application of a new formulation of nonlinear eddy viscosity based on anisotropy to numerical ocean models

The present paper explores the derivation of an alternative nonlinear eddy viscosity formulation based on Reynolds stress anisotropy and its implementation to numerical ocean models. This formulation takes into account the vorticity in addition to the mean strain rate. The proposed formulation does not include the stability function method which is a common approach in eddy viscosity calculations used in the present state-of-the-art numerical ocean models. Instead, it depends on the second invariant of anisotropy. Initially, the performance of the formulation is checked through a simple channel flow simulation. Consequently for model calibration, an idealised experiment of mixed-layer entrainment into stably stratified flow has been simulated and compared to empirical data. For sensitivity studies related to shear and stable stratification, concept of steady-state Richardson number is applied for homogeneous shear layer. Finally, the performance of the new formulation is tested by implementing it into one-dimensional General Ocean Turbulence Model. Furthermore, a realistic oceanic test case of a storm has been investigated considering different physical processes for the Fladenground Experiment (FLEX’ 76) in the northern North Sea and the results have been compared to the measured data. The main results signify that the overall performance of the nonlinear eddy viscosity model with a different value of steady-state Richardson number is as good as the Mellor–Yamada model in terms of predictability, and the eddy viscosity and diffusivity profiles follow the principle of law of the wall. Additionally, the present formulation does not require computing the stability functions and the ease of implementation into numerical ocean models gives the present formulation an upper hand over the existing formulations in the field of turbulence modelling in oceanography.

Evaluation of the influence of micrometeorological data on concentration estimates

A dispersion model for continuous releases of pollutants in the atmospheric boundary layer is applied to study the influence on modelled concentrations of different estimates of the key micrometeorological variables that represent the dispersion processes. The modelling approach is based on the advection-diffusion equation and includes profiles of wind and eddy diffusivity for the entire atmospheric boundary layer. Their functional forms depend on relevant parameters that represent the turbulent mechanisms in a wide range of stabilities. The Prairie Grass experiments were considered for the evaluation. The model performed satisfactorily in the estimation of the near surface crosswind integrated concentrations. The distinct micrometeorological parameters caused, in general, minor differences in the concentrations. However, a greater impact was found during very stable or unstable conditions. In consequence, in these particular situations, the methodologies to obtain the micrometeorological parameters must be carefully analysed.

A non-monotonic eddy diffusivity profile of Titan's atmosphere revealed by Cassini observations

Recent measurements from the limb-view soundings of Cassini/CIRS and the stellar occultations from Cassini/UVIS revealed the complete vertical profiles of minor species (e.g., C2H2 and C2H4) from 100 to 1000km in the atmosphere of Titan. In this study, we developed an inversion technique to retrieve the eddy diffusion profile using C2H2 as a tracer species. The retrieved eddy profile features a low eddy diffusion zone near the altitude of the detached haze layer (~550km), which could be a consequence of stabilization through aerosol heating. Photochemical modeling results using the retrieved eddy profile are in better agreement with the Cassini measurements than previous models. The underestimation of C2H4 in the stratosphere has been a long-standing problem in planetary photochemical modeling, and the new eddy diffusion profile does not solve this problem. In order to match the observations, we suggest a new expression for the rate coefficient of the key reaction, H+C2H4+M⟶C2H5+M. The new reaction rate coefficient is estimated to be ~10 times lower than that used by Moses et al. (2005)'s model, and should be validated in the laboratory and tested against the hydrocarbon chemistry of giant planets.

A two dimensional numerical model of primary pollutant emitted from an urban area source with mesoscale wind, dry deposition and chemical reaction

A two dimensional numerical model has been developed to study the dispersion of a primary pollutant emitted from an urban area source in the presence of mesoscale wind. The model takes into account the transformation and removal mechanisms through chemical reaction, dry deposition and gravitational settling processes. The numerical model is solved using the Crank–Nicolson finite difference scheme under the stability dependent meteorological parameters involved in wind velocities and eddy diffusivity profiles. The urban heat island effect generates its own mesoscale winds and consequently prevents the dispersal of pollutants which will result in an increase in the concentration of pollution in the atmosphere. The analysis shows that the mesoscale wind reduces the concentration of a primary pollutant in the upwind side of centre of heat island and increases the concentration in the downwind side of centre of heat island.

Experimental measurement and modeling of downflow condensation in a circular tube

This study explores the interfacial and heat transfer characteristics of annular condensation of FC-72 in vertical downflow. Two separate condensation test modules are employed, one for high-speed video imaging of the film interface and the second for heat transfer measurements. Condensation in both test modules is achieved by rejecting the heat to a counterflow of cooling water. The heat transfer measurements are obtained along the inner wall of an 11.89-mm i.d. and 1259.84-mm long stainless steel tube. For very low FC-72 flow rates, the film is observed to be both smooth and laminar. The film turns turbulent with a very wavy interface as the flow rate of FC-72 is increased, especially for exit film Reynolds numbers above 1800. The heat transfer coefficient decreases axially because of a gradual thickening of the liquid film. However, the data show a downstream minimum before the heat transfer coefficient increases again towards the outlet as the film transitions to turbulent flow, enhanced by the more intense downstream waves. A control-volume-based model is proposed, which incorporates an eddy diffusivity profile for the liquid film that accounts for interfacial dampening of turbulence due to surface tension. The model shows good accuracy in predicting the average condensation heat transfer coefficient data, evidenced by a mean absolute error of 12.59%.