Eddy Diffusivity Research Articles

Effects of the internal temperature on vertical mixing and on cloud structures in ultra-hot Jupiters

The vertical mixing in hot-Jupiter atmospheres plays a critical role in the formation and spacial distribution of cloud particles in their atmospheres. This affects the observed spectra of a planet through cloud opacity, which can be influenced by the degree of cold trapping of refractory species in the deep atmosphere. We aim to isolate the effects of the internal temperature on the mixing efficiency in the atmospheres of ultra-hot Jupiters (UHJs) and the spacial distribution of cloud particles across the planet. We combined a simplified tracer-based cloud model, a picket fence radiative-transfer scheme, and a mixing length theory to the Exo-FMS general circulation model. We ran the model for five different internal temperatures at typical UHJ atmosphere system parameters. Our results show the convective eddy diffusion coefficient remains low throughout the vast majority of the atmosphere, with mixing dominated by advective flows. However, some regions can show convective mixing in the upper atmosphere for colder interior temperatures. The vertical extent of the clouds is reduced as the internal temperature is increased. Additionally, a global cloud layer gets formed below the radiative--convective boundary (RCB) in the cooler cases. Convection is generally strongly inhibited in UHJ atmospheres above the RCB due to their strong irradiation. Convective mixing plays a minor role compared to advective mixing in keeping cloud particles aloft in UHJs with warm interiors. Higher vertical turbulent heat fluxes and the advection of potential temperature inhibit convection in warmer interiors. Our results suggest that isolated upper atmosphere regions above cold interiors may exhibit strong convective mixing in isolated regions around Rossby gyres, allowing aerosols to be better retained in these areas.

A dynamically adaptive Langmuir turbulence parameterization scheme for variable wind wave conditions: Model application

Langmuir circulations and turbulence (LT) are crucial in the upper ocean mixed layer, significantly affecting the air-sea exchange of momentum, heat, and mass. The development of an appropriate LT parameterization scheme is vital for ocean modeling. This study employed the Large-eddy Simulation (LES) and the Physics-informed Neural Network (PINN) to optimize the KC04 Langmuir turbulence scheme by dynamically adjusting E6 as a key parameter determined by winds and waves. The LES simulations under different wind wave states indicated the PINN-inferred values for E6. Modelling results from GOTM in OCSPapa station demonstrated that the optimized scheme outperformed the original KC04 scheme in simulating the vertical eddy diffusivity and temperature, with an ∼6.24% annual reduction in the root mean square error (RMSE) for the temperature and an ∼8.23% reduction in the RMSE during autumn. Furthermore, the optimized scheme resulted in a thicker mixed layer, reaching 4.9 m. This enhanced LT parameterization scheme exhibited the improved robustness for variable spatiotemporal resolutions, significantly improving the modeling accuracy.

Altimeter-derived poleward Lagrangian pathways in the California Current System: Part 1

We use altimeter-derived geostrophic velocities, with and without the addition of surface Ekman transports, to create trajectories for virtual parcels in the California Current System (CCS). The goal is to investigate the poleward transport of passive water parcels in the surface 50–100 m of the nominally equatorward system. Motivation for the study is provided by observations of anomalous biomass of copepods with warm water affinities along the Newport Hydrographic Line off central Oregon (44.7°N) during El Niño years, as well as during and following the 2014–2016 marine heat wave. By backward tracking virtual parcels from 44.7°N, we find that the most distant source of passive water parcels in the upper ocean during a one-year period of travel is from within the Southern California Bight (SCB), north of 30°N. To make that journey, parcels use the Inshore Countercurrent off southern and central California during summer–winter and the Davidson Current off northern California and Oregon during autumn–winter. The inclusion of small-scale eddy diffusion usually increases the number of parcels that reach more northern latitudes, while the inclusion of Ekman velocities more often reduces those numbers. Even so, parcels can travel from the SCB to central Oregon in either the Ekman layer or beneath it in the geostrophic flow. Using backward tracking, we find that parcels arrive at 44.7°N most often in winter–spring, least often in autumn. They arrive from within the large-cape region off northern California (41°–42°N) during all years and all months, from just south of the large-cape region (38°–39°N) during most years but seldom in autumn, from south of Monterey Bay along central California (36°N) and within the SCB (34.5°N) during a third (or less) of the years and only in winter-spring. The shortest average transit times are found in winter: for parcels reaching 44.7°N in February, the average transit time is 2 months for parcels coming from 41°–42°N, 4 months for parcels coming from 38°–39°N, and 5–6 months or more for parcels coming from south of 36°N. Transit times increase as the arrival time progresses from winter to autumn. The longest average transit times are for parcels reaching central Oregon in autumn (9–12 months in October for parcels coming from south of 39°N). This makes the journey a multi-generational task for the copepods. Interannual variability in the observed southern copepod species biomass off central Oregon correlates highly with years when more virtual parcels from the south reach central and northern Oregon, providing increased confidence in the results found with the altimeter-derived parcel trajectories.

Spatial Distribution of the Eddy Diffusion Coefficient in the Plasma Sheet of Earth’s Magnetotail and its Dependence on the Interplanetary Magnetic Field and Geomagnetic Activity based on MMS Satellite Data

The article presents the results of a statistical analysis of the distribution of the eddy diffusion coef-ficient depending on the coordinates in the plasma sheet of Earth’s magnetosphere based on data from the Magnetospheric Multiscale Mission satellite system (MMS) for the period from 2017 to 2022. The localization of satellites inside the plasma sheet was recorded from the concentration and temperature of plasma ions according to the data of the same instruments and the value of plasma parameter β. Significant anisotropy of the eddy diffusion coefficient was revealed. The dependence of the eddy diffusion coefficient on the inter-planetary magnetic field is analyzed, showing that with the southern orientation of the interplanetary magnetic field, the eddy diffusion coefficients are 1.5–2 times greater than with the northern orientation. It is also shown that under disturbed geomagnetic conditions (SML –200 nT), the eddy diffusion coefficients are several times greater than under quiet geomagnetic conditions (SML –50 nT).

A Tale of Two Molecules: The Underprediction of CO2 and Overprediction of PH3 in Late T and Y Dwarf Atmospheric Models

The sensitivity and spectral coverage of JWST are enabling us to test our assumptions of ultracool dwarf atmospheric chemistry, especially with regards to the abundances of phosphine (PH3) and carbon dioxide (CO2). In this paper, we use Near Infrared Spectrograph PRISM spectra (∼0.8−5.5 μm, R ∼ 100) of four late T and Y dwarfs to show that standard substellar atmosphere models have difficulty replicating the 4.1−4.4 μm wavelength range, as they predict an overabundance of phosphine and an underabundance of carbon dioxide. To help quantify this discrepancy, we generate a grid of models using PICASO, based on the Elf Owl chemical and temperature profiles, where we include the abundances of these two molecules as parameters. The fits to these PICASO models show a consistent preference for orders-of-magnitude higher CO2 abundances and a reduction in PH3 abundance as compared to the nominal models. This tendency means that the claimed phosphine detection in UNCOVER−BD−3 could instead be explained by a CO2 abundance in excess of standard atmospheric model predictions; however, the signal-to-noise ratio of the spectrum is not high enough to discriminate between these cases. We discuss atmospheric mechanisms that could explain the observed underabundance of PH3 and overabundance of CO2, including a vertical eddy diffusion coefficient (K zz) that varies with altitude, incorrect chemical pathways, or elements condensing out in forms such as NH4H2PO4. However, our favored explanation for the required CO2 enhancement is that the quench approximation does not accurately predict the CO2 abundance, as CO2 remains in chemical equilibrium with CO after CO quenches.

An investigation into Venusian atmospheric chemistry based on an open-access photochemistry-transport model at 0–112 km

Atmospheric chemistry plays a crucial role in the evolution of climate habitability on Venus. It has been widely explored by chemistry-transport models, but some characteristics are still poorly interpreted. This study is devoted to developing an open-access chemistry-transport model spanning both the middle and lower atmospheres of Venus. It provides a scheme for the structure of the chemistry, especially for the sulfur and oxygen, and investigates the influence of the cloud diffusivity and the SO2 dissolution that are adopted in the clouds. The developed model is based on the VULCAN framework and was updated with the state-of-the-art Venusian atmospheric chemistry. It includes vertical eddy diffusion retrieved recently with the Venus Express observations, and it resolves radiative transfer containing gas absorption and scattering, Mie scattering of the cloud droplets, and absorption of the unknown UV absorber. The obtained abundance profiles of SO, SO2, CO, COS, O, O2, O3, HCl, and NO are in overall agreement with the observations. The results show that the increase in cloud diffusivity has slight effects on the chemical structure. The SO2 mainly dissolves in 50–90 km and evaporates below the clouds. The rapid dissolution-release cycle is responsible for the large upward flux of SO2 at 58 km. At around 70 km, SO has a significant peak that is larger than that of previous studies by an order of magnitude, and S and SO2 also show slight increases. They are attributed to the buffering effects of liquid SO2 in the clouds. O2 is significantly eliminated by SO in this layer. We emphasize the superior regulation of the sulfur cycle on O2 at 70 km and its potential contributions to the long-standing problem of the overestimated O2 abundance.

Characteristics of Eddy Diffusion in the Southwest Coastal Zone of Korea

Characteristics of Eddy Diffusion in the Southwest Coastal Zone of Korea

Mean temperature profiles in turbulent internal flows

We derive explicit formulas for the mean profiles of temperature (modeled as a passive scalar) in forced turbulent convection, as a function of the Reynolds and Prandtl numbers. The derivation leverages on the observed universality of the inner-layer thermal eddy diffusivity with respect to Reynolds and Prandtl number variations and across different flows, and on universality of the passive scalar defect in the core flow. Matching of the inner- and outer-layer expression yields a smooth compound mean temperature profile. We find excellent agreement of the analytical profile with data from direct numerical simulations of pipe and channel flows under various thermal forcing conditions, and over a wide range of Reynolds and Prandtl numbers.

Direct numerical simulation study on wall-modeling of turbulent water channel flows with temperature-dependent viscosity

We discuss wall-modeling of turbulent heat transfer of water channel flows with temperature-dependent viscosity via direct numerical simulations. We considered a top-cooled wall (293[K]) and a bottom-heated wall (353[K]) and varied the friction Reynolds numbers from 300 to 1000. The fluid viscosity varied depending on the local fluid temperature, whereas the other physical properties were assumed to be constant. The results show that semi-local scaling based on the local viscosity and wall friction velocity reasonably accounts for the effects of variable viscosity on turbulent flows, except in the vicinity of the wall, where wall cooling intensifies the turbulent vortical motion, leading to increased semi-locally scaled eddy diffusivities compared with those near the heated wall. In the vicinity of the cooled wall, turbulent transport is enhanced by increased viscous transport, which transfers more turbulent kinetic energy toward the cooled wall. The effectiveness of semi-local scaling for wall-modeling was validated by performing a wall-modeled large-eddy simulation at Reτ=1000, where we incorporated the semi-local viscous length scale into the classical mixing-length model. The modified mixing-length model reasonably reproduced the effects of variable viscosity on turbulent flows.

Effect of background wind and dissipation processes on the diurnal component of atmospheric solar tides

The radiation coming from the Sun heats the Earth’s atmosphere and generates atmospheric tides. In this paper, we model atmospheric tides in the presence of background wind and dissipation processes and investigate their effects. The equations for tidal oscillations of wind and temperature in the atmosphere encompass factors such as background wind, temperature profile, and background composition including ozone, carbon dioxide, hydro-magnetic interactions, Newtonian cooling, eddy, and molecular diffusion. These components interact to define the behavior of tidal phenomena comprehensively. Thermal forcing processes include the insolation absorption of H2O in the troposphere, O3 in the stratosphere, and a contribution from O2 absorption in the thermosphere. The method of solution for the equations is outlined for the solar diurnal tides during the March equinox by considering all these dissipation processes and the background wind. The obtained results are in good agreement with the Global Scale Wave Model (GSWM-00). It is found that the background wind plays significant role in affecting the horizontal wind oscillations below 100 km. At higher altitudes (100–200 km), the background wind, ion drag force, divergence of momentum, and heat fluxes due to molecular and eddy diffusion have a considerable role in affecting the zonal and meridional winds.

Probing the Heights and Depths of Y Dwarf Atmospheres: A Retrieval Analysis of the JWST Spectral Energy Distribution of WISE J035934.06–540154.6

We present an atmospheric retrieval analysis of the Y0 brown dwarf WISE J035934.06−540154.6 using the low-resolution 0.96–12 μm James Webb Space Telescope (JWST) spectrum presented in Beiler et al. We obtain volume number mixing ratios of the major gas-phase absorbers (H2O, CH4, CO, CO2, PH3, and H2S) that are three to five times more precise than previous work that used Hubble Space Telescope (HST) spectra. We also find an order-of-magnitude improvement in the precision of the retrieved thermal profile, a direct result of the broad wavelength coverage of the JWST data. We used the retrieved thermal profile and surface gravity to generate a grid of chemical forward models with varying metallicity, (C/O)atm, and strengths of vertical mixing as encapsulated by the eddy diffusion coefficient K zz. Comparison of the retrieved abundances with this grid of models suggests that the deep atmosphere of WISE 0359−54 shows signs of vigorous vertical mixing with K zz = 109 [cm2 s−1]. To test the sensitivity of these results to our five-knot spline thermal profile model, we performed a second retrieval using the Madhusudhan & Seager thermal profile model. While the results of the two retrievals generally agree well, we do find differences between the retrieved values of mass and volume number mixing ratio of H2S with fractional differences of the median values of −0.64 and −0.10, respectively. In addition, the five-knot thermal profile is consistently warmer at pressure between 1 and 70 bar. Nevertheless, our results underscore the power that the broad-wavelength infrared spectra obtainable with the JWST have to characterize the atmospheres of cool brown dwarfs.

Controls of Cross‐Shore Planktonic Ecosystem Structure in an Idealized Eastern Boundary Upwelling System

AbstractEastern boundary upwelling systems (EBUSs) are among the most productive regions in the ocean because deep, nutrient‐rich waters are brought up to the surface. Previous studies have identified winds, mesoscale eddies and offshore nutrient distributions as key influences on the net primary production in EBUSs. However uncertainties remain regarding their roles in setting cross‐shore primary productivity and ecosystem diversity. Here, we use a quasi‐two‐dimensional (2D) model that combines ocean circulation with a spectrum of planktonic sizes to investigate the impact of winds, eddies, and offshore nutrient distributions in shaping EBUS ecosystems. A key finding is that variations in the strength of the wind stress and the nutrient concentration in the upwelled waters control the distribution and characteristics of the planktonic ecosystem. Specifically, a strengthening of the wind stress maximum, driving upwelling, increases the average planktonic size in the coastal upwelling zone, whereas the planktonic ecosystem is relatively insensitive to variations in the wind stress curl. Likewise, a deepening nutricline shifts the location of phytoplankton blooms shore‐ward, shoals the deep chlorophyll maximum offshore, and supports larger phytoplankton across the entire domain. Additionally, increased eddy stirring of nutrients suppresses coastal primary productivity via “eddy quenching,” whereas increased eddy restratification has relatively little impact on the coastal nutrient supply. These findings identify the wind stress maximum, isopycnal eddy diffusion, and nutricline depth as particularly influential on the coastal ecosystem, suggesting that variations in these quantities could help explain the observed differences between EBUSs, and influence the responses of EBUS ecosystems to climate shifts.

Evaluation of the eddy diffusivity in a pollutant dispersion model in the planetary boundary layer

Evaluation of the eddy diffusivity in a pollutant dispersion model in the planetary boundary layer

Comparison of the adsorption dynamics of leucyl-leucine enantiomers and glycyl-glycine on Chirobiotic R and Chirobiotic V columns

The adsorption dynamics of the LL- and DD-enantiomers of Leu-Leu and Gly-Gly on a Chirobiotic V column packed with a CSP bearing glycopeptide antibiotic vancomycin was studied and compared with the adsorption dynamics of the same dipeptides on a Chirobiotic R column packed with a CSP with bonded antibiotic ristocetin A. The column efficiencies were essentially different. The heights equivalent to a theoretical plate (HETP) on Chirobiotic R were 2-4 times larger than on Chirobiotic V, and the shape of van Deemter plots, strongly convex-upwards on the former column, demonstrated minor (Leu-Leu) or lacking (Gly-Gly) convexity on the latter column. This difference is attributed to differences in the binding kinetics of dipeptides to the antibiotics, fast for vancomycin and slow for ristocetin A. Since the kinetic C term of the van Deemter equation cannot explain such a large discrepancy in HETP for the same analyte on two columns, and since the A and B terms for the Chirobiotic R column were essentially larger than for the Chirobiotic V column, it is suggested that binding kinetics influences eddy and longitudinal diffusion processes associated with those terms. It is also hypothesized that unusually high values of van Deemter B coefficients occasionally found in chiral chromatography are not experimental artifacts but the manifestation of coupling the effects of slow adsorption kinetics and longitudinal diffusion.

Using eddy-covariance to measure the effects of COVID-19 restrictions on CO2 emissions in a neighborhood of Indianapolis, IN

Eddy-covariance (EC) flux measurements in Indianapolis were used to quantify the impact of the COVID-19 lockdown on CO and CO2 emissions from a highway and a suburban neighborhood. CO2 fluxes were measured for 6 weeks pre-lockdown (January 22, 2020–March 3, 2020) and during lockdown (March 25, 2020– May 5, 2020) using EC instrumentation at 41 m AGL. Fossil fuel CO2 emissions (CO2ff) were estimated by calculating eddy diffusivity to obtain CO flux and then scaling by the CO:CO2ff emissions ratio (RCO). Flux measurements segregated by wind direction were compared to hourly emissions from the 2020 Hestia inventory model. The lockdown CO2ff average weekday emissions from the highway estimated by EC decreased by 51.5 ± 10.9% (11.2 ± 2.2 µmol m−2 s−1) compared to pre-lockdown, similar to Hestia’s estimate 56 ± 7% (12 ± 1 µmol m−2 s−1). The EC measurements detected a significant (2.2 ± 0.7 µmol m−2 s−1) but smaller magnitude decrease in CO2ff emissions from the suburban neighborhood. The daily cycles of CO2ff emissions were significantly correlated with Hestia estimates from the highway but not from the suburbs. This study demonstrates that EC flux towers and high-resolution inventory models in regions with mixed and spatially heterogeneous sources can quantify abrupt changes in sector- and source-specific CO2 fluxes.

Toward a Unified Understanding of Estimating Evapotranspiration: The Linkage Between Three Effective Parsimonious Models

AbstractThe maximum information entropy production model (MaxEnt), the relative humidity at equilibrium approach (ETRHEQ), and the Surface Flux Equilibrium model (SFE) are three recently developed models to estimate evapotranspiration. Although the connection between ETRHEQ and SFE is evident, no attempts have been made to investigate the congruence, distinctions, or potential complementarity between the two models and MaxEnt. Our mathematical analysis demonstrates that minimizing the vertical variance of RH in ETRHEQ is equivalent to minimizing the dissipation function of energy fluxes in MaxEnt, under the assumption of the same eddy diffusivity of heat and water vapor and with a specific expression for the ratio between the thermal inertia terms for H and LE. The connection between ETRHEQ, SFE, and MaxEnt is independent of Monin‐Obukhov similarity theory (MOST)’s extremum solution, and MOST's extreme solution can be viewed as equivalent to introducing a constant correction factor to account for atmospheric stability. While ETRHEQ and MaxEnt can be united within a single hydrometeorological framework, they diverge in their approaches to modeling evapotranspiration, particularly in how they address the roles of vegetation and land surface heterogeneity. More importantly, the unified framework suggests that turbulence fluxes within the atmospheric boundary layer adhere to the principles of maximum information entropy production. The way in which dissipation, along with its associated entropy production, is established using information entropy theory deviates from traditional thermodynamic entropy formulations. Exploring the connection between thermodynamic and information entropy and developing proper formulations of dissipation for energy fluxes presents an appealing avenue for prospective research.

Representing effects of surface heterogeneity in a multi-plume eddy diffusivity mass flux boundary layer parameterization

Representing effects of surface heterogeneity in a multi-plume eddy diffusivity mass flux boundary layer parameterization

A model for drift velocity mediated scalar eddy diffusivity in homogeneous turbulent flows

A model for drift velocity mediated scalar eddy diffusivity in homogeneous turbulent flows

Impact of the Turbulent Vertical Mixing on Chemical and Cloud Species in the Venus Cloud Layer

AbstractThe Venusian atmosphere hosts a 10 km deep convective layer that has been studied by various spacecrafts. However, the impact of the strong vertical mixing on the chemistry of this region is still unknown. This study presents the first realistic coupling between resolved small‐scale turbulence and a chemical network. The resulting vertical mixing is different for each species: those with longer chemical timescales will tend to be well‐mixed. Vertical eddy diffusion due to resolved convection motions was estimated, ranging from 102 to 104 m2/s for the 48–55 km convective layer, several orders of magnitude above the typically used value. In the 48–55 km convective layer, the impact of the small‐scale turbulence on the cloud layer boundaries was between 200 m and 1 km. The impact of turbulence on cloud chemistry is consistent with Venus Express/Visible and Infrared Thermal Imaging Spectrometer observations. The observability at the cloud‐top of small‐scale turbulence by VenSpec‐U spectrometer would be challenging.

Generative Convective Parametrization of a Dry Atmospheric Boundary Layer

AbstractTurbulence parametrizations will remain a necessary building block in kilometer‐scale Earth system models. In convective boundary layers, where the mean vertical gradients of conserved properties such as potential temperature and moisture are approximately zero, the standard ansatz which relates turbulent fluxes to mean vertical gradients via an eddy diffusivity has to be extended by mass‐flux parametrizations for the typically asymmetric up‐ and downdrafts in the atmospheric boundary layer. We present a parametrization for a dry and transiently growing convective boundary layer based on a generative adversarial network. The training and test data are obtained from three‐dimensional high‐resolution direct numerical simulations. The model incorporates the physics of self‐similar layer growth following from the classical mixed layer theory of Deardorff by a renormalization. This enhances the training data base of the generative machine learning algorithm and thus significantly improves the predicted statistics of the synthetically generated turbulence fields at different heights inside the boundary layer, above the surface layer. Differently to stochastic parametrizations, our model is able to predict the highly non‐Gaussian and transient statistics of buoyancy fluctuations, vertical velocity, and buoyancy flux at different heights thus also capturing the fastest thermals penetrating into the stabilized top region. The results of our generative algorithm agree with standard two‐equation mass‐flux schemes. The present parametrization provides additionally the granule‐type horizontal organization of the turbulent convection which cannot be obtained in any of the other model closures. Our proof of concept‐study also paves the way to efficient data‐driven convective parametrizations in other natural flows.