Boundary Layer Eddies Research Articles

Updraft Width Implications for Cumulonimbus Growth in a Moist Marine Environment

Abstract An idealized large-eddy simulation of a tropical marine cloud population was performed. At any time, it contained hundreds of clouds, and updraft width in shallow convection emerging from a subcloud layer appeared to be an important indicator of whether specific convective elements deepened. In an environment with 80%–90% relative humidity below the 0°C level, updrafts that penetrated the 0°C level were larger at and above cloud base, which occurred at the lifting condensation level near 600 m. Parcels rising in these updrafts appeared to emerge from boundary layer eddies that averaged ∼200 m wider than those in clouds that only reached 1.5–3 km height. The deeply ascending parcels (growers) possessed statistically similar values of effective buoyancy below the level of free convection (LFC) as parcels that began to ascend in a cloud but stopped before reaching 3000 m (nongrowers). The growers also experienced less dilution above the LFC. Nongrowers were characterized by negative effective buoyancy and rapid deceleration above the LFC, while growers continued to accelerate well above the LFC. Growers occurred in areas with a greater magnitude of background convergence (or weaker divergence) in the subcloud layer, especially between 300 m and cloud base, but whether the convergence actually led to eddy widening is unclear. Significance Statement Cumulonimbus clouds are responsible for many extreme weather phenomena and are important contributors to Earth’s energy balance. However, the processes leading to the growth of individual clouds are not completely understood nor well-represented in weather prediction models. We find that the clouds containing updrafts that start out wider at early stages of their life cycles grow taller, possibly because they are protected more from drier air outside the cloud than narrow clouds. In addition, this work shows how the initial width of clouds might be related to convergence in the lowest part of the atmosphere, at heights where clouds initially develop. However, meteorologists must be careful not to overinterpret these results because numerical simulations inherently include assumptions that may not reflect reality. This reinforces the need to also observe processes occurring at the scales of individual clouds.

Improving Stratocumulus Cloud Amounts in a 200‐m Resolution Multi‐Scale Modeling Framework Through Tuning of Its Interior Physics

AbstractHigh‐Resolution Multi‐scale Modeling Frameworks (HR)—global climate models that embed separate, convection‐resolving models with high enough resolution to resolve boundary layer eddies—have exciting potential for investigating low cloud feedback dynamics due to reduced parameterization and ability for multidecadal throughput on modern computing hardware. However low clouds in past HR have suffered a stubborn problem of over‐entrainment due to an uncontrolled source of mixing across the marine subtropical inversion manifesting as stratocumulus dim biases in present‐day climate, limiting their scientific utility. We report new results showing that this over‐entrainment can be partly offset by using hyperviscosity and cloud droplet sedimentation. Hyperviscosity damps small‐scale momentum fluctuations associated with the formulation of the momentum solver of the embedded large eddy simulation. By considering the sedimentation process adjacent to default one‐moment microphysics in HR, condensed phase particles can be removed from the entrainment zone, which further reduces entrainment efficiency. The result is an HR that can produce more low clouds with a higher liquid water path and a reduced stratocumulus dim bias. Associated improvements in the explicitly simulated sub‐cloud eddy spectrum are observed. We report these sensitivities in multi‐week tests and then explore their operational potential alongside microphysical retuning in decadal simulations at operational 1.5° exterior resolution. The result is a new HR having desired improvements in the baseline present‐day low cloud climatology, and a reduced global mean bias and root mean squared error of absorbed shortwave radiation. We suggest it should be promising for examining low cloud feedbacks with minimal approximation.

The ultimate state of convection: a unifying picture of very high Rayleigh numbers experiments

The long-standing puzzle of diverging heat transport measurements at very high Rayleigh numbers (Ra) is addressed by a simple model based on well-known properties of classical boundary layers. The transition to the ‘ultimate state’ of convection in Rayleigh–Bénard cells is modeled as sub-critical transition controlled by the instability of large-scale boundary-layer eddies. These eddies are restricted in size either by the lateral wall or by the horizontal plates depending on the cell aspect ratio (in cylindrical cells, the cross-over occurs for a diameter-to-height ratio around 2 or 3). The large-scale wind known to settle across convection cells is assumed to have antagonist effects on the transition depending on its strength, leading to wind-immune, wind-hindered or wind-assisted routes to the ultimate regime. In particular winds of intermediate strength are assumed to hinder the transition by disrupting heat transfer, contrary to what is assumed in standard models. This phenomenological model is able to reconcile observations from more than a dozen of convection cells from Grenoble, Eugene, Trieste, Göttingen and Brno. In particular, it accounts for unexplained observations at high Ra, such as Prandtl number and aspect ratio dependences, great receptivity to details of the sidewall and differences in heat transfer efficiency between experiments.

Wall-Modeled Large-Eddy Simulation for Complex Turbulent Flows.

Large-eddy simulation (LES) has proven to be a computationally tractable approach to simulate unsteady turbulent flows. However, prohibitive resolution requirements induced by near-wall eddies in high-Reynolds number boundary layers necessitate the use of wall models or approximate wall boundary conditions. We review recent investigations in wall-modeled LES, including the development of novel approximate boundary conditions and the application of wall models to complex flows (e.g., boundary-layer separation, shock/boundary-layer interactions, transition). We also assess the validity of underlying assumptions in wall-model derivations to elucidate the accuracy of these investigations, and offer suggestions for future studies.

Using the Artificial Tracer e90 to Examine Present and Future UTLS Tracer Transport in WACCM

Abstract Large-scale tracer transport in the upper troposphere and lower stratosphere (UTLS) is investigated using simulations of the Whole Atmosphere Community Climate Model (WACCM) over the period 1955–2099. The analyses are based on e90, an artificial passive tracer with constant emissions and atmospheric loss rates. The separate contributions of advection by the residual circulation, eddy mixing, and subgrid convection to total transport are explicitly evaluated. The results highlight distinct large-scale transport regimes in the tropics, characterized by efficient vertical tracer transport, and the extratropics, dominated by isentropic mixing. One novel result is the important role of vertical eddy mixing in the tropical upper troposphere. It is shown that interannual variability in e90 is largely driven by El Niño–Southern Oscillation and the quasi-biennial oscillation. The long-term trends emphasize a strong impact of a rising tropopause with climate change on UTLS dynamics and tracer transport. The analyses directly attribute the e90 trends to changes in the different transport components. Stronger residual circulation in the future leads to increased tracer concentrations in the tropical lower stratosphere. Enhanced eddy mixing increases e90 in the extratropical lowermost stratosphere, linked to an upward shift of wave dissipation tied to the tropopause rise. In the troposphere, reduced concentrations in the future are due to weaker convective transport out of the boundary layer and weaker extratropical isentropic eddy mixing.

A Physically Based Horizontal Subgrid-Scale Turbulent Mixing Parameterization for the Convective Boundary Layer

Abstract Compared to the representation of vertical turbulent mixing through various planetary boundary layer (PBL) schemes, the treatment of horizontal turbulent mixing in the boundary layer has received much less attention. In mesoscale and convective-scale models, subgrid-scale horizontal turbulent mixing has traditionally been associated with mesoscale circulations or eddies. Its parameterization most often adopts the gradient-diffusion model, where the horizontal mixing coefficients are usually set constant, or through the 2D Smagorinsky formulation, or in some cases based on the 1.5-order turbulence kinetic energy (TKE) closure. For horizontal turbulent mixing associated with boundary layer eddies, the traditional schemes are shown to perform poorly. This work investigates the characteristic turbulence velocity and length scales based on analysis of a well-resolved, wide-domain large-eddy simulation of a convective boundary layer (CBL). To improve the representation of horizontal turbulent mixing by CBL eddies, a class of schemes is proposed with different levels of sophistication. The first two schemes can be used together with first-order PBL schemes, while the third uses TKE to define its characteristic velocity scale and can be used together with TKE-based higher-order PBL schemes. The proposed parameterizations are tested a posteriori in idealized simulations of turbulent dispersion of a passive scalar. Comparisons show improved horizontal dispersion by the proposed schemes and further demonstrate the weakness of the existing schemes.

Atmospheric Observation under Sampling Problem: The Impact of Unresolved Micro-Scale Boundary Layer Eddies on Climate Trends

The observed basic weather variables are the main representative of climate trends and the atmosphere. The unresolved meteorological scale in weather observation such as micro scale, can produce a noticeable bias in amplitude, frequency, phase and climate trend of each observed variable time series. The bias in climate trend due to a small scale eddy can be as high as the amplitude of the eddy which could be greater than 1°C in a temperature trend. Such biased measurements of the state of the atmosphere limit all climate related studies.

Flux-Profile Relationship for Dust Concentration in the Stratified Atmospheric Surface Layer

Flux-profile relationships are usually obtained under the assumption that the mean field of interest is in equilibrium with the associated surface fluxes. In this study, the existence of an equilibrium state for dust concentration in the atmospheric surface layer above sources and sinks is evaluated using large-eddy simulation. Results show that for steady-state turbulence and negligible horizontal advection, an equilibrium mean vertical profile of dust concentration is reached after one boundary-layer eddy turnover time. This is true for cases over a source or sink, under different atmospheric stabilities, and for particles with negligible or significant settling velocity. A new model relating the net surface flux to the vertical concentration profile that accounts for both atmospheric stability and particle settling velocity is proposed. The model compares well with the simulation results for all particle sizes and atmospheric stability conditions evaluated, and it can be used to estimate the concentration profile based on the surface flux, and also to estimate the surface flux by fitting the vertical concentration profile. The resulting equation can be considered as an extension of Monin-Obukhov similarity theory to the concentration of settling particles, such as mineral dust, sea-salt, pollen and other suspended aerosols.

Low-Reynolds number flow computation for eppler 387 wing using hybrid DES/transition model

Detached eddy simulations were successfully applied to assess fully-turbulent external flows. DES exploits the advantages of RANS modeling inside of the boundary layer and large eddy simulation outside of the turbulent boundary layer. The DES results have generally shown excellent solutions for unsteady wake flows, but not for transitional flows because DES is fundamentally based on a fully turbulent assumption. A hybrid model that combines the DES and γ-Reθ transition models is hereby proposed to simulate both the unsteady wake and the laminar/turbulent transition inside of the boundary layer. The numerical results provided by the simulation are compared to experimental data obtained from an Eppler 387 airfoil. The results indicate that the hybrid DES/Transition model predicts both strong laminar/turbulent transition phenomena including the laminar separation bubble and flow separation at high angles of attack.

Ventilation of multi-entranced rodent burrows by boundary layer eddies.

Rodent burrows are often assumed to be environments wherein the air has a high concentration of CO₂. Although high burrow [CO₂] has been recorded, many studies report burrow [CO₂] that differs only slightly from atmospheric concentrations. Here, we advocate that one of the reasons for these differences is the penetration into burrows of air gusts (eddies), which originate in the turbulent boundary layer and prevent build-up of CO₂. We have characterized the means by which burrows of Sundevall's jird, which are representative of the burrows of many rodent species with more than one entrance, are ventilated. Our results demonstrate that, even at low wind speeds, the random penetration of eddies into a burrow through its openings is sufficient to keep the burrow [CO₂] low enough to be physiologically inconsequential, even in its deep and remote parts.

Quantifying particle size and turbulent scale dependence of dust flux in the Sahara using aircraft measurements

The first size-resolved airborne measurements of dust fluxes and the first dust flux measurements from the central Sahara are presented and compared with a parameterization by Kok (2011a). High-frequency measurements of dust size distribution were obtained from 0.16 to 300 µm diameter, and eddy covariance fluxes were derived. This is more than an order of magnitude larger size range than previous flux estimates. Links to surface emission are provided by analysis of particle drift velocities. Number flux is described by a −2 power law between 1 and 144 µm diameter, significantly larger than the 12 µm upper limit suggested by Kok (2011a). For small particles, the deviation from a power law varies with terrain type and the large size cutoff is correlated with atmospheric vertical turbulent kinetic energy, suggesting control by vertical transport rather than emission processes. The measured mass flux mode is in the range 30–100 µm. The turbulent scales important for dust flux are from 0.1 km to 1–10 km. The upper scale increases during the morning as boundary layer depth and eddy size increase. All locations where large dust fluxes were measured had large topographical variations. These features are often linked with highly erodible surface features, such as wadis or dunes. We also hypothesize that upslope flow and flow separation over such features enhance the dust flux by transporting large particles out of the saltation layer. The tendency to locate surface flux measurements in open, flat terrain means these favored dust sources have been neglected in previous studies.

The Relationships among Wind, Horizontal Pressure Gradient, and Turbulent Momentum Transport during CASES-99

Abstract Relationships among the horizontal pressure gradient, the Coriolis force, and the vertical momentum transport by turbulent fluxes are investigated using data collected from the 1999 Cooperative Atmosphere–Surface Exchange Study (CASES-99). Wind toward higher pressure (WTHP) adjacent to the ground occurred about 50% of the time. For wind speed at 5 m above the ground stronger than 5 m s−1, WTHP occurred about 20% of the time. Focusing on these moderate to strong wind cases only, relationships among horizontal pressure gradients, Coriolis force, and vertical turbulent transport in the momentum balance are investigated. The magnitude of the downward turbulent momentum flux consistently increases with height under moderate to strong winds, which results in the vertical convergence of the momentum flux and thus provides a momentum source and allows WTHP. In the along-wind direction, the horizontal pressure gradient is observed to be well correlated with the quadratic wind speed, which is demonstrated to be an approximate balance between the horizontal pressure gradient and the vertical convergence of the turbulent momentum flux. That is, antitriptic balance occurs in the along-wind direction when the wind is toward higher pressure. In the crosswind direction, the pressure gradient varies approximately linearly with wind speed and opposes the Coriolis force, suggesting the importance of the Coriolis force and approximate geotriptic balance of the airflow. A simple one-dimensional planetary boundary layer eddy diffusivity model demonstrates the possibility of wind directed toward higher pressure for a baroclinic boundary layer and the contribution of the vertical turbulent momentum flux to this phenomenon.

A simple model for the streamwise fluctuations in the log-law region of a boundary layer

We build on the work of Davidson et al. [Phys. Fluids 18, 065112 (2006)] and propose an elementary model for the log-law region of a boundary layer. The model is remarkably simple, contains only one free parameter (which we set equal to unity) and, unlike Davidson et al., assumes very little about the shape of the boundary-layer eddies. The physical content of the model is simple: we assume that the two-point statistics of the streamwise velocity fluctuations know about the presence of the wall only to the extent that, over a range of eddy sizes, it imposes a kinetic energy scale proportional to the square of the shear velocity. Little else is assumed, other than classic Kolmogorov phenomenology for the small scales. Despite its naivety, and the minimal number of free parameters, the model is a good fit to experimental data for the k−1 law of the one-dimensional, longitudinal spectrum, Φuu(k), and also to Φuu(k) in the inertial range. It is also an excellent fit to experimental data for the real-space analog of the k−1 law; that is, the logarithmic law for the longitudinal structure function. In addition, the model predicts the cross-stream variation of the variance of the streamwise velocity fluctuations, ⟨ux2⟩, and, to within an additive constant, it too is a reasonable fit to the data. Our model differs from the classic analyses of Townsend [J. Fluid Mech. 165, 163 (1986)] and Perry et al. [J. Fluid Mech. 165, 163 (1986)] in three respects. First, we do not invoke the attached eddy hypothesis, which assumes that the vortical structures in the log-layer extend to the wall. Second, we predict the precise shape of Φuu(k) for all values of k and not just the k−1 region. Third, there are three adjustable parameters in the theory of Perry et al., whereas we have only one. It is instructive that a model which contains very little information about the morphology of the vorticity field, and has only one free parameter, is able to reproduce both the structural form for, and magnitude of, many features of the one-dimensional spectrum and the second-order structure function. This suggests that these two measures of the scale-by-scale energy distribution are insensitive to the detailed structure of the vorticity field. We argue that this is indeed the case.

Multidimensional Longwave Forcing of Boundary Layer Cloud Systems

Abstract The importance of multidimensional (MD) longwave radiative effects on cloud dynamics is evaluated in an eddy-resolving model (ERM)—the two-dimensional analog to large-eddy simulation (LES)—framework employing multidimensional radiative transfer [Spherical Harmonics Discrete Ordinate Method (SHDOM)]. Simulations are performed for a case of unbroken, marine boundary layer stratocumulus and a broken field of trade cumulus. “Snapshot” calculations of MD and independent pixel approximation (IPA; 1D) radiative transfer applied to simulated cloud fields show that the total radiative forcing changes only slightly, although the MD effects significantly modify the spatial structure of the radiative forcing. Simulations of each cloud type employing MD and IPA radiative transfer, however, differ little. For the solid cloud case, relative to using IPA, the MD simulation exhibits a slight reduction in entrainment rate and boundary layer total kinetic energy (TKE) relative to the IPA simulation. This reduction is consistent with both the slight decrease in net radiative forcing and a negative correlation between local vertical velocity and radiative forcing, which implies a damping of boundary layer eddies. Snapshot calculations of the broken cloud case suggest a slight increase in radiative cooling, although few systematic differences are noted in the interactive simulations. This result is attributed to the fact that radiative cooling is a relatively minor contribution to the total energetics. For the cloud systems in this study, the use of IPA longwave radiative transfer is sufficiently accurate to capture the dynamical behavior of boundary layer clouds. Further investigations are required to generalize this conclusion for other cloud types and longer time integrations.

The Impact on a GCM Climate of an Extended Mosaic Technique for the Land–Atmosphere Coupling

Heterogeneities in the land surface on scales smaller than the typical general circulation model (GCM) grid size can have a profound influence on the grid-scale mean climate. There exists observational and modeling evidence that the direct effects of surface heterogeneities may be felt by the atmosphere well into the planetary boundary layer. The impact of including an “extended mosaic” (EM) scheme, which accounts for the vertical influence of land surface heterogeneities in a GCM, is evaluated here by comparing side-by-side GCM simulations with EM and with the more standard mosaic formulation (M). Differences between the EM and M simulations are observed in the boundary layer structure, in fields that link the boundary layer and the general circulation, and in fields that represent the general circulation itself. Large EM − M differences are found over the eastern United States, eastern Asia, and southern Africa in the summertime, and are associated with a boundary layer eddy diffusion feedback mechanism. The feedback mechanism operates as a positive or negative feedback depending on the local Bowen ratio. Significant EM − M differences are also found in the region of the Australian monsoon and in the strength of the stationary Pacific–North America pattern in the northern Pacific.

MHD flow simulation in subsonic disk MHD generator driven by a shock tube facility

AbstractThe MHD flow behavior and the performance of an experimental nonequilibrium subsonic disk MHD generator driven by a shock‐tube facility have been examined with time‐dependent r−z two‐dimensional and r−θ−z three‐dimensional Large Eddy Simulation for the first time. The calculation region is extended and covers a hot duct through a downstream duct including the subsonic MHD generator with two throats. For optimal and high load operations, the flow chokes at the downstream throat and the subsonic flow is maintained in the generator channel. The discharge structure is uniform in the θ direction, and suitable fluid flow is realized in the generator channel, although the large boundary layer separations and eddies are observed behind the downstream throat. For low load operations, the flow chokes at the upstream throat and the flow becomes supersonic, where pseudo‐shock waves and large eddies are observed in the generator channel and the downstream duct. The ionization instability in the r−θ plane occurs in the generator channel, which deteriorates the generator performance. Asymmetric flow at the generator inlet, which is attributed to the change of flow direction from the hot duct, seems not to be significant for the generator performance. © 2003 Wiley Periodicals, Inc. Electr Eng Jpn, 143(3): 1–8, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/eej.10130

衝撃波管駆動亜音速非平衡ディスク形MHD発電機内の電磁流体シミュレーション

The MHD flow behavior and the performance of an experimental nonequilibrium subsonic disk MHD generator driven by a shock-tube facility have been examined with time-dependent r−z two-dimensional and r−θ−z three-dimensional Large Eddy Simulation for the first time. The calculation region is extended and covers a hot duct through a downstream duct including the subsonic MHD generator with two throats. For optimal and high load operations, the flow chokes at the downstream throat and the subsonic flow is maintained in the generator channel. The discharge structure is uniform in the θ direction, and suitable fluid flow is realized in the generator channel, although the large boundary layer separations and eddies are observed behind the downstream throat. For low load operations, the flow chokes at the upstream throat and the flow becomes supersonic, where pseudo-shock waves and large eddies are observed in the generator channel and the downstream duct. The ionization instability in the r−θ plane occurs in the generator channel, which deteriorates the generator performance. Asymmetric flow at the generator inlet, which is attributed to the change of flow direction from the hot duct, seems not to be significant for the generator performance. © 2003 Wiley Periodicals, Inc. Electr Eng Jpn, 143(3): 1–8, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/eej.10130

Importance of Low-Frequency Contributions to Eddy Fluxes Observed over Rough Surfaces

Abstract Eddy covariance flux observations at a deciduous temperate forest site (83 days) and at a boreal forest site (21 days) are analyzed for midday periods (1100–1400 LT). Approximate stationarity of the time series is demonstrated, and the ensemble-averaged roughness sublayer cospectra are presented. Spectral and cospectral forms in the roughness sublayer are more peaked than those found in an inertial sublayer. They exhibit similar forms dependent on (z − d)/(h − d), where d is the displacement height and h is the canopy height. The inertial-layer spectral forms are recovered when observations are made where this scaled height is approximately 4. For a sample summer at the midlatitude deciduous forest, large eddies with periods from 4 to 30 min contribute about 17% to surface eddy fluxes of heat, water vapor, and carbon dioxide (CO2). Much larger contributions can occur in light-wind conditions. This effect, likely caused by the passage of convective boundary layer eddies, is not observed when using...

SIMULATION OF ACOUSTIC SCATTERING FROM A TRAILING EDGE

Three model problems were examined to assess the difficulties involved in using a hybrid scheme coupling flow computation with the Ffowcs Williams and Hawkings equation to predict the noise generated by vortices passing over a sharp edge. The results indicate that the Ffowcs Williams and Hawkings equation correctly propagates the acoustic signals when provided with accurate flow information on the integration surface. The most difficult of the model problems investigated flow over a two-dimensional, thin NACA airfoil with a bluff-body vortex generator positioned at 98% chord. Vortices rolled up downstream of the bluff body. The shed vortices possessed similarities to large coherent eddies in boundary layers in that they interacted and occasionally paired as they convected past the sharp trailing edge of the airfoil. The calculations showed acoustic waves emanating from the airfoil trailing edge. Acoustic directivity and Mach number scaling were obtained.

Variation of boundary layer heights and eddy diffusivities over dry and moist convective regions of monsoon trough during different phases of monsoon

Temperature, wind, and humidity data at 6 levels over meteorological towers at Kharagpur and Jodhpur and fast data at Jodhpur (Sonic anemometer at 4m and Gill anemometer 15 m) and Kharagpur (Sonic anemometer at 8m and Gill anemometer at 15m) were analysed. Diurnal variation of boundary layer heights and eddy diffusivity coefficient of moment, heat and moisture at dry convective region Jodhpur (26° N, 73°E) and moist convective region Kharagpur (22.3°N, 87.2°E) of monsoon trough during onset of monsoon, mid-monsoon and end-monsoon phases of the Indian southwest monsoon are studied using micro meteorological tower data. Boundary layer height is computed by eddy correlation (direct method) and profile method {indirect method). Indirect method underestimates the boundary layer height.