Net Vertical Flux Research Articles

Shedding light on the MRI-driven dynamo in a stratified shearing box

ABSTRACT We study the magneto-rotational instability (MRI) dynamo in a geometrically thin disc (H/R ≪ 1) using stratified zero net (vertical) flux shearing box simulations. We find that mean fields and electromotive forces (EMFs) oscillate with a primary frequency fdyn = 0.017 Ω (approximately nine orbital period), but also have higher harmonics at 3fdyn. Correspondingly, the current helicity has two frequencies 2fdyn and 4fdyn, which appear to be the beat frequencies of mean fields and EMFs, respectively, as expected from the magnetic helicity density evolution equation. Further, we adopt a novel inversion algorithm called the ‘Iterative Removal Of Sources’, to extract the turbulent dynamo coefficients in the mean-field closure using the mean magnetic fields and EMFs obtained from the shearing box simulation. We show that an α-effect (αyy) is predominantly responsible for the creation of the poloidal field from the toroidal field, while shear generates back a toroidal field from the poloidal field, indicating that an α–Ω-type dynamo is operative in MRI-driven accretion discs. We also find that both strong outflow ($\bar{v}_z$) and turbulent pumping (γz) transport mean fields away from the mid-plane. Instead of turbulent diffusivity, they are the principal sink terms in the mean magnetic energy evolution equation. We find encouraging evidence that a generative helicity flux is responsible for the effective α-effect. Finally, we point out potential limitations of horizontal (x − y) averaging in defining the ‘mean’ on the extraction of dynamo coefficients and their physical interpretations.

Validation of key Arctic energy and water budget components in CMIP6

We investigate historical simulations of relevant components of the Arctic energy and water budgets for 39 Coupled Model Intercomparison Project Phase 6 (CMIP6) models and validate them against observation-based estimates. We look at simulated seasonal cycles, long-term averages and trends of lateral transports and storage rates in atmosphere and ocean as well as vertical fluxes at top-of-atmosphere and the surface. We find large inter-model spreads and systematic biases in the representation of annual cycles and long-term averages. Surface freshwater fluxes associated with precipitation and evaporation as well as runoff from Arctic lands tend to be overestimated by most CMIP6 models and about two thirds of the analysed models feature an early timing bias of one month in the runoff cycle phase, related to an early snow melt bias and the lack of realistic river routing schemes. Further, large biases are found for oceanic volume transports, partly because data required for accurate oceanic transport computations has not been archived. Biases are also present in the simulated energy budget components. The net vertical energy flux out of the ocean at the Arctic surface as well as poleward oceanic heat transports are systematically underestimated by all models. We find strong anti-correlation between average oceanic heat transports and mean sea ice cover, atmospheric heat transports, and also the long-term ocean warming rate. The latter strongly suggests that accurate depiction of the mean state is a prerequisite for realistic projections of future warming of the Arctic. Our diagnostics also provide useful process-based metrics for model selection to constrain projections.

Exploring the Differences in Kinetic Energy Spectra between the NCEP FNL and ERA5 Datasets

Abstract Two global atmospheric circulation datasets (ERA5 and NCEP FNL) with horizontal resolutions of 0.25° × 0.25° are investigated in terms of kinetic energy (KE) spectra at 200 hPa (roughly between 11 and 12 km). The horizontal KE (HKE) in NCEP FNL is larger and flatter than that in ERA5 at subsynoptic scales and mesoscales. Restoring the energy of this wavenumber range to the physical space shows that the HKE in NCEP FNL is larger than that in ERA5 over most areas but smaller mainly in the Indo-Pacific warm pool. The spectral budgets show that at these scales, the positive contribution from net vertical flux in ERA5 is stronger than that in NCEP FNL, while the negative contribution from available potential energy (APE) conversion is smaller; assuming that the atmosphere is in a quasi-stationary state, more dissipation is found in ERA5 than in NCEP FNL, which should be responsible for the HKE spectrum in ERA5 to be steeper and weaker than that in NCEP FNL. Our formulation shows that the APE conversion and net vertical flux are related to the pressure vertical velocity (PVV). The APE conversion and net vertical flux differences between the two datasets, like the PVV difference, are mainly from the tropical region. At large scales, the vertical motion in ERA5 is larger than that in NCEP FNL. The amplitude differences of the PVV spectra between two datasets are consistent with those of the large-scale precipitation spectra associated with microphysics parameterizations. These results support that vertical motion is a key dynamical factor explaining energy discrepancies at mesoscales. Significance Statement The atmospheric kinetic energy spectrum reflects energy distribution characteristics in atmospheric motion at different scales. According to the Helmholtz decomposition, the horizontal wind field can be decomposed into two parts: rotational wind field and divergent wind field. We explore the dynamical causes of the atmospheric energy spectra differences among different datasets from the perspective of rotational and divergent components of motion. Our results reveal that the differences in energy spectra and their energy budget at scales below a few hundred kilometers are relatively significant in tropical regions and are closely related to vertical motion. A better understanding of the differences in kinetic energy spectra will contribute to the improvement of atmospheric models.

Shear-Relative Asymmetric Kinematic Characteristics of Intensifying Hurricanes as Observed by Airborne Doppler Radar

Abstract While recent observational studies of intensifying (IN) versus steady-state (SS) hurricanes have noted several differences in their axisymmetric and asymmetric structures, there remain gaps in the characterization of these differences in a fully three-dimensional framework. To address these limitations, this study investigates differences in the shear-relative asymmetric structure between IN and SS hurricanes using airborne Doppler radar data from a dataset covering an extended period of time. Statistics from individual cases show that IN cases are characterized by peak wavenumber-1 ascent concentrated in the upshear-left (USL) quadrant at ∼12-km height, consistent with previous studies. Moderate updrafts (2–6 m s−1) occur more frequently in the downshear eyewall for IN cases than for SS cases, likely leading to a higher frequency of moderate to strong updrafts USL above 9-km height. Composites of IN cases show that low-level outflow from the eye region associated with maximum wavenumber-1 vorticity inside the radius of maximum wind (RMW) in the downshear-left quadrant converges with low-level inflow outside the RMW, forming a stronger local secondary circulation in the downshear eyewall than SS cases. The vigorous eyewall convection of IN cases produces a net vertical mass flux increasing with height up to ∼5 km and then is almost constant up to 10 km, whereas the net vertical mass flux of SS cases decreases with height above 4 km. Strong USL upper-level ascent provides greater potential for the vertical development of the hurricane vortex, which is argued to be favorable for continued intensification in shear environments.

Local models of two-temperature accretion disc coronae – I. Structure, outflows, and energetics

ABSTRACT We use local stratified shearing-box simulations to elucidate the impact of two-temperature thermodynamics on the thermal structure of coronae in radiatively efficient accretion flows. Rather than treating the coronal plasma as an isothermal fluid, we use a simple, parametrized cooling function that models the collisional transfer of energy from the ions to the rapidly cooling leptons. Two-temperature models naturally form temperature inversions, with a hot, magnetically dominated corona surrounding a cold disc. Simulations with net vertical flux (NF) magnetic fields launch powerful magnetocentrifugal winds that would enhance accretion in a global system. The outflow rates are much better converged with increasing box height than analogous isothermal simulations, suggesting that the winds into two-temperature coronae may be sufficiently strong to evaporate a thin disc and form a radiatively inefficient accretion flow under some conditions. We find evidence for multiphase structure in the corona, with broad density and temperature distributions, and we propose criteria for the formation of a multiphase corona. The fraction of cooling in the surface layers of the disc is substantially larger for NF fields compared to zero net-flux configurations, with moderate NF simulations radiating ≳30 per cent of the flow’s total luminosity above two mid-plane scale heights. Our work shows that NF fields may efficiently power the coronae of luminous Seyfert galaxies and quasars, providing compelling motivation for future studies of the heating mechanisms available to NF fields and the interplay of radiation with two-temperature thermodynamics.

Large-Aspect-Ratio Structures in Simulated Ocean Surface Boundary Layer Turbulence under a Hurricane

AbstractA large-eddy simulation (LES) initialized and forced using observations is used to conduct a process study of ocean surface boundary layer (OSBL) turbulence in a 2-km box of ocean nominally under Hurricane Irene (2011) in 35 m of water on the New Jersey shelf. The LES captures the observed deepening, cooling, and persistent stratification of the OSBL as the storm approaches and passes. As the storm approaches, surface-intensified Ekman-layer rolls, with horizontal wavelengths of about 200 m and horizontal-to-vertical aspect and velocity magnitude ratios of about 20, dominate the kinetic energy and increase the turbulent Prandtl number from about 1 to 1.5 due partially to their restratifying vertical buoyancy flux. However, as the storm passes, these rolls are washed away in a few hours due to the rapid rotation of the wind. In the bulk OSBL, the gradient Richardson number of the mean profiles remains just above (just below) 1/4 as the storm approaches (passes). At the base of the OSBL, large-aspect-ratio Kelvin–Helmholtz billows, with Prandtl number below 1, intermittently dominate the kinetic energy. Overall, large-aspect-ratio covariance modifies the net vertical fluxes of buoyancy and momentum by about 10%, but these fluxes and the analogous diffusivity and viscosity still approximately collapse to time-independent dimensionless profiles, despite rapid changes in the forcing and the large structures. That is, the evolutions of the mean temperature and momentum profiles, which are driven by the net vertical flux convergences, mainly reflect the evolution of the wind and the initial ocean temperature profile.

One-dimensional morphodynamic model for retrogressive erosion based on a sediment entrainment theory at high flow velocity

Retrogressive erosion is a high-speed erosion process that usually occurs during the rapid release of stored water in reservoirs built on sandy rivers. Retrogressive erosion has been utilized in the practice of reservoir sedimentation control, but accurate prediction of the bed deformation process by numerical models has rarely been reported. The current study presents a one-dimensional morphodynamic model for simulating the evolution process of retrogressive erosion induced by high-velocity flows on steep slopes. The governing equations apply a Cartesian coordinate system with a vertically oriented z axis. The bed surface gradient and friction terms in the flow equations include correction factors to take account of the effects of high slope on flow movement. The net vertical sediment flux term in the sediment transport and bed deformation equations is calculated using an equation of erosion velocity. Particularly, this equation is based on an empirical relation between the sediment entrainment rate and the Shields parameter in contrast to the traditional sediment transport capacity, and the critical Shields parameter is modified by taking into account the permeability of the sediment layer and the stability of particles on a slope. The feedback of scoured sediment on the flow movement is considered by additional terms in the governing equations. Flume experiments of retrogressive erosion in literature were simulated to validate the model. The temporal variations of the longitudinal profiles of the free surface and channel bed and the sediment transport rate were well predicted. The algorithm calculating sediment entrainment in the proposed model also was validated for an experiment measuring entrainment rate from the literature. More importantly, it was found that the morphodynamic model using the sediment transport capacity equation predicts the trend of cumulative erosion contrary to the measurements, while results of the proposed model can follow a similar trend with the observed data in the retrogressive erosion process.

Submesoscales Enhance Storm‐Driven Vertical Mixing of Nutrients: Insights From a Biogeochemical Large Eddy Simulation

AbstractStorms deepen the mixed layer, entrain nutrients from the pycnocline, and fuel phytoplankton blooms in midlatitude oceans. However, the effects of oceanic submesoscale (0.1–10 km horizontal scale) physical heterogeneity on the physical‐biogeochemical response to a storm are not well understood. Here, we explore these effects numerically in a Biogeochemical Large Eddy Simulation (BLES), where a four‐component biogeochemical model is coupled with a physical model that resolves some submesoscales and some smaller turbulent scales (2 km to 2 m) in an idealized storm forcing scenario. Results are obtained via comparisons to BLES in smaller domains that do not resolve submesoscales and to one‐dimensional column simulations with the same biogeochemical model, initial conditions, and boundary conditions but parameterized turbulence and submesoscales. These comparisons show different behaviors during and shortly after the storm. During the storm, resolved submesoscales double the vertical nutrient flux. The vertical diffusivity is increased by a factor of 10 near the mixed layer base, and the mixing‐induced increase in potential energy is double. Resolved submesoscales also enhance horizontal nutrient and phytoplankton variance by a factor of 10. After the storm, resolved submesoscales maintain higher nutrient and phytoplankton variance within the mixed layer. However, submesoscales reduce net vertical nutrient fluxes by 50% and nearly shut off the turbulent diffusivity. Over the whole scenario, resolved submesoscales double storm‐driven biological production. Current parameterizations of submesoscales and turbulence fail to capture both the enhanced nutrient flux during the storm and the enhanced biological production.

Turbulent Transport of Spray Droplets in the Vicinity of Moving Surface Waves

AbstractA common technique for estimating the sea surface generation functions of spray and aerosols is the so-called flux–profile method, where fixed-height concentration measurements are used to infer fluxes at the surface by assuming a form of the concentration profile. At its simplest, this method assumes a balance between spray emission and deposition, and under these conditions the concentration profile follows a power-law shape. It is the purpose of this work to evaluate the influence of waves on this power-law theory, as well as investigate its applicability over a range of droplet sizes. Large-eddy simulations combined with Lagrangian droplet tracking are used to resolve the turbulent transport of spray droplets over moving, monochromatic waves at the lower surface. The wave age and the droplet diameter are varied, and it is found that droplets are highly influenced both by their inertia (i.e., their inability to travel exactly with fluid streamlines) and the wave-induced turbulence. Deviations of the vertical concentration profiles from the power-law theory are found at all wave ages and for large droplets. The dynamics of droplets within the wave boundary layer alter their net vertical fluxes, and as a result, estimates of surface emission based on the flux–profile method can yield significant errors. In practice, the resulting implication is that the flux–profile method may unsuitable for large droplets, and the combined effect of inertia and wave-induced turbulence is responsible for the continued spread in their surface source estimates.

Shearing-box simulations of MRI-driven turbulence in weakly collisional accretion discs.

We present a systematic shearing-box investigation of MRI-driven turbulence in a weakly collisional plasma by including the effects of an anisotropic pressure stress, i.e. anisotropic (Braginskii) viscosity. We constrain the pressure anisotropy (Δp) to lie within the stability bounds that would be otherwise imposed by kinetic microinstabilities. We explore a broad region of parameter space by considering different Reynolds numbers and magnetic-field configurations, including net vertical flux, net toroidal-vertical flux and zero net flux. Remarkably, we find that the level of turbulence and angular-momentum transport are not greatly affected by large anisotropic viscosities: the Maxwell and Reynolds stresses do not differ much from the MHD result. Angular-momentum transport in Braginskii MHD still depends strongly on isotropic dissipation, e.g., the isotropic magnetic Prandtl number, even when the anisotropic viscosity is orders of magnitude larger than the isotropic diffusivities. Braginskii viscosity nevertheless changes the flow structure, rearranging the turbulence to largely counter the parallel rate of strain from the background shear. We also show that the volume-averaged pressure anisotropy and anisotropic viscous transport decrease with increasing isotropic Reynolds number (Re); e.g., in simulations with net vertical field, the ratio of anisotropic to Maxwell stress (α A/α M) decreases from ~ 0.5 to ~ 0.1 as we move from Re ~ 103 to Re ~ 104, while 〈4πΔp/B 2〉 → 0. Anisotropic transport may thus become negligible at high Re. Anisotropic viscosity nevertheless becomes the dominant source of heating at large Re, accounting for ≳50% of the plasma heating. We conclude by briefly discussing the implications of our results for RIAFs onto black holes.

Local Simulations of MRI turbulence with Meshless Methods

Abstract The magneto-rotational instability (MRI) is one of the most important processes in sufficiently ionized astrophysical disks. Grid-based simulations, especially those using the local shearing box approximation, provide a powerful tool to study the nonlinear turbulence the MRI produces. On the other hand, meshless methods have been widely used in cosmology, galactic dynamics, and planet formation, but have not been fully deployed on the MRI problem. We present local unstratified and vertically stratified MRI simulations with two meshless MHD schemes: a recent implementation of smoothed-particle magnetohydrodynamics (SPH MHD), and a meshless finite-mass (MFM) MHD scheme with constrained gradient divergence cleaning, as implemented in the GIZMO code. Concerning variants of the SPH hydro force formulation, we consider both the “vanilla” SPH and the PSPH variant included in GIZMO. We find, as expected, that the numerical noise inherent in these schemes significantly affects turbulence. Furthermore, a high-order kernel, free of the pairing instability, is necessary. Both schemes adequately simulate MRI turbulence in unstratified shearing boxes with net vertical flux. The turbulence, however, dies out in zero-net-flux unstratified boxes, probably due to excessive numerical dissipation. In zero-net-flux vertically stratified simulations, MFM can reproduce the MRI dynamo and its characteristic butterfly diagram for several tens of orbits before ultimately decaying. In contrast, extremely strong toroidal fields, as opposed to sustained turbulence, develop in equivalent simulations using SPH MHD. The latter unphysical state is likely caused by a combination of excessive artificial viscosity, numerical resistivity, and the relatively large residual errors in the divergence of the magnetic field.

Understanding Atmospheric Anomalies Associated With Seasonal Pluvial‐Drought Processes Using Southwest China as an Example

AbstractSeasonal pluvial‐drought transition processes are unique natural phenomena. To explore possible mechanisms, we considered Southwest China (SWC) as the study region and comprehensively investigated the temporal evolution or spatial patterns of large‐scale and regional atmospheric variables with the simple method of Standardized Anomalies (SA). Some key procedures and results include the following: (1) Because regional atmospheric variables are more directly responsible for the transition processes, we investigate it in detail. The temporal evolution of net vertical integral water vapor flux (net VIWVF) across SWC, together with vertical SA‐based patterns of regional horizontal divergence (D) and vertical motion (ω), coincides well with pluvial‐drought transition processes. (2) With respect to large‐scale circulation patterns, a well‐organized Eurasian (EU) Pattern is one important feature during the pluvial‐drought transitions over SWC. (3) Based on these large‐scale and regional atmospheric anomalous features, relevant SA‐based indices were built, to explore the possibility of simulating drought development using previous pluvial anomalies. As a whole, simulated drought development only with SA‐based indices of large‐scale circulation patterns does not perform well. Further, it can be improved a lot when SA‐based indices of regional D and net VIWVF are introduced. (4) In addition, the potential drought prediction using pluvial anomalies, together with the deep understanding of physical mechanisms responsible for pluvial‐drought transitions, need to be further explored.

Surface-atmosphere exchange in a box: Space-time resolved storage and net vertical fluxes from tower-based eddy covariance

Systematic bias in eddy-covariance flux measurements are pervasive. These arise both from unmeasured terms such as advection, and sampling bias in representativeness of the footprint for both turbulent and storage fluxes. As a result, the majority of eddy-covariance towers suffer from unaccounted bias when comparing to gridded earth system models and fail to close the surface energy balance. We hypothesize that one cause for these two problems is a mismatch between mass and energy fluxes measured within a time-varying source area and the actual storage and net vertical flux over a presumed “control volume”, a novel concept derived theoretically in Metzger (this issue). Here, we practically implement this theory to estimate the true net surface-atmosphere exchange (NSAE) over such control volume, thus resolving “storage flux” and “vertical advection” issues by applying the environmental response function (ERF) technique to a virtual control volume (VCV). In this method, flux observations are related at high spatio-temporal resolution to meteorological forcings and surface properties within the estimated flux footprint, and these relationships are utilized to map the control volume explicitly in 3-D over space and time. Volume integration then allows, for the first time, retrieval of the NSAE. When ERF was applied to eddy covariance and profile observations in July and August 2014 from the AmeriFlux Park Falls WLEF tower in Wisconsin, USA, heat emission integrated over the target domain increased substantially over the tower observations by +18.2 Wm−2 (+20.6%). Storage flux contributes up to 30% of NSAE at hourly timescale. The systematic uncertainty of ERF-VCV method applied for vertical flux and storage flux is within 15% and 20%, respectively. This systematic uncertainty is effectively corrected in projections. Volume-controlled NSAE provides improvements for mapping unbiased surface-atmosphere exchange for model-data comparison, assimilation and model building at model grid scale. These advances also present a promising direction for reconciling energy balance non-closure.

Net carbon dioxide emissions from central London

Carbon dioxide (CO2) emissions from cities drive increased global atmospheric CO2 concentrations and associated climate change. Urban CO2 emissions can be evaluated using an inventory approach (summing all know emissions and sequestrations of CO2 within a defined area), and/or a micrometeorological approach (summing the exchanges of CO2 through the sides of a defined volume of air, and the change in the total stored within the volume). Generally the micrometeorological approach, with the assumption that only the net turbulent vertical flux of CO2 is significant on annual timescales, is preferred. This study evaluates that assumption with respect to storage and vertical advection of CO2, and calculates net CO2 emissions in central London using both methods for June 2012 to May 2013. Data sources include an eddy covariance system, switched horizontal and vertical CO2 profiles, traffic counts and vegetation surveys. Annual total emissions were 51.4 and 53.5kg CO2 m−2y−1 (micrometeorological and inventory methods, respectively) i.e., within 4% (1.3% with the assumption that the net vertical turbulent flux is the only non-negligible micrometeorological term). This study supports the use of vertical fluxes calculated from eddy covariance measurements at a single location to estimate total emissions from high density urban environments.

Strongly magnetized accretion discs require poloidal flux

Motivated by indirect observational evidence for strongly magnetized accretion discs around black holes, and the novel theoretical properties of such solutions, we investigate how a strong magnetization state can develop and persist. To this end, we perform local simulations of accretion discs with an initially purely toroidal magnetic field of equipartition strength. We demonstrate that discs with zero net vertical magnetic flux and realistic boundary conditions cannot sustain a strong toroidal field. However, a magnetic pressure-dominated disc can form from an initial configuration with a sufficient amount of net vertical flux and realistic boundary conditions. Our results suggest that poloidal flux is a necessary prerequisite for the sustainability of strongly magnetized accretion discs.

On the structure of turbulent gravel bed flow: Implications for sediment transport

The main objective of this study was to examine the turbulent flow field over gravel particles as a first step towards understanding sediment transport in a gravel bed river. Specifically, the vertical momentum flux in gravel bed turbulent flow was investigated with particular attention to the near-bed region. Spatial organization of vertical momentum flux was studied with stereoscopic Particle Image Velocimetry (PIV) measurements in a horizontal layer 1mm above the gravel crests. The vertical momentum flux through the water column was described with digital PIV measurements in three vertical planes. The data showed that near the gravel bed, net turbulent momentum flux spatially varies with respect to bed topography. Analysis of the vertical velocity data revealed that near the gravel particle crests, there is a significant net vertical form-induced momentum flux approximately with the same order of magnitude as the net vertical turbulent momentum flux. Above the crests, total net vertical momentum flux is positive. However, below the crests, despite noticeable positive form-induced momentum flux, total net vertical momentum flux is negative. Results of quadrant analysis show that variation of turbulent net vertical momentum flux through water column is in agreement with prevalence of upward movement of low velocity flow (known as ejection) above gravel crests and downward movement of high velocity flow (known as sweep) below gravel crests. Below gravel crests (−0.1<z/H<0.0), there is a region where the contribution of second quadrant to Reynolds shear stress is lower than fourth quadrant, while the contribution of second quadrant to vertical momentum flux is higher than fourth quadrant. This can be interpreted that ejection events in this region are strong enough to lift up fine particles but their contribution is not sufficient to move fine particles in the longitudinal direction.

Diapycnal oxygen supply to the tropical North Atlantic oxygen minimum zone

Abstract. The replenishment of consumed oxygen in the open ocean oxygen minimum zone (OMZ) off northwest Africa is accomplished by oxygen transport across and along density surfaces, i.e. diapycnal and isopycnal oxygen supply. Here the diapycnal oxygen supply is investigated using a large observational set of oxygen profiles and diapycnal mixing data from years 2008 to 2010. Diapycnal mixing is inferred from different sources: (i) a large-scale tracer release experiment, (ii) microstructure profiles, and (iii) shipboard acoustic current measurements plus density profiles. From these measurements, the average diapycnal diffusivity in the studied depth interval from 150 to 500 m is estimated to be 1 × 10−5 m2 s−1, with lower and upper 95% confidence limits of 0.8 × 10−5 m2 s−1 and 1.4 × 10−5 m2 s−1. Diapycnal diffusivity in this depth range is predominantly caused by turbulence, and shows no significant vertical gradient. Diapycnal mixing is found to contribute substantially to the oxygen supply of the OMZ. Within the OMZ core, 1.5 μmol kg−1 yr−1 of oxygen is supplied via diapycnal mixing, contributing about one-third of the total demand. This oxygen which is supplied via diapycnal mixing originates from oxygen that has been laterally supplied within the upper Central Water layer above the OMZ, and within the Antarctic Intermediate Water layer below the OMZ. Due to the existence of a separate shallow oxygen minimum at about 100 m depth throughout most of the study area, there is no net vertical oxygen flux from the surface layer into the Central Water layer. Thus all oxygen supply of the OMZ is associated with remote pathways.

LOW-MASS PLANETS IN PROTOPLANETARY DISKS WITH NET VERTICAL MAGNETIC FIELDS: THE PLANETARY WAKE AND GAP OPENING

We study wakes and gap opening by low mass planets in gaseous protoplanetary disks threaded by net vertical magnetic fields which drive magnetohydrodynamical (MHD) turbulence through the magnetorotational instabilty (MRI), using three dimensional simulations in the unstratified local shearing box approximation. The wakes, which are excited by the planets, are damped by shocks similar to the wake damping in inviscid hydrodynamic (HD) disks. Angular momentum deposition by shock damping opens gaps in both MHD turbulent disks and inviscid HD disks even for low mass planets, in contradiction to the "thermal criterion" for gap opening. To test the "viscous criterion", we compared gap properties in MRI-turbulent disks to those in viscous HD disks having the same stress, and found that the same mass planet opens a significantly deeper and wider gap in net vertical flux MHD disks than in viscous HD disks. This difference arises due to the efficient magnetic field transport into the gap region in MRI disks, leading to a larger effective \alpha within the gap. Thus, across the gap, the Maxwell stress profile is smoother than the gap density profile, and a deeper gap is needed for the Maxwell stress gradient to balance the planetary torque density. We also confirmed the large excess torque close to the planet in MHD disks, and found that long-lived density features (termed zonal flows) produced by the MRI can affect planet migration. The comparison with previous results from net toroidal flux/zero flux MHD simulations indicates that the magnetic field geometry plays an important role in the gap opening process. Overall, our results suggest that gaps can be commonly produced by low mass planets in realistic protoplanetary disks, and caution the use of a constant \alpha-viscosity to model gaps in protoplanetary disks.

The Inflow to Tropical Cyclone Humberto (2001) as Viewed with Azimuth–Height Surfaces over Three Days

Abstract The deployment of 228 global positioning system dropwindsondes (GPS sondes), over three consecutive days in Tropical Cyclone Humberto (2001), allows for the creation of azimuth–height (ϕ–z) surfaces from sea level to 3-km altitude at 0.25° and 0.5° latitude distance from the storm center. The authors estimate the radial flow along these ϕ–z surfaces to diagnose the mass flux through said surfaces as Humberto deepens from 1000 to 983 hPa from the first to the second day, then fills to 992 hPa by the third day. As the tropical cyclone (TC) intensifies the width, depth, and rate of inflow increase. The inflow remains a wavenumber-1 pattern throughout the three days. The center of the inflow rotates clockwise over this period following the expected forcing due to both the tropical cyclone motion and deep layer shear vectors. Net vertical mass flux, based on continuity within a given volume, is correlated with TC intensity only for the inner 0.25° ϕ–z surface. Slightly farther from the center, at 0.5° radial distance, the net mass flux is much larger but is not correlated with intensity. The rainbands that exist between the 0.25° and the 0.50° rings are ineffective at either creating or maintaining a warm core and lowering the surface pressure. The authors speculate that the warming associated with convective bands at larger radii is more easily eroded by the strong wind shear; convective bands nearer the center produce a more complete wind field that protects the warm core.

LOCAL STUDY OF ACCRETION DISKS WITH A STRONG VERTICAL MAGNETIC FIELD: MAGNETOROTATIONAL INSTABILITY AND DISK OUTFLOW

We perform 3D vertically-stratified local shearing-box ideal MHD simulations of the magnetorotational instability (MRI) that include a net vertical magnetic flux, which is characterized by beta_0 (ratio of gas pressure to magnetic pressure of the net vertical field at midplane). We have considered beta_0=10^2, 10^3 and 10^4 and in the first two cases the most unstable linear MRI modes are well resolved in the simulations. We find that the behavior of the MRI turbulence strongly depends on beta_0: The radial transport of angular momentum increases with net vertical flux, achieving alpha=0.08 for beta_0=10^4 and alpha>1.0 for beta_0=100, where alpha is the Shakura-Sunyaev parameter. A critical value lies at beta_0=10^3: For beta_0>10^3, the disk consists of a gas pressure dominated midplane and a magnetically dominated corona. The turbulent strength increases with net flux, and angular momentum transport is dominated by turbulent fluctuations. The magnetic dynamo that leads to cyclic flips of large-scale fields still exists, but becomes more sporadic as net flux increases. For beta_0<10^3, the entire disk becomes magnetic dominated. The turbulent strength saturates, and the magnetic dynamo is quenched. Stronger large-scale fields are generated with increasing net flux, which dominates angular momentum transport. A strong outflow is launched from the disk by the magnetocentrifugal mechanism, and the mass flux increases linearly with net vertical flux and shows sign of saturation at beta_0=10^2. However, the outflow is unlikely to be directly connected to a global wind: for beta_0>10^3, the large-scale field has no permanent bending direction due to dynamo activities, while for beta_0<10^3, the outflows from the top and bottom sides of the disk bend towards opposite directions, inconsistent with a physical disk wind geometry. Global simulations are needed to address the fate of the outflow.