Stochastic Low-frequency Variability in Three-dimensional Radiation Hydrodynamical Models of Massive Star Envelopes

Increasing main-sequence stellar luminosity with stellar mass leads to the eventual dominance of radiation pressure in stellar-envelope hydrostatic balance. As the luminosity approaches the Eddington limit, additional instabilities (beyond conventional convection) can occur. These instabilities readily manifest in the outer envelopes of OB stars, where the opacity increase associated with iron yields density and gas-pressure inversions in 1D models. Additionally, recent photometric surveys (e.g., TESS) have detected excess broadband low-frequency variability in power spectra of OB star lightcurves, called stochastic low-frequency variability (SLFV). This motivates our novel 3D Athena++ radiation hydrodynamical (RHD) simulations of two 35 M ⊙ star envelopes (the outer ≈15% of the stellar radial extent), one on the zero-age main sequence and the other in the middle of the main sequence. Both models exhibit turbulent motion far above and below the conventional iron-opacity peak convection zone (FeCZ), obliterating any “quiet” part of the near-surface region and leading to velocities at the photosphere of 10–100 km s−1, directly agreeing with spectroscopic data. Surface turbulence also produces SLFV in model lightcurves with amplitudes and power-law slopes that are strikingly similar to those of observed stars. The characteristic frequencies associated with SLFV in our models are comparable to the thermal time in the FeCZ (≈3–7 day−1). These ab initio simulations are directly validated by observations and, though more models are needed, we remain optimistic that 3D RHD models of main-sequence O-star envelopes exhibit SLFV originating from the FeCZ.

Generalized lapse rate formulas for use in entraining CAPE calculations

Common assumptions in temperature lapse rate formulas for lifted air parcels include neglecting mixing, hydrostatic balance, the removal of all condensate once it forms (pseudoadiabatic), and/or the retention of all condensate within the parcel (adiabatic). These formulas are commonly derived from the conservation of entropy, which leads to errors when non-equilibrium mixed-phase condensate is present. To evaluate these assumptions, a new general lapse rate formula is derived from an expression for energy conservation, rather than entropy conservation. This new formula incorporates mixing of the parcel with its surroundings, relaxes the hydrostatic assumption, allows for non-equilibrium mixed-phase condensate, and can be formulated for pseudoadiabatic or adiabatic ascent. The new formula is shown to exactly conserve entropy for reversible ascent. Predictions by the new formula are compared to that of older and less general formulas. The errors in previous formulas arise from the assumption of hydrostatic balance, which results in considerable warm biases due to the neglect of the energy sink from buoyancy. Predictions of ascent with entrainment using the new formula are then compared to parcel properties along trajectories in large eddy simulations. Simulated parcel properties are better predicted by the formula using a diluted analogy to adiabatic ascent, wherein condensate is diluted at the same rate as other parcel properties, than by the diluted analogy to pseudoadiabatic ascent, wherein all condensate is removed. These results suggest that CAPE should be computed with adiabatic, rather than pseudoadiabatic, parcel ascent.

The complex basal morphology and ice dynamics of Nansen Ice Shelf, East Antarctica

Ice shelf dynamics and morphology play an important role in the stability of floating bodies of ice, in turn impacting their ability to buttress upstream grounded ice. We use a combination of satellite-derived data, airborne and ground-based radar data, and oceanographic data collected at the Nansen Ice Shelf in East Antarctica to examine the spatial variations in ice shelf draft, the cause and effects of ice shelf strain rates, and the role of a suture zone driving channelization of ocean water and resulting sub-ice shelf melt and freeze-on. We also use the datasets to assess limitations that may arise from examining only a sub-set of the data, in particular the reliance on hydrostatic balance equations applied to surface digital elevation models to determine ice draft morphology. We find that the Nansen Ice Shelf has highly variable basal morphology driven primarily by the formation of basal crevasses near the onset of floating ice convergence in the suture zone. This complex morphology is reflected in the ice shelf strain rates but not in the calculated hydrostatic balance thickness, which underestimates the scale of vertical and horizontal variability at the ice shelf base. The combination of thinner ice in the channelized suture zone, enhanced melt rates near the ice shelf edge, and complex strain rates driven by ice dynamics and morphology have led to the formation of fractures within the suture zone that have resulted in large-scale calving events. Other Antarctic ice shelves may also have complex morphology, which is not reflected in the satellite data, yet may influence their stability.

Evaluating the conservation of energy variables in simulations of deep moist convection

It is often assumed in parcel theory calculations, numerical models, and cumulus parameterizations that moist static energy (MSE) is adiabatically conserved. However, the adiabatic conservation of MSE is only approximate because of the assumption of hydrostatic balance. Two alternative variables are evaluated here: MSE −IB and MSE +KE, wherein IB is the path integral of buoyancy (B) and KE is kinetic energy. Both of these variables relax the hydrostatic assumption and are more precisely conserved than MSE. This article quantifies the errors that result from assuming that the aforementioned variables are conserved in large eddy simulations (LES) of both disorganized and organized deep convection. Results show that both MSE −IB and MSE +KE better predict quantities along trajectories than MSE alone. MSE −IB is better conserved in isolated deep convection, whereas MSE −IB and MSE +KE perform comparably in squall line simulations. These results are explained by differences between the pressure perturbation behavior of squall lines and isolated convection. Errors in updraft B diagnoses are universally minimized when MSE−IB is assumed to be adiabatically conserved, but only when moisture dependencies of heat capacity and temperature dependency of latent heating are accounted for. When less accurate latent heat and heat capacity formulae were used, MSE−IB yielded poorer B predictions than MSE due to compensating errors. Our results suggest that various applications would benefit from using either MSE −IB or MSE +KE instead of MSE with properly formulated heat capacities and latent heats.

EFFECT OF THE FINAL CARBONIZATION TEMPERATURE ON THE QUALITY OF FIVE SPECIES OF CERRADO

The objective of the research was to characterize the energetic properties of the charcoal from species from the cerrado sensu stricto, as well as to evaluate the effect of the final carbonization temperature. Five species were selected for study. Ten specimens were obtained from the logs of each species, submitted to two treatments with five replicates each. The basic density of the wood was calculated by the hydrostatic balance method. The charcoal was produced by the pyrolysis process of the wood in a muffle furnace adapted to capture the pyrolignous liquor, in which two heating speeds were used with final temperatures of 500 °C and 550 °C. Through the pyrolysis process, the total gravimetric yield of the coal, yield in condensable gas, and non-condensable gas were obtained. The apparent density, the immediate chemical analysis (ICA) of the charcoal was determined and, finally, its calorific value was calculated. The YC presented acceptable values for the species Terminalia glabrescens (35.43%) and Vatairea macrocarpa (32.59%). The volatile material content of Vatairea macrocarpa (22.53%) presented satisfactory values. Fixed carbon, ash and heat content were also considered acceptable for the species Terminalia glabrescens (74.43%, 0.96% 7457.40 kcal.kg-¹), Vatairea macrocarpa (75.21% 0.55% and 7443.57 kcal.kg-¹) and Xylopia aromatica (74.27%, 0.67% and 7365.56 kcal.kg-¹), presenting high energy potential. The YC, YL and YNNC were influenced by the heating speeds as well as the content of volatile materials. The recommended final carbonization temperature is 550 °C.

A new method for the detection of incompressible turbulence as a deviation from the hydrostatic balance assumption

<p>This study aims at introducing a simple and physically consistent method for identification and analysis of turbulent layers in the free atmosphere that can supplement the traditional methods (Richardson number criterion, Thorpe scale). The method is based on differences between the observed and hydrostatically derived (with floating level of initialization) pressure. In the paper we derive the method analytically from the Navier Stokes equations and propose a methodology how to isolate information on turbulence from an internal gravity wave and atmospheric structure signal in the pressure differences. Finally we apply the methodology on high vertical-resolution radiosonde data to demonstrate the utility of the novel method by contrasting the results with traditional diagnostics. </p>

Regularity “in Large” for the 3D Salmon’s Planetary Geostrophic Model of Ocean Dynamics

It is well known, by now, that the three-dimensional non-viscous planetary geostrophic model, with vertical hydrostatic balance and horizontal Rayleigh friction/damping, coupled to the heat diffusion and transport, is mathematically ill-posed. This is because the no-normal flow physical boundary condition implicitly produces an additional boundary condition for the temperature at the lateral boundary. This additional boundary condition is different, because of the Coriolis forcing term, than the no-heat-flux physical boundary condition. Consequently, the second order parabolic heat equation is over-determined with two different boundary conditions. In a previous work we proposed one remedy to this problem by introducing a fourth-order artificial hyper-diffusion to the heat transport equation and proved global regularity for the proposed model. A shortcoming of this higher-oder diffusion is the loss of the maximum/minimum principle for the heat equation. Another remedy for this problem was suggested by R. Salmon by introducing an additional Rayleigh-like friction/damping term for the vertical component of the velocity in the hydrostatic balance equation. In this paper we prove the global, for all time and all initial data, well-posedness of strong solutions to the three-dimensional Salmon’s planetary geostrophic model of ocean dynamics. That is, we show global existence, uniqueness and continuous dependence of the strong solutions on initial data for this model. Unlike the 3D viscous PG model, we are still unable to show the uniqueness of the weak solution. Notably, we also demonstrate in what sense the additional damping term, suggested by Salmon, annihilate the ill-posedness in the original system; consequently, it can be viewed as “regularizing” term that can possibly be used to regularize other related systems.

Magnetic inhibition of convection in O-star envelopes

ABSTRACT It has been suggested that the absence of macroturbulence in the atmosphere of NGC 1624−2 is due its strong magnetic field (the strongest known for a massive O star) suppressing convection in its outer layers, removing the mechanism thought responsible for the observed macroturbulence in stars with lower field strengths. Here, we develop and apply a criterion for a uniform magnetic field to suppress convection in stellar envelopes in which radiation pressure is a significant contributor to hydrostatic balance. We find upper mass limits of ∼55 and ∼30 M⊙ for magnetic suppression to be possible in zero-age main-sequence and terminal-age main-sequence stars, respectively. For evolved stars, magnetic suppression of convection can significantly alter the stars’ evolution. For NGC 1624−2, we find that a polar dipole strength of 16.5 ± 5.9 kG is required to suppress convection, in good agreement with the value ∼20 kG measured by spectropolarimetry.

A Numerical Method for Calculation of Ship-Ship Hydrodynamics Interaction in Shallow Water Accounting for Sinkage and Trim

Sinkage and trim, which often occur to ships moving in shallow water, do not only have an effect on the ship-ship hydrodynamic interaction forces, but also increase the risk of grounding. An algorithm based on the potential theory has been devised for real-time simulation of the hydrodynamic interaction between two ships in shallow water accounting for sinkage and trim. The shallow water condition is modeled using the mirror image method; while the sinkage and trim are solved iteratively based on the principle of hydrostatic balance, where a mesh trimming procedure is performed when the waterline is changed. Simulations are performed with and without accounting for the sinkage and trim, and comparison with experimental results shows a fair agreement.