Hydrostatic Balance between Pressure and Gravity

2021 ◽  
pp. 101-106
Keyword(s):  
Hydrostatic Balance

scholarly journals The Formation of a Cavity in a 3D Flux Rope

2013 ◽  
Vol 8 (S300) ◽  
pp. 147-150 ◽  
Author(s):  
Donald Schmit ◽  
Sarah Gibson
Keyword(s):  
Ad Hoc ◽  
Numerical Models ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Flux Rope ◽  
Multiple Structures ◽  
Field Lines ◽  
Hydrostatic Balance ◽  
Distinct Field ◽  
Three Dimensional Space

AbstractThere are currently no three dimensional numerical models which describe the magnetic and energetic formation of prominences self-consistently. Consequently, there has not been significant progress made in understanding the connection between the dense prominence plasma and the coronal cavity. We have taken an ad-hoc approach to understanding the energetic implications of the magnetic models of prominence structure. We extract one dimensional magnetic field lines from a 3D MHD model of a flux rope and solve for hydrostatic balance along these field lines incorporating field-aligned thermal conduction, uniform heating, and radiative losses. The 1D hydrostatic solutions for density and temperature are then mapped back into three dimensional space, which allows us to consider the projection of multiple structures. We find that the 3D flux rope is composed of several distinct field line types. A majority of the flux rope interior field lines are twisted but not dipped. These field lines are density-reduced relative to unsheared arcade field lines. We suggest the cavity may form along these short interior field lines which are surrounded by a sheath of dipped field lines. This geometric arrangement would create a cavity on top of a prominence, but the two structures would not share field lines or plasma.

How is the Balance of a Forecast Ensemble Affected by Adaptive and Nonadaptive Localization Schemes?

2015 ◽  
Vol 143 (9) ◽  
pp. 3680-3699 ◽  
Author(s):  
Ross N. Bannister
Keyword(s):  
Forecast Error ◽  
Covariance Matrices ◽  
Error Statistics ◽  
Error Covariance ◽  
Localization Scheme ◽  
Adaptive Schemes ◽  
Convective Scale ◽  
Free Parameters ◽  
Hydrostatic Balance ◽  
First Time

Abstract This paper investigates the effect on balance of a number of Schur product–type localization schemes that have been designed with the primary function of reducing spurious far-field correlations in forecast error statistics. The localization schemes studied comprise a nonadaptive scheme (where the moderation matrix is decomposed in a spectral basis), and two adaptive schemes: a simplified version of Smoothed Ensemble Correlations Raised to a Power (SENCORP) and Ensemble Correlations Raised to a Power (ECO-RAP). The paper shows, the author believes for the first time, how the degree of balance (geostrophic and hydrostatic) implied by the error covariance matrices localized by these schemes can be diagnosed. Here it is considered that an effective localization scheme is one that reduces spurious correlations adequately, but also minimizes disruption of balance (where the “correct” degree of balance or imbalance is assumed to be possessed by the unlocalized ensemble). By varying free parameters that describe each scheme (e.g., the degree of truncation in the schemes that use the spectral basis, the “order” of each scheme, and the degree of ensemble smoothing), it is found that a particular configuration of the ECO-RAP scheme is best suited to the convective-scale system studied. According to the diagnostics this ECO-RAP configuration still weakens geostrophic and hydrostatic balance, but overall this is less so than for other schemes.

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

2021 ◽  
Author(s):  
Christine F. Dow ◽  
Derek Mueller ◽  
Peter Wray ◽  
Drew Friedrichs ◽  
Alexander L. Forrest ◽  
...  
Keyword(s):  
Large Scale ◽  
Radar Data ◽  
Suture Zone ◽  
East Antarctica ◽  
Strain Rates ◽  
Floating Bodies ◽  
Ice Shelf ◽  
Ice Dynamics ◽  
Complex Morphology ◽  
Hydrostatic Balance

Abstract. 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

2021 ◽  
Author(s):  
John M. Peters ◽  
Daniel R. Chavas
Keyword(s):  
Heat Capacity ◽  
Numerical Models ◽  
Deep Convection ◽  
Squall Line ◽  
Moist Convection ◽  
Conservation Of Energy ◽  
Deep Moist Convection ◽  
Static Energy ◽  
Hydrostatic Balance ◽  
Latent Heats

AbstractIt 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.

Generalized lapse rate formulas for use in entraining CAPE calculations

2021 ◽  
Author(s):  
John M. Peters ◽  
Jake P. Mulholland ◽  
Daniel R. Chavas
Keyword(s):  
Large Eddy Simulations ◽  
Mixed Phase ◽  
Lapse Rate ◽  
Temperature Lapse Rate ◽  
Large Eddy ◽  
Energy Sink ◽  
Entropy Conservation ◽  
Hydrostatic Balance ◽  
New Formula ◽  
Non Equilibrium

AbstractCommon 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 hydrostatic balance revisited

1996 ◽  
Vol 34 (8) ◽  
pp. 500-500 ◽  
Author(s):  
Iain MacInnes ◽  
Rory McPherson
Keyword(s):  
Hydrostatic Balance

scholarly journals Thawing the frozen-in approximation: implications for self-gravity in deeply plunging tidal disruption events

2019 ◽  
Vol 485 (1) ◽  
pp. L146-L150 ◽  
Author(s):  
Elad Steinberg ◽  
Eric R Coughlin ◽  
Nicholas C Stone ◽  
Brian D Metzger
Keyword(s):  
Free Fall ◽  
Tidal Disruption ◽  
Massive Black Hole ◽  
High Penetration ◽  
Order Of Magnitude ◽  
Sphere Radius ◽  
Hydrodynamical Simulations ◽  
Self Gravity ◽  
Hydrostatic Balance ◽  
Mesh Technique

ABSTRACT The tidal destruction of a star by a massive black hole, known as a tidal disruption event (TDE), is commonly modelled using the ‘frozen-in’ approximation. Under this approximation, the star maintains exact hydrostatic balance prior to entering the tidal sphere (radius rt), after which point its internal pressure and self-gravity become instantaneously negligible and the debris undergoes ballistic free fall. We present a suite of hydrodynamical simulations of TDEs with high penetration factors β ≡ rt/rp = 5−7, where rp is the pericentre of the stellar centre of mass, calculated using a Voronoi-based moving-mesh technique. We show that basic assumptions of the frozen-in model, such as the neglect of self-gravity inside rt, are violated. Indeed, roughly equal fractions of the final energy spread accumulate exiting and entering the tidal sphere, though the frozen-in prediction is correct at the order-of-magnitude level. We also show that an $\mathcal {O}(1)$ fraction of the debris mass remains transversely confined by self-gravity even for large β which has implications for the radio emission from the unbound debris and, potentially, for the circularization efficiency of the bound streams.

A note on the adjustment to hydrostatic balance

Tellus ◽  
1982 ◽  
Vol 34 (1) ◽  
pp. 50-54 ◽  
Author(s):  
J. P. GUIRAUD ◽  
R. Kh. ZEYTOUNIAN
Keyword(s):  
Hydrostatic Balance
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