scholarly journals Eigenvectors, Circulation, and Linear Instabilities for Planetary Science in 3 Dimensions (ECLIPS3D)

2019 ◽  
Vol 631 ◽  
pp. A36 ◽  
Author(s):  
F. Debras ◽  
N. Mayne ◽  
I. Baraffe ◽  
T. Goffrey ◽  
J. Thuburn
Keyword(s):  
Steady State ◽  
Energy Equation ◽  
Planetary Science ◽  
Staggered Grid ◽  
A Posteriori ◽  
Linear Processes ◽  
Hot Jupiters ◽  
Global Circulation Models ◽  
Simplifying Assumptions ◽  
Steady Solutions

Context. The study of linear waves and instabilities is necessary to understand the physical evolution of an atmosphere, and can provide physical interpretation of the complex flows found in simulations performed using global circulation models (GCMs). In particular, the acceleration of superrotating flow at the equator of hot Jupiters has mostly been studied under several simplifying assumptions, the relaxing of which may impact final results. Aims. We develop and benchmark a publicly available algorithm to identify the eigenmodes of an atmosphere around any initial steady state. We also solve for linear steady states indicated to be essential in existing theories of the acceleration of hot Jupiter superrotation. Methods. We linearise the hydrodynamical equations of a planetary atmosphere in a steady state with arbitrary velocities and thermal profile. We then discretise the linearised equations on an appropriate staggered grid, and solve for eigenvectors and linear steady solutions with the use of a parallel library for linear algebra: ScaLAPACK. We also implement a posteriori calculation of an energy equation in order to obtain more information on the underlying physics of the mode. Results. Our code is tested using classical wave and instability test cases in multiple geometries (2D, 3D, two-layer equivalent depth). The steady linear circulation calculations also reproduce expected results for the atmosphere of hot Jupiters. We finally show the robustness of our energy equation, and its power to obtain physical insight into the modes. Conclusions. We developed and tested a code for the study of linear processes in planetary atmospheres with an arbitrary steady state. The calculation of an a posteriori energy equation provides both increased robustness and physical meaning to the obtained eigenmodes. This code can be applied to various problems, and notably used to further study the initial spin up of superrotation of GCM simulations of hot Jupiters.

Selection of one-dimensional sedimentation: models for on-line use

1995 ◽  
Vol 31 (2) ◽  
pp. 193-204 ◽  
Author(s):  
Koen Grijspeerdt ◽  
Peter Vanrolleghem ◽  
Willy Verstraete
Keyword(s):  
Steady State ◽  
Selection Criteria ◽  
Data Sets ◽  
Concentration Profiles ◽  
A Posteriori ◽  
One Dimensional ◽  
On Line ◽  
Dynamic Concentration ◽  
Selection Of ◽  
Modelling Task

A comparative study of several recently proposed one-dimensional sedimentation models has been made. This has been achieved by fitting these models to steady-state and dynamic concentration profiles obtained in a down-scaled secondary decanter. The models were evaluated with several a posteriori model selection criteria. Since the purpose of the modelling task is to do on-line simulations, the calculation time was used as one of the selection criteria. Finally, the practical identifiability of the models for the available data sets was also investigated. It could be concluded that the model of Takács et al. (1991) gave the most reliable results.

An Assessment of the Value of Theory in Predicting Gas-Bearing Performance

1961 ◽  
Vol 83 (2) ◽  
pp. 195-200 ◽  
Author(s):  
S. Cooper
Keyword(s):  
Steady State ◽  
Slip Velocity ◽  
Reynolds Equation ◽  
Energy Equation ◽  
Experimental Methods ◽  
Experimental Results ◽  
Theoretical Investigations ◽  
Gas Bearing ◽  
Theoretical Results

The object of the paper is to indicate the value of theoretical investigations of hydrodynamic finite bearings under steady-state conditions. Methods of solution of Reynolds equation by both desk and digital computing, and methods of stabilizing the processes of solution, are described. The nondimensional data available from the solutions are stated. The outcome of an attempted solution of the energy equation is discussed. A comparison between some theoretical and experimental results is shown. Experimental methods employed and some difficulties encountered are discussed. Some theoretical results are given to indicate the effects of the inclusion of slip velocity, stabilizing slots, and a simple case of whirl.

The Elastic-Plastic Analysis of Tubes—IV: Thermal Ratchetting

1992 ◽  
Vol 114 (2) ◽  
pp. 236-245 ◽  
Author(s):  
W. Jiang
Keyword(s):  
Steady State ◽  
Plastic Strain ◽  
Centrifugal Force ◽  
Kinematic Hardening ◽  
Elastic Plastic ◽  
External Pressures ◽  
Plastic Analysis ◽  
Steady Solutions ◽  
Number Of Cycles

This paper continues the investigation of the shakedown behavior of tubes subjected to cyclic centrifugal force and temperature, and sustained internal and external pressures. It is found that when ratchetting occurs, the plastic strain builds up with each cycle, but finally reaches a steady state after a large number of cycles for kinematic hardening materials. The steady solutions for three kinds of ratchetting behavior are found and given in this paper.

An exact electrostatic shock solution for a collisionless plasma

1970 ◽  
Vol 4 (3) ◽  
pp. 549-561 ◽  
Author(s):  
A. Smith
Keyword(s):  
Exact Solution ◽  
Steady State ◽  
Energy Equation ◽  
Collisionless Plasma ◽  
Debye Length ◽  
Elementary Functions ◽  
One Dimensional ◽  
Particle Distributions ◽  
Vlasov Equations ◽  
Shock Solution

An exact solution to the steady-state Vlasov equations and Poisson's equation for a one-dimensional plasma of electrons and protons is obtained by splitting the energy equation into two integral equations for the trapped particle distributions. This solution has the properties that the number densities and electric potential are moiiotonic functions of space and do most of their changing over a distance of the order of the Debye length for electrons. The distributions are everywhere differentiable in phase space and are Maxwellian-like, and in terms of elementary functions. Evidence is given to support stability for restricted shock strengths.

scholarly journals On incorporating diffusion and viscosity concepts into compartmental models for analysing faecal marker excretion patterns in ruminants

1993 ◽  
Vol 70 (1) ◽  
pp. 369-378 ◽  
Author(s):  
J. France ◽  
J. H. M. Thornley ◽  
R. C. Siddons ◽  
M. S. Dhanoa
Keyword(s):  
Steady State ◽  
Streamline Flow ◽  
Longitudinal Diffusion ◽  
Basic Scheme ◽  
First Order ◽  
First Order Kinetics ◽  
Simplifying Assumptions ◽  
Mathematical Equations ◽  
Future Work ◽  
The Impact

Deterministic mathematical equations are derived to describe the pattern of marker excretion in the faeces of ruminants under steady-state conditions when diffusion and viscosity concepts are introduced into a simple two-compartment scheme of the gastrointestinal tract. The basic scheme comprises a pure-mixing pool obeying first-order kinetics and a second compartment exhibiting streamline flow. Introduction of a velocity gradient, longitudinal diffusion or both into the second compartment, even with various simplifying assumptions, yields analytically insoluble equations. The impact of these mechanisms is to be investigated numerically rather than analytically in future work.

Wind of Change: Atmospheric wind retrieval and its implications for hot Jupiters

2020 ◽  
Author(s):  
Julia Seidel ◽  
David Ehrenreich ◽  
Vincent Bourrier ◽  
Lorenzo Pino ◽  
Aurelien Wyttenbach ◽  
...  
Keyword(s):  
High Spectral Resolution ◽  
Wind Retrieval ◽  
Hot Jupiters ◽  
Global Circulation ◽  
Hot Gas ◽  
Global Circulation Models ◽  
Pressure Profiles ◽  
Profile Fitting ◽  
Wide Range ◽  
Hot Jupiter

<p><span>The sodium doublet is one of the most powerful probes of exoplanet atmospheric properties when observed in transmission spectroscopy during transits. Recent high-spectral resolution observations of the sodium doublet in hot gas giants allowed us to resolve the line shape, opening the way for extracting atmospheric properties using line-profile fitting. </span></p><p><span>Using the MERC code (Seidel et al. 2020a), a retrieval tool to determine temperature-pressure profiles and high-altitude winds in exoplanet thermospheres, we have studied the curiously broadened sodium signatures of various hot Jupiters. We have updated the MERC code to a quasi 3D treatment of the atmosphere (Seidel et al. 2020c, in prep.) and analysed three hot Jupiters, spanning a wide range of this class of exoplanets (see figure). Using the sodium signature of three examples - WASP-76b (a highly irradiated ultra-hot Jupiter, Seidel et al. 2019), KELT-11b (a puffy hot Jupiter, Mounzer et al. 2020, in prep.), and lastly HD189733b (one of the most studied hot Jupiters to date, Wyttenbach et al. 2015) - we explore possible trends in the atmospheric structure of hot Jupiters.</span></p><p><span>We will first introduce the new quasi 3D retrieval of MERC, and proceed to show that high-velocity winds in the thermosphere are one possible explanation of the broadened sodium features seen in hot Jupiters. We plan to highlight various caveats and present likely origin scenarios for the observed wind patterns. We will then put these results in the context of past studies using global circulation models (GCMs) on hot Jupiters.</span></p><p><img src="https://contentmanager.copernicus.org/fileStorageProxy.php?f=gnp.2223b4ea02fe54080292951/sdaolpUECMynit/0202CSPE&app=m&a=0&c=4c9f1f886978a365f195c38f0ef4783d&ct=x&pn=gnp.elif" alt=""></p>

scholarly journals Acceleration of superrotation in simulated hot Jupiter atmospheres

2019 ◽  
Vol 633 ◽  
pp. A2 ◽  
Author(s):  
F. Debras ◽  
N. Mayne ◽  
I. Baraffe ◽  
E. Jaupart ◽  
P. Mourier ◽  
...  
Keyword(s):  
Steady State ◽  
Vertical Component ◽  
Nonlinear Effects ◽  
Linear Wave ◽  
Initial Development ◽  
Hot Jupiters ◽  
Propagating Waves ◽  
Slow Evolution ◽  
Physical Phenomena ◽  
Hot Jupiter

Context. Atmospheric superrotating flows at the equator are a nearly ubiquitous result when conducting simulations of hot Jupiters. One theory explaining how this zonally-coherent flow reaches equilibrium has already been developed in the literature. This understanding, however, relies on the existence of either an initial superrotating flow or a sheared flow, coupled with a slow evolution that permits a linear steady state to be reached. Aims. A consistent physical understanding of superrotation is needed for arbitrary drag and radiative timescales, along with the relevance of taking linear steady states into account, needs to be assessed. Methods. We obtained an analytical expression for the structure, frequency, and decay rate of propagating waves in hot Jupiter atmospheres around a state at rest in the 2D shallow-water β-plane limit. We solved this expression numerically and confirmed the robustness of our results with a 3D linear wave algorithm. We then compared it with 3D simulations of hot Jupiter atmospheres and studied the nonlinear momentum fluxes. Results. We show that under strong day-night heating, the dynamics do not transit through a linear steady state when starting from an initial atmosphere in solid body rotation. We further demonstrate that nonlinear effects favor the initial spin-up of superrotation and that acceleration due to the vertical component of the eddy-momentum flux is critical to the initial development of superrotation. Conclusions. We describe the initial phases of the acceleration of superrotation, including the consideration of differing radiative and drag timescales, and we conclude that eddy-momentum-driven superrotating equatorial jets are robust, physical phenomena in simulations of hot Jupiter atmospheres.

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