scholarly journals Scale-free convection theory

2015 ◽  
Vol 11 (A29B) ◽  
pp. 747-747
Author(s):  
Stefano Pasetto ◽  
Cesare Chiosi ◽  
Mark Cropper ◽  
Eva K. Grebel
Keyword(s):  
Surrounding Medium ◽  
Stellar Structure ◽  
Time Dependent ◽  
Length Scale ◽  
The Sun ◽  
Mixing Length ◽  
Local Pressure ◽  
Scale Free ◽  
Non Local ◽  
Stellar Models

AbstractConvection is one of the fundamental mechanisms to transport energy, e.g., in planetology, oceanography, as well as in astrophysics where stellar structure is customarily described by the mixing-length theory, which makes use of the mixing-length scale parameter to express the convective flux, velocity, and temperature gradients of the convective elements and stellar medium. The mixing-length scale is taken to be proportional to the local pressure scale height of the star, and the proportionality factor (the mixing-length parameter) must be determined by comparing the stellar models to some calibrator, usually the Sun. No strong arguments exist to claim that the mixing-length parameter is the same in all stars and all evolutionary phases. Because of this, all stellar models in the literature are hampered by this basic uncertainty. In a recent paper (Pasetto et al. 2014) we presented the first fully analytical scale-free theory of convection that does not require the mixing-length parameter. Our self-consistent analytical formulation of convection determines all the properties of convection as a function of the physical behaviour of the convective elements themselves and the surrounding medium (be it a star, an ocean, or a primordial planet). The new theory of convection is formulated starting from a conventional solution of the Navier-Stokes/Euler equations, i.e. the Bernoulli equation for a perfect fluid, but expressed in a non-inertial reference frame co-moving with the convective elements. In our formalism, the motion of convective cells inside convective-unstable layers is fully determined by a new system of equations for convection in a non-local and time dependent formalism. We obtained an analytical, non-local, time-dependent solution for the convective energy transport that does not depend on any free parameter. The predictions of the new theory in astrophysical environment are compared with those from the standard mixing-length paradigm in stars with exceptional results for atmosphere models of the Sun and all the stars in the Hertzsprung-Russell diagram.

scholarly journals New Theory of Stellar Convection without the mixing-length parameter: new stellar atmosphere models

2015 ◽  
Vol 11 (A29B) ◽  
pp. 154-155
Author(s):  
Stefano Pasetto ◽  
Cesare Chiosi ◽  
Mark Cropper
Keyword(s):  
Energy Transport ◽  
Surrounding Medium ◽  
Time Dependent ◽  
Length Scale ◽  
The Sun ◽  
Mixing Length ◽  
Local Pressure ◽  
Stellar Convection ◽  
Non Local ◽  
Stellar Models

AbstractStellar convection is customarily described by the mixing-length theory, which makes use of the mixing-length scale to express the convective flux, velocity, and temperature gradients of the convective elements and stellar medium. The mixing-length scale is taken to be proportional to the local pressure scale height, and the proportionality factor (the mixing-length parameter) must be determined by comparing the stellar models to some calibrator, usually the Sun. No strong arguments exist to suggest that the mixing-length parameter is the same in all stars and all evolutionary phases. Because of this, all stellar models in the literature are hampered by this basic uncertainty.In a recent paper (Pasettoet al.2014) we presented a new theory that does not require the mixing length parameter. Our self-consistent analytical formulation of stellar convection determines all the properties of stellar convection as a function of the physical behavior of the convective elements themselves and the surrounding medium. The new theory of stellar convection is formulated starting from a conventional solution of the Navier-Stokes/Euler equations, i.e. the Bernoulli equation for a perfect fluid, but expressed in a non-inertial reference frame co-moving with the convective elements. In our formalism, the motion of stellar convective cells inside convective-unstable layers is fully determined by a new system of equations for convection in a non-local and time-dependent formalism.We obtained an analytical, non-local, time-dependent solution for the convective energy transport that does not depend on any free parameter. The predictions of the new theory are compared with those from the standard mixing-length paradigm with positive results for atmosphere models of the Sun and all the stars in the Hertzsprung-Russell diagram.

scholarly journals Theory of stellar convection: removing the mixing-length parameter

2015 ◽  
Vol 11 (A29B) ◽  
pp. 608-613
Author(s):  
Stefano Pasetto ◽  
Cesare Chiosi ◽  
Mark Cropper ◽  
Eva K. Grebel
Keyword(s):  
Energy Transport ◽  
Surrounding Medium ◽  
Time Dependent ◽  
Length Scale ◽  
The Sun ◽  
Mixing Length ◽  
Local Pressure ◽  
Stellar Convection ◽  
Non Local ◽  
Stellar Models

AbstractStellar convection is customarily described by the mixing-length theory, which makes use of the mixing-length scale to express the convective flux, velocity, and temperature gradients of the convective elements and stellar medium. The mixing-length scale is taken to be proportional to the local pressure scale height, and the proportionality factor (the mixing-length parameter) must be determined by comparing the stellar models to some calibrator, usually the Sun. No strong arguments exist to suggest that the mixing-length parameter is the same in all stars and all evolutionary phases. Because of this, all stellar models in the literature are hampered by this basic uncertainty.In a recent paper (Pasettoet al.2014) we presented a new theory that does not require the mixing length parameter. Our self-consistent analytical formulation of stellar convection determines all the properties of stellar convection as a function of the physical behaviour of the convective elements themselves and the surrounding medium. The new theory of stellar convection is formulated starting from a conventional solution of the Navier-Stokes/Euler equations, i.e. the Bernoulli equation for a perfect fluid, but expressed in a non-inertial reference frame co-moving with the convective elements. In our formalism, the motion of stellar convective cells inside convective-unstable layers is fully determined by a new system of equations for convection in a non-local and time-dependent formalism.We obtained an analytical, non-local, time-dependent solution for the convective energy transport that does not depend on any free parameter. The predictions of the new theory are compared with those from the standard mixing-length paradigm with positive results for atmosphere models of the Sun and all the stars in the Hertzsprung-Russell diagram.

scholarly journals Inclusion of a time-dependent, non-local convection theory in a stellar evolution code

2006 ◽  
Vol 2 (S239) ◽  
pp. 314-316 ◽  
Author(s):  
Achim Weiss ◽  
Martin Flaskamp
Keyword(s):  
Velocity Field ◽  
Local Time ◽  
Stellar Evolution ◽  
Time Dependent ◽  
Test Cases ◽  
The Sun ◽  
Specific Test ◽  
Non Local ◽  
Convective Boundaries

AbstractThe non-local, time-dependent convection theory of Kuhfuß (1986) in both its one- and three-equation form has been implemented in the Garching stellar evolution code. We present details of the implementation and the difficulties encountered. Specific test cases have been calculated, among them a 5 M⊙ star and the Sun. These cases point out deficits of the theory. In particular, the assumption of an isotropic velocity field leads to too extensive overshooting and has to be modified at convective boundaries. Some encouraging aspects are indicated as well.

scholarly journals Recent Advances in Convection Theory and Modelling

1995 ◽  
Vol 10 ◽  
pp. 433-434
Author(s):  
S. Sofia
Keyword(s):  
Stellar Evolution ◽  
Numerical Models ◽  
Spatial Scales ◽  
Stellar Structure ◽  
Wave Number ◽  
The Sun ◽  
Mixing Length ◽  
Number Range ◽  
Wide Range ◽  
Non Locality

This Joint Discussion (Number 13), took place on August 22, 1994 at The Hague, in connection with the XXII General Assembly of the IAU. At the one-day long meeting, there were presentations by 15 invited speakers and 15 posters.The Joint Discussions had been organized in response to the considerable progress made in this field of research during the previous decade. Although it had long been known that the prevailing mixing length theory (MLT), used extensively and very successfully in Astrophysics for several decades had become needlessly limited, until recently it was impractical to contemplate more realistic approaches. The situation has changed recently as a consequence of advances in numerical techniques and computational capabilities, and thus JD 13 was organized to discuss the advances, and perhaps to understand the strengths and weaknesses of each approach.There were two presentations which addressed the main issues in convection theory (E. Schatzman), and the astrophysical implications (P. Demarque). Several talks covered current numerical codes, which included deep convection in a rotating reference frame (K. Chan), convection in the presence of magnetic fields (P. Fox), and shallower solar convection simulations on a wide range of spatial scales (A. Nordlund). Although these approaches have enriched (and are continuing to enrich) our understanding of the physics of convective fluids, they are much too detailed (both in space and in time) to be integrated in the study of stellar evolution. To overcome this shortcoming, S. Sofia described a technique developed together with Lydon and Fox to use relationships between dynamical and thermodynamic properties of convective flows derived in numerical models to be applied in stellar structure and evolution codes by performing small modifications of the standard MLT formalism. The advantage of this technique is that it does not contain a mixing length or any other arbitrary parameter, and it was used successfully in modeling the evolution of the Sun and other solar analogues. V. Canuto also presented a formulation of convection both amenable to be used in stellar evolution studies, and not requiring an arbitrary mixing length-like parameter. His formulation uses the Reynolds stress method, which has the advantage of modeling the full eddy spectrum of the turbulence, rather than the narrow wave number range for energy containing eddies assumed in the MLT. Additionally, this technique can address the problems of non-locality and overshoot. M. Stix also addressed non-locality and overshoot by presenting results of a non-local mixing length model of the Sun derived from the Shaviv and Salpeter model.

scholarly journals Overcoming the structural surface effect with a realistic treatment of turbulent convection in 1D stellar models

2019 ◽  
Vol 488 (3) ◽  
pp. 3463-3473 ◽  
Author(s):  
Andreas Christ Sølvsten Jørgensen ◽  
Achim Weiss
Keyword(s):  
Surface Effect ◽  
Stellar Structure ◽  
The Sun ◽  
Time Step ◽  
Simplifying Assumptions ◽  
Structural Surface ◽  
Stellar Models ◽  
Stellar Oscillation ◽  
Mixing Length Theory ◽  
Oscillation Frequencies

Abstract State-of-the-art 1D stellar evolution codes rely on simplifying assumptions, such as mixing length theory, in order to describe superadiabatic convection. As a result, 1D stellar structure models do not correctly recover the surface layers of the Sun and other stars with convective envelopes. We present a method that overcomes this structural drawback by employing 3D hydrodynamic simulations of stellar envelopes: at every time-step of the evolution interpolated 3D envelopes are appended to the 1D structure and are used to supply realistic boundary conditions for the stellar interior. In contrast to previous attempts, our method includes mean 3D turbulent pressure. We apply our method to model the present Sun. The structural shortcomings of standard stellar models lead to systematic errors in the stellar oscillation frequencies inferred from the model. We show that our method fully corrects for this error. Furthermore, we show that our realistic treatment of superadiabatic convection alters the predicted evolution of the Sun. Our results hence have important implications for the characterization of stars. This has ramifications for neighbouring fields, such as exoplanet research and galactic archaeology, for which accurate stellar models play a key role.

scholarly journals Turbulence Characteristics Across a Range of Idealized Urban Canopy Geometries

2021 ◽  
Author(s):  
Lewis P. Blunn ◽  
Omduth Coceal ◽  
Negin Nazarian ◽  
Janet F. Barlow ◽  
Robert S. Plant ◽  
...  
Keyword(s):  
Momentum Flux ◽  
Mixing Layer ◽  
Urban Canopy ◽  
Turbulence Closure ◽  
Length Scale ◽  
Good Representation ◽  
Mixing Length ◽  
Turbulence Characteristics ◽  
First Order ◽  
Turbulent Momentum

AbstractGood representation of turbulence in urban canopy models is necessary for accurate prediction of momentum and scalar distribution in and above urban canopies. To develop and improve turbulence closure schemes for one-dimensional multi-layer urban canopy models, turbulence characteristics are investigated here by analyzing existing large-eddy simulation and direct numerical simulation data. A range of geometries and flow regimes are analyzed that span packing densities of 0.0625 to 0.44, different building array configurations (cubes and cuboids, aligned and staggered arrays, and variable building height), and different incident wind directions ($$0^\circ $$ 0 ∘ and $$45^\circ $$ 45 ∘ with regards to the building face). Momentum mixing-length profiles share similar characteristics across the range of geometries, making a first-order momentum mixing-length turbulence closure a promising approach. In vegetation canopies turbulence is dominated by mixing-layer eddies of a scale determined by the canopy-top shear length scale. No relationship was found between the depth-averaged momentum mixing length within the canopy and the canopy-top shear length scale in the present study. By careful specification of the intrinsic averaging operator in the canopy, an often-overlooked term that accounts for changes in plan area density with height is included in a first-order momentum mixing-length turbulence closure model. For an array of variable-height buildings, its omission leads to velocity overestimation of up to $$17\%$$ 17 % . Additionally, we observe that the von Kármán coefficient varies between 0.20 and 0.51 across simulations, which is the first time such a range of values has been documented. When driving flow is oblique to the building faces, the ratio of dispersive to turbulent momentum flux is larger than unity in the lower half of the canopy, and wake production becomes significant compared to shear production of turbulent momentum flux. It is probable that dispersive momentum fluxes are more significant than previously thought in real urban settings, where the wind direction is almost always oblique.

scholarly journals Solar structure and evolution

2021 ◽  
Vol 18 (1) ◽  
Author(s):  
Jørgen Christensen-Dalsgaard
Keyword(s):  
Solar Surface ◽  
Solar Neutrinos ◽  
Solar Interior ◽  
Stellar Structure ◽  
The Sun ◽  
Physical Processes ◽  
Solar Evolution ◽  
Internal Properties ◽  
Atmospheric Phenomena

AbstractThe Sun provides a critical benchmark for the general study of stellar structure and evolution. Also, knowledge about the internal properties of the Sun is important for the understanding of solar atmospheric phenomena, including the solar magnetic cycle. Here I provide a brief overview of the theory of stellar structure and evolution, including the physical processes and parameters that are involved. This is followed by a discussion of solar evolution, extending from the birth to the latest stages. As a background for the interpretation of observations related to the solar interior I provide a rather extensive analysis of the sensitivity of solar models to the assumptions underlying their calculation. I then discuss the detailed information about the solar interior that has become available through helioseismic investigations and the detection of solar neutrinos, with further constraints provided by the observed abundances of the lightest elements. Revisions in the determination of the solar surface abundances have led to increased discrepancies, discussed in some detail, between the observational inferences and solar models. I finally briefly address the relation of the Sun to other similar stars and the prospects for asteroseismic investigations of stellar structure and evolution.

scholarly journals A carbuncle cure for the Harten-Lax-van Leer contact (HLLC) scheme using a novel velocity-based sensor

2021 ◽  
Author(s):  
U. S. Vevek ◽  
B. Zang ◽  
T. H. New
Keyword(s):  
Data Structures ◽  
Numerical Experiments ◽  
Additional Data ◽  
Shear Layers ◽  
Hybrid Scheme ◽  
Local Pressure ◽  
Numerical Flux ◽  
Shear Sensor ◽  
Non Local

AbstractA hybrid numerical flux scheme is proposed by adapting the carbuncle-free modified Harten-Lax-van Leer contact (HLLCM) scheme to smoothly revert to the Harten-Lax-van Leer contact (HLLC) scheme in regions of shear. This hybrid scheme, referred to as the HLLCT scheme, employs a novel, velocity-based shear sensor. In contrast to the non-local pressure-based shock sensors often used in carbuncle cures, the proposed shear sensor can be computed in a localized manner meaning that the HLLCT scheme can be easily introduced into existing codes without having to implement additional data structures. Through numerical experiments, it is shown that the HLLCT scheme is able to resolve shear layers accurately without succumbing to the shock instability.

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