Theory of stellar convection: removing the mixing-length parameter

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.

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

Proceedings of the International Astronomical Union ◽

10.1017/s1743921316004671 ◽

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.

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Scale-free convection theory

Proceedings of the International Astronomical Union ◽

10.1017/s1743921316006700 ◽

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.

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

Proceedings of the International Astronomical Union ◽

10.1017/s1743921307000646 ◽

2006 ◽

Vol 2 (S239) ◽

pp. 314-316 ◽

Cited By ~ 1

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.

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Stellar Convection

Publications of the Astronomical Society of Australia ◽

10.1017/s1323358000024802 ◽

1991 ◽

Vol 9 (1) ◽

pp. 26-31 ◽

Cited By ~ 2

Author(s):

Da Run Xiong

Keyword(s):

Time Dependent ◽

Hydrodynamic Equations ◽

Dynamic Coupling ◽

Stellar Convection ◽

Non Linear ◽

Non Local ◽

The Difference ◽

Thermodynamic Coupling

AbstractTime-dependent convection theory and non-local convection theory are described. The difference between the convection theories results from the different treatment of the non-linear terms of the hydrodynamic equations. We have obtained a better understanding of the thermodynamic coupling between convection and oscillations in comparison to the dynamic coupling.

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Bayesian inference of stellar parameters based on 1D stellar models coupled with 3D envelopes

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/stz2825 ◽

2019 ◽

Vol 490 (2) ◽

pp. 2890-2904 ◽

Cited By ~ 5

Author(s):

Andreas Christ Sølvsten Jørgensen ◽

George C Angelou

Keyword(s):

Bayesian Inference ◽

Structural Changes ◽

Energy Transport ◽

Parameter Estimates ◽

Mixing Length ◽

Milky Way Galaxy ◽

3D Simulations ◽

Robust Parameter ◽

Stellar Models ◽

Oscillation Frequencies

ABSTRACT Stellar models utilizing 1D, heuristic theories of convection fail to adequately describe the energy transport in superadiabatic layers. The improper modelling leads to well-known discrepancies between observed and predicted oscillation frequencies for stars with convective envelopes. Recently, 3D hydrodynamic simulations of stellar envelopes have been shown to facilitate a realistic depiction of superadiabatic convection in 1D stellar models. The resulting structural changes of the boundary layers have been demonstrated to impact not only the predicted oscillation spectra but evolution tracks as well. In this paper, we quantify the consequences that the change in boundary conditions has for stellar parameter estimates of main-sequence stars. For this purpose, we investigate two benchmark stars, Alpha Centauri A and B, using Bayesian inference. We show that the improved treatment of turbulent convection makes the obtained 1D stellar structures nearly insensitive to the mixing length parameter. By using 3D simulations in 1D stellar models, we hence overcome the degeneracy between the mixing length parameter and other stellar parameters. By lifting this degeneracy, the inclusion of 3D simulations has the potential to yield more robust parameter estimates. In this way, a more realistic depiction of superadiabatic convection has important implications for any field that relies on stellar models, including the study of the chemical evolution of the Milky Way Galaxy and exoplanet research.

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Turbulence Characteristics Across a Range of Idealized Urban Canopy Geometries

Boundary-Layer Meteorology ◽

10.1007/s10546-021-00658-6 ◽

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.

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

Applied Mathematics and Mechanics ◽

10.1007/s10483-021-2762-6 ◽

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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