scholarly journals Convection with misaligned gravity and rotation: simulations and rotating mixing length theory

2020 ◽  
Vol 493 (4) ◽  
pp. 5233-5256 ◽  
Author(s):  
Laura K Currie ◽  
Adrian J Barker ◽  
Yoram Lithwick ◽  
Matthew K Browning
Keyword(s):  
Temperature Gradient ◽  
Heat Transport ◽  
Three Dimensional ◽  
Single Mode ◽  
Small Region ◽  
Spatial Spectrum ◽  
Mixing Length ◽  
Zonal Flows ◽  
Polar Latitude ◽  
Mixing Length Theory

ABSTRACT We present numerical simulations, using two complementary set-ups, of rotating Boussinesq thermal convection in a three-dimensional Cartesian geometry with misaligned gravity and rotation vectors. This model represents a small region at a non-polar latitude in the convection zone of a star or planet. We investigate the effects of rotation on the bulk properties of convection at different latitudes, focusing on determining the relation between the heat flux and temperature gradient. We show that our results may be interpreted using rotating mixing length theory (RMLT). The simplest version of RMLT (due to Stevenson) considers the single mode that transports the most heat. This works reasonably well in explaining our results, but there is a systematic departure from these predictions (up to approximately $30{{\ \rm per\ cent}}$ in the temperature gradient) at mid-latitudes. We develop a more detailed treatment of RMLT that includes the transport afforded by multiple modes, and we show that this accounts for most of the systematic differences. We also show that convectively generated zonal flows and meridional circulations are produced in our simulations, and that their properties depend strongly on the dimensions of the box. These flows also affect the heat transport, contributing to departures from RMLT at some latitudes. However, we find the theoretical predictions of the multi-mode theory for the mid-layer temperature gradient, the root-mean-square (rms) vertical velocity, the rms temperature fluctuation, and the spatial spectrum of the heat transport at different latitudes are all in reasonably good agreement with our numerical results when zonal flows are small.

Finite-amplitude cellular convection in a fluidsaturated porous layer

1980 ◽  
Vol 373 (1753) ◽  
pp. 199-222 ◽  
Keyword(s):  
Rayleigh Number ◽  
Temperature Gradient ◽  
Heat Transport ◽  
Critical Rayleigh Number ◽  
Three Dimensional ◽  
Finite Amplitude ◽  
Onset Of Convection ◽  
Optimum Heat ◽  
Square Cells

The local nonlinear stability of thermal convection in fluid-saturated porous media, subjected to an adverse temperature gradient, is investigated. The critical Rayleigh number at the onset of convection and the corresponding heat transfer are determined. An approximate analytical method is presented to determine the form and amplitude of convection. To facilitate the determination of the physically preferred cell pattern, a detailed study of both two- and three-dimensional motions is made and a very good agreement with available experimental data is found. The finite-amplitude effects on the horizontal wavenumber, and the effect of the Prandtl number on the motion are discussed in detail. We find that, when the Rayleigh number is just greater than the critical value, two dimensional motion is more likely than three-dimensional motion, and the heat transport is shown to have two regions for n =1. In particular, it is shown that optimum heat transport occurs for a mixed horizontal plan form formed by the linear combination of general rectangular and square cells. Since an infinite number of steady-state finite-amplitude solutions exist for Rayleigh numbers greater than the critical number A c * , a relative stability criterion is discussed th at selects the realized solution as that having the maximum mean-square temperature gradient.

Granulation and Supergranulation as a Diagnostic Test of Solar Structure

1983 ◽  
Vol 5 (2) ◽  
pp. 168-169 ◽  
Author(s):  
R. Van der Borght ◽  
P. Fox
Keyword(s):  
Temperature Gradient ◽  
Diagnostic Test ◽  
Convective Transport ◽  
Combined Effects ◽  
Mixing Length ◽  
Solar Structure ◽  
Satisfactory Model ◽  
Mixing Length Theory ◽  
Satisfactory Theory

One of the most difficult tasks facing theoretical astrophysics today is to find a satisfactory model for the convective transport of energy in regions where the temperature gradient is superadiabatic. A number of such models have been proposed, such as the mixing-length theory and its extensions (Vitense 1953, Böhm-Vitense 1958, Spiegel 1963, Travis and Matsushima 1973 a, b, Parson 1969), to take into account the combined effects of convection and turbulence but it is generally agreed that, to-date, no satisfactory theory has been put forward.

scholarly journals A non-local mixing-length theory able to compute core overshooting

2018 ◽  
Vol 612 ◽  
pp. A21 ◽  
Author(s):  
M. Gabriel ◽  
K. Belkacem
Keyword(s):  
Temperature Gradient ◽  
Mean Field ◽  
Mixing Length ◽  
Field Equations ◽  
Mean Field Equations ◽  
Convective Core ◽  
Non Local ◽  
The Mean ◽  
Free Parameters ◽  
Mixing Length Theory

Turbulent convection is certainly one of the most important and thorny issues in stellar physics. Our deficient knowledge of this crucial physical process introduces a fairly large uncertainty concerning the internal structure and evolution of stars. A striking example is overshoot at the edge of convective cores. Indeed, nearly all stellar evolutionary codes treat the overshooting zones in a very approximative way that considers both its extent and the profile of the temperature gradient as free parameters. There are only a few sophisticated theories of stellar convection such as Reynolds stress approaches, but they also require the adjustment of a non-negligible number of free parameters. We present here a theory, based on the plume theory as well as on the mean-field equations, but without relying on the usual Taylor’s closure hypothesis. It leads us to a set of eight differential equations plus a few algebraic ones. Our theory is essentially a non-mixing length theory. It enables us to compute the temperature gradient in a shrinking convective core and its overshooting zone. The case of an expanding convective core is also discussed, though more briefly. Numerical simulations have quickly improved during recent years and enabling us to foresee that they will probably soon provide a model of convection adapted to the computation of 1D stellar models.

Analysis of Thrust Bearings Operating in Turbulent Regime

1988 ◽  
Vol 110 (3) ◽  
pp. 555-560 ◽  
Author(s):  
M. Harada ◽  
H. Aoki
Keyword(s):  
Steady State ◽  
Thrust Bearing ◽  
Three Dimensional ◽  
Cross Coupling ◽  
Fluid Film ◽  
Turbulent Regime ◽  
Pressure Gradients ◽  
Mixing Length ◽  
Thrust Bearings ◽  
Mixing Length Theory

This paper relates to the turbulent motion in the lubricant fluid film with centrifugal effects and the lubrication theory for thrust bearings operating in turbulent regime. Using Prandtl’s mixing-length theory, three-dimensional turbulent velocity distributions, including pressure gradients and centrifugal effects, are calculated, and the cross-coupling of nonplanar flow of the lubricant fluid film is discussed. From these results, turbulent lubrication equations with centrifugal effects are derived. Applying these lubrication equations to a sectorial inclined thrust bearing, the steady-state characteristics and the dynamic ones are calculated.

Analysis of Bearings Operating in Turbulent Regime

1962 ◽  
Vol 84 (1) ◽  
pp. 139-151 ◽  
Author(s):  
V. N. Constantinescu
Keyword(s):  
Three Dimensional ◽  
Lubricant Layer ◽  
Turbulent Regime ◽  
Mixing Length ◽  
Thrust Bearings ◽  
Mixing Length Theory

Proceeding from the results obtained previously [5] this paper analyzes theoretically the three-dimensional motion in the lubricant layer by using Prandtl’s mixing length theory. Formulas and diagram are presented for calculating journal and thrust bearings subjected to turbulent lubrication.

scholarly journals The Mixing Length Ratio, Eddy Diffusivity and Acoustic Waves

1988 ◽  
Vol 108 ◽  
pp. 191-192
Author(s):  
Kwing L. Chan ◽  
Sabatino Sofia
Keyword(s):  
Acoustic Waves ◽  
Stokes Equations ◽  
Numerical Study ◽  
Three Dimensional ◽  
Eddy Diffusivity ◽  
Rectangular Domain ◽  
Numerical Results ◽  
Length Ratio ◽  
Mixing Length ◽  
Mixing Length Theory

Many processes in the convection zone of a star affect the evolution and the atmospheric diagnostics. Here, a progress report is given on our numerical study of some convection related phenomena. The numerical results are obtained by solving the Navier Stokes equations in a three dimensional rectangular domain. The units are chosen such that the initial temperature, pressure, density, and the depth of the domain are all normalized to 1.The mixing length theory relates the convective (enthalpy) flux FC to the envelope structure quite well (Chan and Sofia 1987). For efficient convection that occurs in deep convective regions, the numerical results are compatible with a mixing length ratio of 2.1. The mixing length theory fails to address the significance of the flux of kinetic energy FKE (see Figure 1). FKE is negative and has a magnitude comparable to the total flux. These results are qualitatively similar to those of two dimensional computations (Hurlburt et. al. 1984).

Pulsating white dwarfs and convection

2019 ◽  
Vol 15 (S357) ◽  
pp. 127-130
Author(s):  
J. L. Provencal ◽  
M. H. Montgomery ◽  
H. L. Shipman ◽  
Keyword(s):  
Local Time ◽  
White Dwarfs ◽  
Recent Progress ◽  
Three Dimensional ◽  
Theoretical Uncertainty ◽  
Mixing Length ◽  
Mixing Length Theory

AbstractConvection is a highly turbulent, three dimensional process that is traditionally treated using a simple, local, time independent description. Convection is one of the largest sources of theoretical uncertainty in stellar modeling. We outline recent progress in studies using pulsating white dwarfs to constrain convection and calibrate mixing length theory.

Comparison between fluid electron-temperature-gradient driven simulations and Tore Supra experiments on electron heat transport

2007 ◽  
Vol 73 (2) ◽  
pp. 199-206
Author(s):  
B. LABIT ◽  
M. OTTAVIANI
Keyword(s):  
Thermal Conductivity ◽  
Temperature Gradient ◽  
Electron Temperature ◽  
Heat Transport ◽  
Three Dimensional ◽  
High Electron ◽  
Present Contribution ◽  
Electron Thermal Conductivity ◽  
Electron Temperature Gradient ◽  
Electron Heat

Abstract.In recent years, much attention has been devoted to the electron-temperature-gradient (ETG) driven instability as a possible explanation for the high electron thermal conductivity found in most tokamaks. The present contribution assesses whether a specific three-dimensional fluid ETG model can reproduce the conductivity observed in the Tore Supra tokamak [Equipe Tore Supra (presented by R. Aymar) 1989 Plasma Physics and Controlled Nuclear Fusion Research (Proc. 12th Int. Conf., Nice, 1988, Vol. 1.) Vienna: IAEA, p. 9]. Although the model reproduces fairly well the observed critical gradient, a large discrepancy factor, of the order of 50, is found for the ratio between the experimental and the simulated conductivity. On the basis of this study, one must conclude that the electron heat transport cannot be explained only with a fluid ETG turbulence model.

scholarly journals An energy landscape approach to locomotor transitions in complex 3D terrain

2020 ◽  
Vol 117 (26) ◽  
pp. 14987-14995 ◽  
Author(s):  
Ratan Othayoth ◽  
George Thoms ◽  
Chen Li
Keyword(s):  
Potential Energy ◽  
Complex Terrain ◽  
Statistical Physics ◽  
Energy Landscape ◽  
Three Dimensional ◽  
Single Mode ◽  
Physical Interaction ◽  
Landscape Approach ◽  
3D Terrain ◽  
Potential Energy Landscape

Effective locomotion in nature happens by transitioning across multiple modes (e.g., walk, run, climb). Despite this, far more mechanistic understanding of terrestrial locomotion has been on how to generate and stabilize around near–steady-state movement in a single mode. We still know little about how locomotor transitions emerge from physical interaction with complex terrain. Consequently, robots largely rely on geometric maps to avoid obstacles, not traverse them. Recent studies revealed that locomotor transitions in complex three-dimensional (3D) terrain occur probabilistically via multiple pathways. Here, we show that an energy landscape approach elucidates the underlying physical principles. We discovered that locomotor transitions of animals and robots self-propelled through complex 3D terrain correspond to barrier-crossing transitions on a potential energy landscape. Locomotor modes are attracted to landscape basins separated by potential energy barriers. Kinetic energy fluctuation from oscillatory self-propulsion helps the system stochastically escape from one basin and reach another to make transitions. Escape is more likely toward lower barrier direction. These principles are surprisingly similar to those of near-equilibrium, microscopic systems. Analogous to free-energy landscapes for multipathway protein folding transitions, our energy landscape approach from first principles is the beginning of a statistical physics theory of multipathway locomotor transitions in complex terrain. This will not only help understand how the organization of animal behavior emerges from multiscale interactions between their neural and mechanical systems and the physical environment, but also guide robot design, control, and planning over the large, intractable locomotor-terrain parameter space to generate robust locomotor transitions through the real world.

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