Theory Of Convection Research Articles

Dependence of Pulsation Stability on the Helium Abundance of Stellar Convective Envelope

By using a non-local and time-dependent theory of convection, the linear non-adiabatic oscillations of radial and low-degree non-radial F-p8 modes are calculated for the stellar evolutionary models in the mass range of 1.4∼3.0 Mʘ, with three helium abundances of convective envelope (Y =0.28, 0.13, 0.00), and the solar metal abundance (Z =0.02). The numerical results show that the red edge of theoretical δ Scuti instability strip almost does not change with the helium abundance. With the decrease of the helium abundance, the blue edge of the δ Scuti instability strip moves toward the direction of low temperatures, the high-temperature stars on the hot side of instability strip become more stable, while the low-temperature stars on the cold side of instability strip become more instable. It seems to be impossible to explain the non-variable stars in the δ Scuti instability strip by using the diffusion of helium. However, the ratios of non-variable stars to variable stars in the hot and cold sides of the δ Scuti strip may be taken as the observational evidence of helium diffusion.

Numerical methodology to implement thermal effects in simulation of long stroke wear tribotests

The present paper reports the methodology used to numerically implement thermal effects in long stroke tribometer (LST) wear tests. Thermal effects correspond to the heating produced by friction between the parts in tests. Those tests consist in the sliding, in reciprocating configuration, of samples of thermoplastic polyurethane, over a fixed steel countermaterial. The numerical implementation of the LST tests is carried out by means of fully coupled thermal-stress finite element simulations, using different theories of convection and conduction for setting up parameters in polymer–steel contact pairs. This methodology is applied to the numerical analysis of different load and test reference temperature conditions, setting up a validation with experimental tests under some specific conditions. This work is only focused on the numerical implementation of thermal effects. As further step to this work, this methodology will be applied to the development and numerical implementation of a polymer–steel wear model with thermal effects, characterised from wear tribometer test results.

Theory of stellar convection: removing the mixing-length parameter

Stellar convection is customarily described by 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 at all evolutionary phases. The aim of this study is to present a new theory of stellar convection that does not require the mixing length parameter. We present a self-consistent analytical formulation of stellar convection that determines the properties of stellar convection as a function of the physical behaviour of the convective elements themselves and of the surrounding medium. This new theory 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 convectively-unstable layers is fully determined by a new system of equations for convection in a non-local and time-dependent formalism. We obtain an analytical, non-local, time-dependent sub-sonic solution for the convective energy transport that does not depend on any free parameter. The theory is suitable for the outer convective zones of solar type stars and stars of all mass on the main sequence band. The predictions of the new theory are compared with those from the standard mixing-length paradigm for the most accurate calibrator, the Sun, with very satisfactory results.

Some remarks on the early evolution of Enceladus

Abstract Thermal history of Enceladus is investigated from the beginning of accretion to formation of its core (~400 My). We consider model with solid state convection (in a solid layer) as well as liquid state convection (in molten parts of the satellite). The numerical model of convection uses full conservative finite difference method. The roles of two modes of convection are considered using the parameterized theory of convection. The following heat sources are included: short lived and long lived radioactive isotopes, accretion, serpentinization, and phase changes. Heat transfer processes are: conduction, solid state convection, and liquid state convection. It is found that core formation was completed only when liquid state convection had slowed down. Eventually, the porous core with pores filled with water was formed. Recent data concerning gravity field of Enceladus confirm low density of the core. We investigated also thermal history for different values of the following parameters: time of beginning of accretion t ini , duration of accretion t acr , viscosity of ice close to the melting point η m , activation energy in formula for viscosity E , thermal conductivity of silicate component k sil , ammonia content X NH3 , and energy of serpentinization c serp . All these parameters are important for evolution, but not dramatic differences are found for realistic values. Moreover, the hypothesis of proto-Enceladus (stating that initially Enceladus was substantially larger) is considered and thermal history of such body is calculated. The last subject is the Mimas-Enceladus paradox. Comparison of thermal models of Mimas and Enceladus indicates that period favorable for ‘excited path of evolution’ was significantly shorter for Mimas than for Enceladus.

THEORY AND SIMULATIONS OF ROTATING CONVECTION

We study thermal convection in a rotating fluid in order to better understand the properties of convection zones in rotating stars and planets. We first derive mixing-length theory for rapidly-rotating convection, arriving at the results of Stevenson (1979) via simple physical arguments. The theory predicts the properties of convection as a function of the imposed heat flux and rotation rate, independent of microscopic diffusivities. In particular, it predicts the mean temperature gradient; the rms velocity and temperature fluctuations; and the size of the eddies that dominate heat transport. We test all of these predictions with high resolution three-dimensional hydrodynamical simulations of Boussinesq convection in a Cartesian box. The results agree remarkably well with the theory across more than two orders of magnitude in rotation rate. For example, the temperature gradient is predicted to scale as the rotation rate to the 4/5th power at fixed flux, and the simulations yield $0.75\pm 0.06$. We conclude that the mixing length theory is a solid foundation for understanding the properties of convection zones in rotating stars and planets.

MODELING CONVECTIVE CORE OVERSHOOT AND DIFFUSION IN PROCYON CONSTRAINED BY ASTEROSEISMIC DATA

We compare evolved stellar models, which match Procyons mass and position in the HR diagram, to current ground-based asteroseismic observations. Diffusion of helium and metals along with two conventional core overshoot descriptions and the Kuhfuss nonlocal theory of convection are considered. We establish that one of the two published asteroseismic data reductions for Procyon, which mainly differ in their identification of even versus odd l-values, is a significantly more probable and self-consistent match to our models than the other. The most probable models according to our Bayesian analysis have evolved to just short of turnoff, still retaining a hydrogen convective core. Our most probable models include Y and Z diffusion and have conventional core overshoot between 0.9 and 1.5 pressure scale heights, which increases the outer radius of the convective core by between 22% to 28%, respectively. We discuss the significance of this comparatively higher than expected core overshoot amount in terms of internal mixing during evolution. The parameters of our most probable models are similar regardless of whether adiabatic or nonadiabatic model p-mode frequencies are compared to the observations, although, the Bayesian probabilities are greater when the nonadiabatic model frequencies are used. All the most probable models (with or without core overshoot, adiabatic or nonadiabatic model frequencies, diffusion or no diffusion, including priors for the observed HRD location and mass or not) have masses that are within one sigma of the observed mass 1.497+/-0.037 Msun.

Bridging local to global dynamics of drop impact onto solid substrates

AbstractThe shape of impacting drops onto a solid surface is investigated by probing the local flow velocity and the local thickness profile of the spreading lamella during the drop impact. First, as a model situation of no viscous coupling between the liquid and the substrate, the impact of a drop onto hot plates, above the Leidenfrost temperature, is considered. In this case, we demonstrate that the velocity and thickness profiles are in good agreement with inviscid convective flow theory. This local description allows us to revisit the modelling of well-studied global behaviour such as drop spreading. Building from this idealized situation, viscous boundary-layer effects emerging from frictional coupling on a cold surface are then captured.

A Numerical Verification of Self-Similar Multiplicative Theory for Small-Scale Atmospheric Turbulent Convection

自我类似的趋于增加的理论(SSM 理论) ，解释温度结构的可伸缩的行为的目的工作。在现在的纸，作者报告源于大气的狂暴的传送对流的数字模拟以便验证这个理论。模拟基于从简化大气的传送对流方程被推出的一个壳模型。数字结果与从第一份订单放大法律到第八份订单的理论预言同意了很好。他们也比由 Kolmogorovs 理论交上 1941 的证明这个理论的预言好， lognormal，和模型理论。

Rearrangement, convection, convexity and entropy

The concepts of convexity and entropy play a crucial role in the mathematical theory of hyperbolic systems of conservation laws. We show that they also play an important role in the mathematical analysis of convection theory, through the mathematical concept of rearrangement.

Solar-like and Mira-like oscillations of stars — A uniform excitation mechanism

Using a non-local and time-dependent theory of convection, we have calculated the linear non-adiabatic oscillations of the radial and low-degree F-p39 modes for evolutionary models from the main sequence to the asymptotic giant branch for stars with solar abundance (X = 0.70, Z = 0.02) in the mass range of 0.6–3.0 M⊙. The results show that low luminosity cool stars tend to be solar-like oscillators, whose low-order modes are stable, but intermediate and high order p-modes are pulsationally unstable; their unstable modes have a wide range in frequency and small values for amplitude growth rates. For stars with increasing luminosity and therefore lower temperature, the unstable modes shift towards lower orders, the corresponding range of frequency decreases, and the amplitude growth rate increases. High luminosity red giant stars behave like typical Mira-like oscillators. The effects of the coupling between convection and oscillations on pulsational instability have been carefully analyzed in this work. Our research shows that convection does not simply act as a damping mechanism for oscillations, and the complex nature of the coupling between convection and oscillations makes turbulent convection sometimes behave as damping, and sometimes as excitation. Such a picture can not only naturally account for the red edge of the instability strip, but also the solar-like oscillations in low luminosity red stars and Mira-like ones in high luminosity red giants.

Heat transfer mechanisms in solidification

Solidification as a heat transfer process accompanying a phase transition plays a major role in manufacturing processes and material evolution processes. However, the complex combinations of solidification mechanisms at interfacial boundaries prevent us from its full understanding. A statistical thermodynamic transport theory for heat transfer has been proposed. We here demonstrate the validity of the heat transfer theory for internal convection and external conduction by examining the solidification processes at the interface of two different phase materials. Three variable separation constants designate particle number constants and play the major roles in exploring the distinct solidification mechanisms. In solidification, the four regimes of convection, nucleation, transient, and film solidification are illustrated and their heat flux curves are explored as a function of temperature difference between electrode and saturation temperature. Three limiting heat fluxes and four activation temperatures are implemented as input parameters. The heat transfer theory pictures that the formation mechanism of dendrites takes place under the control of nucleation solidification, and the relevant parameters in the control mechanism are predicted. Theoretical heat flux profiles in solidification agree with experimental heat flux data, and the theory is capable of predicting the heat flux mechanisms in full temperature regimes of solidification as well as in the spatial and temporal regimes.

Stability of ice/rock mixtures with application to a partially differentiated Titan

Titan’s moment of inertia, calculated assuming hydrostatic equilibrium from gravity field data obtained during the Cassini–Huygens mission, implies an internal mass distribution that may be incompatible with complete differentiation. This suggests that Titan may have a mixed ice/rock core, possibly consistent with slow accretion in a gas-starved disk, which may initially spare Titan from widespread ice melting and subsequent differentiation. A partially differentiated Titan, however, must still efficiently remove radiogenic heat over geologic time. We argue that compositional heterogeneity in the major saturnian satellites indicates that Titan formed from planetesimals with disparate densities. The resulting compositional anomalies would quickly redistribute to form a vertical density gradient that would oppose thermal convection. We use elements of the theory of double-diffusive convection to create a parameterized model for the thermal evolution of ice/rock mixtures with a stabilizing compositional gradient. To account for large uncertainties in material properties and accretionary processes, we perform simulations for a wide range of initial conditions. Ultimately, for realistic density gradients, double-diffusive convection in the ice/rock interior can delay, but not prevent, ice melting and differentiation, even if a substantial fraction of potassium is leached from the rock component. Consequently, Titan is not partially differentiated.

Seismic study of solar convection and overshooting: results of nonlocal convection

Local mixing-length theory is incapable of describing nonlocal phenomena in stellar convection, such as overshooting. Therefore standard solar models constructed with local mixing-length theory significantly deviate from the Sun at the boundariesof the convection zone, where convection becomes less efficient and nonlocal effects are important. The differences between observed and computed frequencies mainly come from the region near the surface, while the localized difference in sound speed is just below the convective envelope. We compute a solar envelope model using Xiong's nonlocal convection theory, and carry out helioseismic analysis. The nonlocal model has a smooth transition at the base of the convection zone, as revealed by helioseismology. It reproduces solar frequencies more accurately, and reduces the localized difference in sound speed between the Sun and standard solar models.

Burning on flat wicks at various orientations

Burning on flat plates was studied at various orientations with respect to gravity. Flat wicks of ceramic (Kaowool PM) board (10 cm wide and 1–10 cm long) were saturated with methanol or ethanol. Steady flames were obtained that ranged from boundary layer flames to plume-type burning. The onset of unsteady flow and transition to turbulence commenced at Grashof numbers of 106–107, increasing with decreasing angle (toward underside burning). The average burning rate per unit area was recorded along with the flame location. Experiments on polymethylmethacrylate were used for comparison with the liquid-wick results. The results roughly correlated with laminar pure convective theory, and improved results were indicated when the gravity term associated with the pressure gradient normal to the plate was included. Theoretical results by the integral method to reduce the partial differential equations to ordinary differential equations are presented.

Analysis of strange-mode instability with time-dependent convection in hot massive stars

AbstractWe carry out nonadiabatic analysis of strange-modes in hot massive stars with time-dependent convection (TDC) for the first time. Although convective luminosity in envelopes of hot massive stars is not as dominative as in stars near the red edge of the classical Cepheid instability strip in the Hertzsprung-Russell (H-R) diagram, we have found that the strange-mode instability can be affected by the treatment of convection. However, existence of the instability around and over the Humphreys-Davidson (H-D) limit is independent of the treatment. This implies that the strange-mode instability could be responsible for the lack of observed stars over the H-D limit regardless of uncertainties on convection theories.

Are There Pulsationally Unstable Low-degree p1 Modes in the Sun?

By using a non-local time-dependent theory of stellar convection, the solar non-adiabatic pulsations of the low- and intermediate-degree (l < 25) modes are calculated. The results show that the non-radial p1 modes of l = 1–5 are pulsationally unstable. However, the adjacent g, f, p2-p5 modes and the p1 modes of l > 5 are stable. From the analysis of the diagram of integrated work it is discovered that the excitation of oscillations comes from the radiation zone beneath the convective region. Whether the sun possesses unstable low-degree p1 modes is of significant importance for clarifying the excitation mechanism of solar five-minute oscillations.

A Theoretical Probe for Excitation Mechanisms of Solar-like and Mira-like Oscillations of Stars

The linear stability analysis of the radial and non-radial oscillations for the evolutionary model of a star with the mass of 0.6∼3 M8 has been per- formed by using the nonlocal and time-dependent convection theory. The results show that the unstable low-temperature stars on the right side of the instabil- ity strip in the HR diagram can be divided into two groups. One is of the stars of solar-like oscillations, composed of the main-sequence dwarfs, subgiants, and the red giants with low- and intermediate-luminosity, which are unstable in the intermediate- and high-order (nr ≥ 12) p-modes, but stable in the low- order (nr ≤ 5) p-modes. Another is of the Mira-like stars, composed of the luminous red giants and AGB stars, which are just contrary to the solar-like stars, unstable in the low-order (nr ≤ 5) p-modes, but stable in the intermediate- and high-order (nr ≥ 12) p-modes. On the red edge of Cepheid (δ Scuti) insta- bility strip, the oscillations of solar-like and Mira-like stars can be explained uniformly by the coupling between convection and oscillations (CCO). For the low-temperature stars on the right side of the instability strip, the CCO is the dominant excitation and damping mechanism for the low- and intermediate-order p-modes, and the stochastic excitation of turbulence becomes important only for the high-order p-modes of solar-like oscillations.

Land–Ocean Warming Contrast over a Wide Range of Climates: Convective Quasi-Equilibrium Theory and Idealized Simulations

Abstract Surface temperatures increase at a greater rate over land than ocean in simulations and observations of global warming. It has previously been proposed that this land–ocean warming contrast is related to different changes in lapse rates over land and ocean because of limited moisture availability over land. A simple theory of the land–ocean warming contrast is developed here in which lapse rates are determined by an assumption of convective quasi-equilibrium. The theory predicts that the difference between land and ocean temperatures increases monotonically as the climate warms or as the land becomes more arid. However, the ratio of differential warming over land and ocean varies nonmonotonically with temperature for constant relative humidities and reaches a maximum at roughly 290 K. The theory is applied to simulations with an idealized general circulation model in which the continental configuration and climate are varied systematically. The simulated warming contrast is confined to latitudes below 50° when climate is varied by changes in longwave optical thickness. The warming contrast depends on land aridity and is larger for zonal land bands than for continents with finite zonal extent. A land–ocean temperature contrast may be induced at higher latitudes by enforcing an arid land surface, but its magnitude is relatively small. The warming contrast is generally well described by the theory, although inclusion of a land–ocean albedo contrast causes the theory to overestimate the land temperatures. Extensions of the theory are discussed to include the effect of large-scale eddies on the extratropical thermal stratification and to account for warming contrasts in both surface air and surface skin temperatures.

Specific absorption rate and temperature increase in the human eye due to electromagnetic fields exposure at different frequencies

This study presents a numerical analysis of the specific absorption rate (SAR) and the heat transfer in a heterogeneous human eye model exposed to electromagnetic (EM) fields of 900 and 1800MHz. In this study, the effect of operating frequency on the SAR and temperature distributions in the eye was systematically investigated. The SAR value and the temperature distribution in various tissues in the eye during exposure to EM fields were obtained by numerical simulation of EM wave propagation and a heat transfer model was then developed based on the natural convection and porous media theories. The study highlights two transport phenomena: heat and mass transfer in the eye during exposure to EM fields at different frequencies. This study indicated that when the eye exposed to EM fields at the frequencies of 900 and 1800MHz, the highest SAR values at two chosen frequencies was in the cornea, and the highest temperature at the frequency of 900MHz was in the anterior chamber while the highest for the frequency of 1800MHz was in the vitreous. The temperature distribution in the eye induced by EM fields was not directly related to the SAR distribution due to the effect of the interaction among the dielectric properties, thermal properties, blood perfusion, and penetration depth of the EM power. Moreover, this study also showed that the exposure time had an influence on the temperature increase in the eye.

Time scales and structures of wave interaction exemplified with water waves

Presently two models for computing energy spectra in weakly nonlinear dispersive media are known: kinetic wave turbulence theory, using a statistical description of an energy cascade over a continuous spectrum (K-cascade), and the D-model, describing resonant clusters and energy cascades (D-cascade) in a deterministic way as interaction of distinct modes. In this letter we give an overview of these structures and their properties and a list of criteria about which model of energy cascade should be used in the analysis of a given experiment, using water waves as an example. Applying the time scale analysis to weakly nonlinear wave systems modeled by the focusing nonlinear Schödinger equation, we demonstrate that K-cascade and D-cascade are not competing processes but rather two processes taking place at different time scales, at different characteristic levels of nonlinearity and based on different physical mechanisms. Applying those criteria to data known from experiments with surface water waves we find that the energy cascades observed occur at short characteristic times compatible only with a D-cascade. The only pre-requisite for a D-cascade being a focusing nonlinear Schödinger equation, the same analysis may be applied to existing experiments with wave systems appearing in hydrodynamics, nonlinear optics, electrodynamics, plasma, convection theory, etc.