Convection Of Mercury Research Articles

Analysis of the Cessation of Convection in Mercury's Mantle

AbstractThe question of whether the present‐day mantle of Mercury is undergoing convection remains unresolved. We address this issue by estimating the minimum value of the core‐mantle boundary (CMB) temperature needed to support mantle convection and considering the time required to cool the mantle below this threshold. A simple mathematical analysis of the cooling of the core, based on the assumption of a quasi‐steady‐state thermal equilibrium of Mercury's mantle, shows that the CMB temperature falls to the critical temperature for cessation of convection roughly halfway through the planet's evolutionary history. To first order, the duration of subsolidus convection does not depend on the absolute value of the viscosity. It depends primarily on parameters that control the viscosity function, such as the stress exponent and the activation energy. Our results based on conventional assumptions suggest the absence of present‐day mantle convection in Mercury, which is consistent with numerical models of Mercury's thermal history. However, because of large uncertainties in the controlling parameters, the possibility of still ongoing mantle convection on Mercury cannot be ruled out.

Did the cessation of convection in Mercury's mantle allow for a dynamo supporting increase in heat loss from its core?

Mercury's large core generates a magnetic field and harbors a solidified inner component. These features constrain models of the planet's thermal history. The mantle provides the boundary condition on Mercury's core that determines heat loss. Recent studies suggest Mercury's mantle may have a higher thermal diffusivity than the silicate shells of other rocky bodies due to iron depletion. Considering the role of diffusivity, we model Mercury's mantle starting from a post magma-ocean state by calculating core-mantle boundary heat flow and the ratio of inner-core boundary radius to core-mantle boundary radius, fc, for periods comparable to the age of the solar system. Core-mantle boundary (CMB) heat flow is calculated using 3D mantle convection simulations for thermal diffusivities, κ, ranging from 1.0 - 3.0 ×10−6 m2/s and initial radiogenic uniform mantle heating rates, χ, of 0 - 40 pW/kg (that decay with a 3 Gyr half-life). Several scenarios can unfold for the range of parameters considered: these include cases featuring both the cessation of mantle convection and its continuation at 4.5 Gyr. We map a trend in κ - χ space and find that for some parameters present-day core heat flux and inner-core size estimates are satisfied for a Mercurian mantle that is cooling by conduction. The influence of initial sulfur fraction in the core was examined for a subset of cases. For a sulfur fraction of 0.10, fc falls between 0.1 and 0.55 which corresponds to planetary radius contractions below 7 km (since the Late Heavy Bombardment). However, fc exceeds 0.55 for a lower initial sulfur fraction and results in planetary contraction in excess of 7 km. In general, we find that the mean core heat flux reaches a temporal local minimum when the mantle transitions from a convective to a conductive regime and subsequently climbs before decreasing. The transition to conduction is delayed with increased mantle internal heating rate but the maximum mean heat flux from the core into the conducting and cooling mantle is always greater than the heat flux observed at the cessation of the stagnant-lid convection. We find that for an initially more vigorously convecting mantle the onset of inner-core growth is earlier while the basal heat flux is marginally reduced at present day. In general, we find that current-day conductive cooling of the Mercurian mantle can satisfy estimates on Mercury's core heat loss inferred from the strength of its magnetic field while also satisfying the limits on the present-day size of its inner core.

Internal forcing of Mercury’s long period free librations

Observations of Mercury’s spin rate do not rule out that, in addition to the forced 88-day mantle libration induced by solar torques, a decadal timescale libration may also be present. It has been proposed that this signal represents an amplified forced libration caused by the periodic 11.86yr perturbation on Mercury’s orbit by Jupiter. Here, we investigate the possibility that a decadal libration may be produced by a forcing internal to the planet. Our mechanism is based on the presence of time-dependent zonal flows generated by turbulent convection in Mercury’s fluid core. Through electromagnetic coupling, these flows entrain longitudinal displacements of the inner core, which then entrain mantle librations by gravitational coupling. We construct a simple model to capture this exchange of angular momentum. Although core zonal flows are expected to have a broad frequency spectrum, we show that the resulting mantle libration is dominated by the amplification that occurs at the period of the free decadal libration of the combined mantle and inner core. Our results suggest that for plausible values of Mercury’s internal magnetic field, if the inner core of Mercury is large (⩾1000km), decadal mantle libration amplitudes of the order of 1arcsec can be generated by zonal flows of the order of 1kmyr−1. Conversely, if future observations can robustly determine an upper bound on the amplitude of Mercury’s decadal librations, our results can be used as constraints on the convective dynamics in Mercury’s core.

Non-destructive ultrasonic velocimetry for central region velocity fields in turbulent Rayleigh–Bénard convection of mercury

A non-destructive method of measuring flow field of opaque fluids is presented for turbulent convection of liquid metal mercury. Two important properties of the turbulent state, namely 2D velocity profiles and energy spectrum, are successfully measured for Rayleigh–Bénard convection of mercury by using ultrasonic Doppler velocimetry. A few key techniques for the method are also explained.

Evidence against ‘ultrahard’ thermal turbulence at very high Rayleigh numbers

Several theories1,2,3,4,5 predict that a limiting and universal turbulent regime — ‘ultrahard’ turbulence — should occur at large Rayleigh numbers (Ra, the ratio between thermal driving and viscous dissipative forces) in Rayleigh–Benard thermal convection in a closed, rigid-walled cell. In this regime, viscosity becomes negligible, gravitationally driven buoyant plumes transport the heat and the thermal boundary layer, where the temperature profile is linear, controls the rate of thermal transport. The ultrahard state is predicted to support more efficient thermal transport than ‘hard’ (fully developed) turbulence: transport efficiency in the ultrahard state grows as Ra1/2, as opposed to Ra2/7 in the hard state6. The detection of a transition to the ultrahard state has been claimed in recent experiments using mercury7 and gaseous helium8. Here we report experiments on Rayleigh–Benard convection in mercury at high effective Rayleigh numbers, in which we see no evidence of a transition to an ultrahard state. Our results suggest that the limiting state of thermal turbulence at high Rayleigh numbers is ordinary hard turbulence.

Effects of a cusp magnetic field on the oscillatory convection coupled with crucible rotation in Czochralski crystal growth

Experimental results are presented of the oscillatory convection of mercury melts coupled with crucible rotation under an imposed cusp shaped magnetic field in a Czochralski crystal growing configuration. It is shown that irregular thermal waves induced by the crucible rotation can be transformed into regular waves by the action of cusp magnetic field. Consequently, temperature fluctuations underneath a fixed nonrotating disk as a crystal model are significantly suppressed. The suppression effect due to the cusp magnetic field is more efficient for lower depth-to-radius aspect ratios of melts in which the more regular wave occurs.

Effects of axial magnetic field on the oscillatory convection coupled with crucible rotation in Czochralski crystal growth

Abstract Experimental results are presented of the oscillatory convection of mercury melts coupled with crucible rotation under an imposed axial magnetic field in Czochralski crystal growing configuration. We have observed that baroclinic traveling thermal wave induced by crucible rotation turns into a standing wave by the action of axial magnetic field, when the crucible rotation rate is relatively low. It is found that a significant damping of the temperature oscillation underneath a crystal disk can be obtained after the transition from the traveling thermal wave to the standing wave.

Matched boundary layers in turbulent Rayleigh-Bénard convection of mercury

We analyzed temperature time series recorded in different positions across the boundary layers of a Rayleigh-B\'enard convection cell using mercury (Pr=0.024) for Rayleigh numbers (Ra) ranging from ${10}^{6}$ to ${10}^{8}$. In the whole range of Ra, several nondimensional quantities have unique, Ra-invariant profiles, if distance is normalized by the thermal boundary layer thickness. This indicates an asymptotic regime of thermal turbulence in which two boundary layers are coupled. Skewness and its time derivative of thermal fluctuations reveal that temperature fluctuations are not buoyancy driven but passively swept by the mean circulation in most of the cell.

Strongly turbulent Rayleigh–Bénard convection in mercury: comparison with results at moderate Prandtl number

An experimental study of Rayleigh–Bénard convection in the strongly turbulent regime is presented. We report results obtained at low Prandtl number (in mercury, Pr = 0.025), covering a range of Rayleigh numbers 5 × 106 < Ra < 5 × 109, and compare them with results at Pr∼1. The convective chamber consists of a cylindrical cell of aspect ratio 1.Heat flux measurements indicate a regime with Nusselt number increasing as Ra0.26, close to the 2/7 power observed at Pr∼1, but with a smaller prefactor, which contradicts recent theoretical predictions. A transition to a new turbulent regime is suggested for Ra ≃ 2 × 109, with significant increase of the Nusselt number. The formation of a large convective cell in the bulk is revealed by its thermal signature on the bottom and top plates. One frequency of the temperature oscillation is related to the velocity of this convective cell. We then obtain the typical temperature and velocity in the bulk versus the Rayleigh number, and compare them with similar results known for Pr∼1.We review two recent theoretical models, namely the mixing zone model of Castaing et al. (1989), and a model of the turbulent boundary layer by Shraiman & Siggia (1990). We discuss how these models fail at low Prandtl number, and propose modifications for this case. Specific scaling laws for fluids at low Prandtl number are then obtained, providing an interpretation of our experimental results in mercury, as well as extrapolations for other liquid metals.

Experimental study of high-Rayleigh-number convection in mercury and water

Abstract Experimental results of Rayleigh-Benard convection in the strongly turbulent regime are presented. The liquids tested are water (Pr ∽ 7) and mercury (Pr = 0.025), covering a range of Rayleigh numbers 4.6 × 10 6 9 . The convective chamber consists of a cylindrical cell of aspect ratio Γ = 1 (Γ = diameter/depth). The heat flux, the temperature fluctuation spectra and the structure of the mean flow have been measured. For Ra > 2 × 10 9 a transition to a new turbulent regime was observed with considerable increase of the Nusselt number. A decrease in Nusselt number with decreasing Prandtl number is observed at given Ra.

F( alpha ) curves: Experimental results.

We study the transition to chaos at the golden and silver means for forced Rayleigh-B\'enard (RB) convection in mercury. We present f(\ensuremath{\alpha}) curves below, at, and above the transition, and provide comparisons to the curves calculated for the one-dimensional circle map. We find good agreement at both the golden and silver means. This confirms our earlier observation that for low amplitude forcing, forced RB convection is well described by the one-dimensional circle map and indicates that the f(\ensuremath{\alpha}) curve is a good measure of the approach to criticality. For selected subcritical experimental data sets we calculate the degree of subcriticality. We also present both experimental and calculated results for f(\ensuremath{\alpha}) in the presence of a third frequency. Again we obtain agreement: The presence of random noise or a third frequency narrows the right-hand (negative q) side of the f(\ensuremath{\alpha}) curve. Subcriticality results in symmetrically narrowed curves. We can also distinguish these cases by examining the power spectra and Poincar\'e sections of the time series.

Structure of Arnold tongues and the f( alpha ) spectrum for period doubling: Experimental results.

We study experimentally the detailed structure of resonances in forced Rayleigh-B\'enard convection in mercury. The resonances appear as Arnold tongues in the phase diagram of the system. We follow a particular tongue beyond the critical line where tongues start to overlap and find a period-doubling curve stretching over the entire tongue. Above this line there is a symmetry breaking with period-doubling cascades at the two sides of the tongue. We also observe a multitude of other periodic windows in this regime together with hysteresis effects caused by overlap of other tongues. We follow one of the period-doubling cascades and study the full scaling structure of the attractor at the onset of chaos by means of an f(\ensuremath{\alpha}) spectrum of scaling indices. The experimental spectrum is, within error, the same as the universal spectrum calculated theoretically.

Stability of convection rolls in the presence of a vertical magnetic field

The stability of two-dimensional convection rolls in a horizontal fluid layer heated from below with rigid boundaries is investigated theoretically for the case when a vertical magnetic field permeates the layer. It is assumed that the magnetic diffusivity is large compared with the thermal and viscous diffusivities of the fluid. Low Prandtl numbers are emphasized in order to make the analysis directly applicable to experiments on convection in mercury and liquid sodium. The theory predicts that the onset of the oscillatory instability of convection rolls is delayed by the effects of the magnetic field and that the parameter range over which steady rolls are stable increases with the magnetic field strength. In the parameter regime investigated, there does not seem to exist a new mode of instability introduced by magnetic forces. It is also found that the magnetic field tends to increase the efficiency of the convective heat transport thereby conpensating in part for the delay in the onset of convection caused by the stabilizing effect on the Lorentz force.

Convection in Mercury

In order to explain why Mercury is trapped in a resonant state of rotation with a period two thirds of its orbital period, it has been proposed that the planet departs from hydrostatic equilibrium. It is shown that its gravity field must include a second-degree harmonic term. It is argued that this must be caused by convection in the solid interior rather than an initial distortion retained by the finite strength of the interior. The presence of an iron core in Mercury poses an interesting question as to why a second-degree harmonic convection pattern in the silicate mantle is present and suggested solutions are discussed.

Natural convection with mercury in a uniformly heated vertical channel during unstable laminar and transitional flow

AbstractExperimental heat transfer correlations were determined for natural convection in mercury in a uniformly heated vertical channel with width‐to‐height ratios varying from 0.25 to infinity (the single plate limit). Local modified Grashof numbers varied between 108 and 1011. Temperature and velocity profiles were obtained for these same channel configurations and local Grashof numbers. Instantaneous velocity plots indicate the range of conditions studied to proceed from unstable laminar flow well into the transition regime. Heat transfer results are in good agreement with earlier results reported for stable laminar flow which were limited to values of modified Grashof number less than 109.

An experimental investigation of natural convection in mercury at low grashof numbers

This paper presents the results of an experimental investigation of natural convection from a uniformly heated, vertical flat plate immersed in mercury. Data were obtained at low Grashof numbers particularly. Temperature profiles about the plate were measured with a copper-constantan thermocouple and the results presented on dimensionless plots. The experimental results deviated from the similarity solution of the boundary layer equations and these deviations are shown to depend on the distance up the plate, the heat flux, and the Nusselt number. A qualitative comparison is made with the predictions of a perturbation analysis. Present experimental data ( Gr ∗ x from 1 to 10 8) were correlated to give a relationship between Nu x and Gr ∗ x and this compared with analytical predictions as well as other correlations ( Gr ∗ x from 10 4 to 10 9). Positive deviation of experimental Nu x from the theoretical value was estimated to be about 20 per cent at Gr ∗ x = 2 × 10 4 and Pr = 0.024.

Heat Transfer by Natural Convection of Mercury in Enclosed Spaces When Heated From Below and Rotated

This paper presents results of an experimental investigation of convective heat transfer in mercury confined by two horizontal plates, heated from below, and spun about its vertical axis. The experiments covered a range of Rayleigh numbers between 1.1(10)6 and 5.17(10)7, and Taylor numbers from 0 to 7.75(10)10. The Prandtl number was practically constant. The results indicate that for low spin rates, up to a certain critical value of Taylor number, the change in the heat-transfer coefficient is insignificant and the equation derived for the stationary case can be used. The critical Taylor number is given by Ta(critical)=0.68(Ra)1.28 Above the critical Taylor number, the heat-transfer coefficient may be computed from the relationship Nu=0.095(Ra)0.852(Ta)−0.463 In this equation the characteristic dimension of length, for Nu, Ra, and Taylor numbers, is the distance between plates.

Effect of Spin on Natural Convection in Mercury Heated from Below

In the absence of spin, natural convection between two horizontal surfaces in mercury heated from below is found to be given by the formula N=0.051R⅓ where N is the Nusselt number and R the Rayleigh number. Spinning the mercury about a vertical axis reduces the amount of convection after a certain value of the spin (Taylor number) is exceeded. This value of the Taylor number increases with increasing heat flux. Turbulent fluctuation of the temperatures of the bounding surfaces are observed and under some circumstances periodic oscillations of the temperature of the bounding surface are also noted.

Experiments on over-stable thermal convection in mercury

In this paper experiments on the onset of thermal instability in rotating layers of mercury are described. In agreement with the recent theoretical work of Chandrasekhar the experiments show that the instability sets in as oscillations of increasing amplitude. Both the temperature gradients at which the instability sets in and periods of the oscillations in the marginal state are in agreement with the theoretical predictions.