Model Of Thermal Convection Research Articles

Difference in the maximum magnitude of interplate earthquakes off Shikoku and in the Hyuganada region, southwest Japan, inferred from the temperature distribution obtained from numerical modeling: – The proposed Hyuganada triangle –

To clarify differences in the maximum magnitude of interplate earthquakes offshore of Shikoku ( ≈ M 8) and in the western adjacent Hyuganada region ( ≤ M 7.5), southwest Japan, where the oceanic Philippine Sea (PHS) plate subducts beneath the continental Amuria plate along the Nankai Trough, we calculated the temperature distribution for the plate interface using a three-dimensional thermal convection model. We attribute the observed very low heat flow values (less than approximately 45 mW/m 2) in the southern part of the Hyuganada region to the subduction of the Kyushu–Palau Ridge, which is presumably older than the adjacent Shikoku Basin to the east. Trial and error methods suggest an age difference of about 20 Myr between these two areas. The heat flow calculated from the temperature distribution fits the observed heat flow in the Hyuganada region well. The results show that Hyuganada earthquakes may take place in the newly proposed “Hyuganada triangle,” bounded by a southeastern isotherm of about 200 °C on the plate interface, a northwestern boundary between the upper surface of the subducting PHS plate and the continental Moho discontinuity, a northern isotherm of about 350 °C, and a northeastern margin-normal zone with a possible barrier or large friction parameter L. Interplate earthquakes in such a limited seismogenic zone may reach a maximum magnitude of M 7.5. Our results also suggest that a seismic gap seaward of the Hyuganada region may be caused by stable sliding arising from low temperature, resulting in a deeper updip limit than that offshore of Shikoku. The seismic gap offshore southwest of southern Kyushu along the Ryukyu Trench may result from the overlapping of two stable sliding regimes on the plate interface: one with low temperature at shallower depths caused by the subduction of the old PHS plate and the other a serpentinized mantle wedge at deeper depths.

Temperature distribution of the upper surface of the subducted Philippine Sea Plate along the Nankai Trough, southwest Japan, from a three-dimensional subduction model: relation to large interplate and low-frequency earthquakes

The Nankai subduction fault in southwest Japan is a plate boundary along which large megathrust earthquakes have repeatedly occurred. A previous 2-D thermal model suggested that the updip and downdip limits of the seismogenic zone are closely related to the temperature of the plate interface. We estimated a new temperature distribution for the plate interface based on a 3-D thermal convection model that incorporates revised governing equations, temporal changes in relative plate motion, the shape of the subducted slab, temperature variations related to basin evolution and more heat flow data and model regions than have been used in previous models. The margin-parallel spatial variation in the temperature of the plate interface was caused by spatio-temporal changes associated with the cooling of the Shikoku Basin. The updip limit of the thermally delineated seismogenic zone (thermal seismogenic zone) was approximately parallel to the trough axis due to a spreading rate that increased with distance from a fossil ridge, although the margin-parallel age dependency of the subducting plate was taken into account. The downdip limit of the thermal seismogenic zone was determined by temperature, except in eastern Kyushu, where it was determined by a boundary between the continental Moho depth and the upper surface of the subducting plate. The maximum coseismic slip associated with the 1944 Tonankai (M 7.9) and the 1946 Nankai (M 8.0) earthquakes, and a strongly coupled region estimated from GPS data inversion obtained by previous studies, were both located in the thermal seismogenic zone on the plate interface. Low-frequency earthquakes located at the downdip of the thermal seismogenic zone took place at temperatures of about 400–500 °C. This may be related to the phase transformation of hydrous minerals in oceanic crust from lawsonite + blueschist + jadeite to amphibole + eclogite and the associated decreases in water content of approximately 2.4 wt%. The thermal seismogenic zone is narrowest off the Kii Peninsula, where the hypocentres of the Tonankai and Nankai earthquakes were located. The narrow seismogenic zone may have determined the rupture initiation points for these earthquakes, as was previously demonstrated by numerical simulations of the earthquake cycle.

Resolution tests of three-dimensional convection models by traveltime tomography: effects of Rayleigh number and regular versus irregular parametrization

SUMMARY We present here the results obtained from 3-D tomographic inversion of synthetic data in order to investigate the ability of tomography to reveal the detailed thermal structures created by mantle convective processes. The synthetic input velocity models are based on the density heterogeneities obtained from a 3-D spherical-shell model of thermal convection. P and pP arrival-times are used in the inversion. We study the effect of the length-scale of the input anomalies characterized by the Rayleigh number of convection simulations (Ra = 3 × 10 5 , 8 × 10 5 ,1 0 6 ) and asses the sensitivity of the inverse problem to parametrization and explicit regularization (damping). We concentrate mainly on the effect of projection error and we show that its role is substantial with increasing chaotic convective behaviour. We use both irregular cell parametrization and regular cell parametrization (equisurface area). Due to the uneven distribution of sources and receivers, we found substantial differences between inversion output for models with regular and irregular cells. For the irregular parametrization, the structures located in the well-covered regions are resolved quite successfully, although the resolving power decreases with depth. In the poorly covered regions, where the ray sampling demands large parametrization cells, the correspondence between the input and output is rather low due to high parametrization error. An explicit regularization is not needed if only the projection error is assumed. On the other hand, for the regular parametrization, the inverse problem is very unstable and oscillations occur, unless an explicit regularization is applied. However, if an optimum damping is applied, the global correlation between the input and output anomalies is substantially higher than in irregular case. Further, we compare the power spectra of input seismic velocity anomalies and the inversion output. In case of irregular parametrization, the spectra of input model and inversion output differ especially in the uppermost part of the lower mantle and in the lowermost mantle, again due to the high parametrization error associated with the large parametrization cells. Much better agreement between the spectra of input and output is obtained in regular parametrization model, provided that a proper damping is applied. Therefore, we conclude that on a global scale, the regular parametrization gives better results than the irregular one, while the inversion with the irregular parametrization is able to resolve much more detailed structures in well-covered regions with the same number of model parameters and thus with the same computational costs.

A quasi-geostrophic convection model for planetary systems using a domain decomposition method

A numerical study is described of a quasi-geostrophic model for thermal convection in rapidly rotating planetary systems where the effect of Coriolis forces is dynamically predominant. In the quasi-geostrophic convection model, a spherical shell is divided into the three domains: a spherical annulus outside the tangent cylinder touching the equator of the inner sphere, the southern and northern polar regions inside the tangent cylinder. Convection in the rotating spherical annulus is investigated using a quasi-two-dimensional geostrophic approximation. Both linear stability analysis and fully nonlinear simulations are carried out. A new domain decomposition method suitable for massively parallel computers is employed in numerical simulations. It is found that, while the structure of mildly nonlinear flows at R = O ( 10 R c ) , where R denotes the Rayleigh number and R c is its critical value at the onset of convection, is spatially complicated and irregular, the structure of strongly nonlinear flows at R = O ( 100 R c ) is dominated by an axisymmetric zonal flow that is largely laminar, stable and nearly time-independent, similar to that on giant planets Jupiter and Saturn. We also model the atmospheric circulation of a 51 Pegasus b-type extrasolar planet which is synchronized with its parent star and receives an intensive radiation on its dayside.

Droplet condensation in two-dimensional Bolgiano turbulence

The evolution of microdroplets transported by a turbulent flow is considered. Droplets surrounded by moist air are able to grow by diffusion of water vapour on their surface. A two-dimensional model of dry Boussinesq thermal convection is considered in which the turbulent velocity field is driven by a temperature gradient. The evolution of the velocity, temperature, vapour fields and of droplet trajectories and radii is analysed by means of high-resolution direct numerical simulations. Despite the fact that the environment becomes drier and drier, a mean growth of droplets is obtained. The mechanism identified is based on the presence of correlations between the vapour field and droplet trajectories. Besides, a spreading of size distribution is observed, with the formation of droplets with very different sizes. Improvements with respect to previous models are discussed.

Mode-to-mode energy transfers in convective patterns

We investigate the energy transfer between various Fourier modes in a low-dimensional model for thermal convection. We have used the formalism of mode-to-mode energy transfer rate in our calculation. The evolution equations derived using this scheme is the same as those derived using the hydrodynamical equations for thermal convection in Boussinesq fluids. Numerical and analytical studies of this model show that convective rolls appear as the Rayleigh number R is raised above its critical value R c. Further increase of Rayleigh number generates rolls in the perpendicular directions as well, and we obtain a dynamic asymmetric square pattern. This pattern is due to Hopf bifurcation. There are two sets of limit cycles corresponding to the two competing asymmetric square patterns. When the Rayleigh number is increased further, the limit cycles become unstable simultaneously, and chaotic motion sets in. The onset of chaos is via intermittent route. The trajectories wander for quite a long time almost periodically before jumping irregularly to one of the two ghost limit cycles.

Hydrodynamic helicity in Boussinesq-type models of the geodynamo

The generation of hydrodynamic helicity is considered in models of thermal convection of a rapidly rotating incompressible liquid (small Rossby numbers). It is shown that a system of cyclonic vortices arising in geodynamo models generates a large-scale hydrodynamic helicity. The spatial distribution of the helicity is analyzed as a function of the intensity of heat sources in models with various boundary conditions for the velocity field.

Charge transport scaling in turbulent electroconvection

We describe a local-power-law scaling theory for the mean dimensionless electric current Nu in turbulent electroconvection. The experimental system consists of a weakly conducting, submicron-thick liquid-crystal film supported in the annulus between concentric circular electrodes. It is driven into electroconvection by an applied voltage between its inner and outer edges. At sufficiently large voltage differences, the flow is unsteady and electric charge is turbulently transported between the electrodes. Our theoretical development, which closely parallels the Grossmann-Lohse model for turbulent thermal convection, predicts the local-power law Nu approximately F(gamma)R(gamma)P(delta). R and P are dimensionless numbers that are similar to the Rayleigh and Prandtl numbers of thermal convection, respectively. The dimensionless function F(gamma), which is specified by the model, describes the dependence of Nu on the aspect ratio gamma. We find that measurements of Nu are consistent with the theoretical model.

Numerical modelling of 3D convection in the Earth mantle

A 3D numerical model of thermal convection in the upper Earth mantle is constructed, which is based on ‘vector potential-vorticity' variables and the subincremental method. Its thorough testing is carried out. Computational results that demonstrate the substantially 3D structure of convective fluxes in the Earth mantle are given.

Resolution tests of global geodynamic models by travel-time tomography

This study presents results of a 2-D tomographic inversion of synthetic data that examines the ability of seismic tomography to reveal structures created by mantle dynamic processes. Our seismic velocity anomaly model is based on the density heterogeneities obtained from models of thermal and thermo-chemical convection. Both layered and whole-mantle models are employed to produce the synthetic input anomalies. We investigate the resolving power of the inversion of P and pP arrival times, and assess the influence of parameterisation and regularisation (damping). We show that the effect of regularisation is substantial and that the optimum damping depends upon the wavelength of the input structures. The resolution of the inversion decreases considerably at depths greater than 1000 km, therefore the ability of the kinematic inversion to distinguish between whole-mantle and layered flows (coupled via thermal coupling) may be limited.

A stochastic model for high-Rayleigh-number convection

A stochastic one-dimensional model for thermal convection is formulated and applied to high-Rayleigh-number convection. Comparisons with experimental data for heat transfer in Rayleigh–Bénard cells are used to estimate two model parameters. Reasonable agreement with experimental results is obtained over a wide range of physical parameter values (six orders of magnitude in Rayleigh number, five orders of magnitude in Prandtl number). Using the model, the statistics of fluctuations in the core of the convection cell are studied. Good agreement with available experimental data is obtained. Two distinct p.d.f. shapes are seen; one at low Prandtl number which matches experimental observations, and another at high Prandtl number for which no experimental data exists. The model results are interpreted in terms of two distinct mechanisms for the production of core fluctuations.

Numerical modelling of 3D convection in the Earth mantle

A 3D numerical model of thermal convection in the upper Earth mantle is constructed, which is based on ‘vector potential-vorticity' variables and the subincremental method. Its thorough testing is carried out. Computational results that demonstrate the substantially 3D structure of convective fluxes in the Earth mantle are given.

Time dependent β-convection in rapidly rotating spherical shells

A quasi-geostrophic, or β, model of nonlinear thermal convection in rapidly rotating spherical fluid shells is investigated. We study time dependent instabilities for a range of Rayleigh number and Ekman number with a Prandtl number set to the unity. Above the onset of convection, increasing the Rayleigh number for a given Ekman number, we reproduce the sequence of bifurcations described by Busse [Phys. Fluids 14, 1301 (2002)] for the three-dimensional case: A first transition results in vacillating flow; a second transition gives rise to chaotic oscillations in time and localized convection in space; then a third leads to quasi-periodic relaxation oscillations. This study shows that the quasigeostrophic model encompasses the desired bifurcation sequence. It allows the investigation of a range of Ekman numbers unavailable to three-dimensional models with present computing resources. Decreasing the Ekman number, we unexpectedly found that all three transitions occur for marginally supercritical Rayleigh number. The range of Rayleigh number for which the amplitude of convection is steady vanishes in the asymptotic limit of small Ekman numbers. This effect could significantly alter the nature of the instability characterizing the onset of convection in particular whether it is a supercritical or subcritical bifurcation.

Effects of sub-lithospheric small-scale convection with a Newtonian rheology on the seafloor topography and heat flux

Seafloor topography and heat flux show clear dependence on the age of seafloor. A half-space cooling (HSC) model can reproduce seafloor topography and heat flux data for younger seafloor, but for older seafloor the observations show reduced variations with the age in comparison with the HSC model predictions. The deviation was attributed to the sub-lithospheric small-scale (SSC) convection first by Parsons and McKenzie (1978). While there is little doubt that the SSC can enhance heat flux at relatively old seafloor, questions were raised as to whether or not the SSC can actually lead to a reduced topography. In this study, the effects of SSC on seafloor topography and heat flux are investigated by formulating a 2-D thermal convection model that is parallel to plate motion. Instead of using closed boundary conditions, which will bring large pressure effects because of return flow, a flow through boundary condition is adopted. The results show that although the SSC enhances the surface heat flux, it has little effects on topography for the fluids with a more realistic rheology. The reason for this is that the SSC transports the heat from the bottom to the top and cools down the whole fluids, and with the existence of a stagnant lid, the whole effects on topography are negligible.

Survival of Archean cratonal lithosphere

I use thermal convection models to search for combinations of physical parameters that are compatible with the results of xenolith studies on the history and present thermal structure of cratonal lithosphere. The cratonal lithosphere above ∼180 km depth formed in the Archean and remained stable until recently sampled. The mantle adiabat cooled ∼150 K over this time. The temperature change across the rheologically active boundary layer at the lithospheric base is <300 K over a depth range of several tens of kilometers. Modern cratonal lithospheric thicknesses are relatively uniform, ∼225 km, much thicker than old oceanic lithosphere. Cratonal lithosphere is now in quasi‐steady state with conductive heat flow to the surface in balance with heat supplied to the base of the lithosphere by convection driven by local temperature contrasts within the rheologically active boundary layer. This heat flow and the lithosphere thickness changed little after the cratonal lithosphere stabilized. One possibility is that chemically buoyant lithosphere forms a conductive lid above the convecting normal mantle. To survive, the chemical lithosphere also needs to be more viscous than normal mantle. A reasonable situation has chemical lithosphere a factor of 20 more viscous than normal mantle with weakly temperature‐dependent viscosity (a factor of e over 100 K) from 0.2 × 1020 Pa s along the modern mantle adiabat. However, a chemical lid is unnecessary for lithospheric thickness to change slowly over time. For example, the base of the lithosphere may be stable if the viscosity at its base (along an adiabat) decreases rapidly with depth.

Europa: Tidal heating of upwelling thermal plumes and the origin of lenticulae and chaos melting

Tidal heating models are linked to thermal convection models for ice having strongly temperature dependent viscosity. In the range of ice viscosity inferred from laboratory experiments, tidal forces will heat up rising diapirs on Europa. Partial melt produced in the rising diapirs is predicted to create disruption of near‐surface materials and formation of lenticulae and chaos, even if the average ice layer thickness overlying an ocean is larger than 20 km.

Chaotic dynamics of a Bose-Einsteincondensate in a double-well trap

The dynamics of Bose-Einstein condensates in a double-wellmagnetic trap is studied using the Gross-Pitaevskii equation (GPE)and a two-mode approximation. The self-trapping instabilityoccurs when a sufficiently high potential barrier is formed inthe centre of the trap. Close to the instability threshold, theGPE is reduced to a simple amplitudeequation. In the case where weakly dissipative effects aretaken into account, the condensate exhibits aperiodicoscillations which can be described by the Lorenz thermal convection model.

Low-order dynamical models of thermal convection in high-aspect ratio enclosures

Low-dimensional dynamical models for transitional buoyancy-driven flow in differentially heated enclosures are presented. The full governing partial differential equations with the associated boundary conditions are solved by a spectral element method. Proper orthogonal decomposition is applied to the oscillatory solutions obtained from the full model in order to construct empirical eigenfunctions. Using the most energetic empirical eigenfunctions for the velocity and temperature fields as basis functions and applying Galerkin's method, low-order models consisting of few non-linear ordinary differential equations are obtained. For all cases, close to the “design” conditions (Pr0,Gr0), the low-order model (LOM) predictions are in excellent agreement with the predictions of the full model. In particular, the critical Grashof number at the onset of the first temporal flow instability (Hopf bifurcation) as well as the frequency and amplitude of oscillations at slightly supercritical conditions are in excellent agreement with the predictions of the full model. Far from design conditions, the LOMs capture some important characteristic properties of the full model solutions. For example, the low-order model derived for a cavity of A = 20 and Gr0 = 3.2 × 104, Pr0 = 0.71, captures the multiplicity of solutions for large values of Grashof number, while it predicts a unique steady solution at small values of Grashof number. In addition, the model predicts that a stationary instability precedes the onset of oscillatory convection. On the other hand, low-order models derived for low-aspect ratio cavities predict that the solution is unique and stable for sufficiently small values of Grashof number and that the primary instability leads to oscillatory time-dependent flow in agreement with experimental and numerical studies based on the full model.

Theoretical analysis of localized heating in human skin subjected to high voltage pulses

Electroporation, the increase in the permeability of bilayer lipid membranes by the application of high voltage pulses, has the potential to serve as a mechanism for transdermal drug delivery. However, the associated current flow through the skin will increase the skin temperature and might affect nearby epidermal cells, lipid structure or even transported therapeutic molecules. Here, thermal conduction and thermal convection models are used to provide upper and lower bounds on the local temperature rise, as well as the thermal damage, during electroporation from exponential voltage pulses (70 V maximum) with a 1 ms and a 10 ms pulse time constant. The peak temperature rise predicted by the conduction model ranges from 19 °C for a 1 ms time constant pulse to 70 °C for the 10 ms time constant pulse. The convection (mass transport) model predicts a 18 °C peak rise for 1 ms time constant pulses and a 51 °C peak rise for a 10 ms time constant pulse. The convection model compares more favorably with previous experimental studies and companion observations of the local temperature rise during electroporation. Therefore, it is expected that skin electroporation can be employed at a level which is able to transport molecules transdermally without causing significant thermal damage to the tissue.

Global water cycle and Earth's thermal evolution

Convergent margin processes play an important role in the distribution of terrestrial volatile species. During subduction processes volatiles are filtered from the subducting package and are restricted to return to the mantle. Water is the most abundant volatile and plays an important role in these processes. There is a number of geochemical investigations to determine the subduction, regassing, and recycling fluxes as well as the regassing ratio of water. The latter describes the partition of subducting water by water that is regassed into the mantle and water that is returned to the surface in arc magmas. Here we present a geophysical-based modelling approach for the calculation of such fluxes and ratios in order to compare them with the geochemical data. In order to assess the recent values and the evolution of the subduction, regassing, and the recycling flux a simple parameterized thermal convection model with a water-dependent rheology and a constant continental growth model is applied. To test the sensitivity of the results different continental growth models were applied and the total amount of water in the system was varied as well as the initial distribution of water in the reservoirs. According to our estimations a value of 0.31 for the time independent regassing ratio of water, R H 2O , is an acceptable upper bound. Lower values of R H 2O give larger water reservoirs on the surface compared to the recent situation. Larger values of R H 2O suggest smaller surface reservoirs of water and, therefore, seem to be unlikely. The model results show a relatively stable value for the regassing ratio of 0.31 by varying the initial conditions of the water distribution in the reservoirs (which are pretty much unknown at the present moment). But R H 2O is very sensitive towards the total amount of water in the system. Altering the value of four ocean masses to ten we get values for the regassing ratio from 0.31 to 0.89. Nevertheless, as a result of all numerical experiments the recent subduction flux is stable and equal to 1.02×10 15 g/a. The influence of the continental growth model on the results could be neglected. The calculated value for the recent subduction water flux fits the modern geochemical data very well while our value for R H 2O is smaller. One possible reason could be that in our experiments R H 2O remains constant and, therefore, represents an average value over Earth's history. In order to check this assumption we apply a simple exponential time dependence of R H 2O . Here, the modern regassing ratio increases to 0.41. Therefore, based on a geophysical modelling approach in contrast to the geochemical investigations we suggest a smaller value for the modern regassing ratio of about 0.3 to 0.4.