Publication List

A. Sakuraba and P. H. Roberts, "Generation of a strong magnetic field using uniform heat flux at the surface of the core", Nature Geoscience, doi:10.1038/NGEO643, 2009.

The Earth's main magnetic field is thought to be generated by motions in the planet's fluid outer core, which lead to an effect similar to that of a dynamo. Recent high-resolution numerical simulations produce only a non-dipolar or a dipolar but comparatively weak magnetic field unlike that of the Earth. Older models that did generate a strong, Earth-like field needed to use unrealistically high viscosities for the core fluid. Common to a majority of the models is the assumption of a laterally uniform core-surface temperature. Here we use a low-viscosity geodynamo model to evaluate the effect of a different and more realistic boundary condition -- a uniform heat flux at the surface of the core -- on the simulation of an Earth-like magnetic field. Our results show that when the surface temperature is laterally uniform, only a weak magnetic field is generated because planetary-scale fluid circulations are suppressed. In contrast, a laterally uniform heat flux at the core's surface leads to large-scale convective flows, and a comparatively strong dipole-type magnetic field. Contrary to previous work, we suggest that thermal conditions at the core surface have a strong effect on low-viscosity geodynamo models.


地球の主磁場は液体の外核(コア)内の流動によって生成されていると考えられ、そこでは発電機(ダイナモ)と同様の効果が生じている。最近の高解像度の数値シミュレーションでは、非双極子磁場、あるいは双極子であっても比較的弱い磁場しか生成されず、これらの結果は地球磁場とは異なっている。以前のモデルは、地球に似た強い磁場をつくりだすことができたが、流体コアをモデル化するには非現実的な高い粘性率をもちいざるをえなかった。こうしたモデルの多くに共通するのは、コア表面で水平方向に一様な温度を課すという仮定である。本研究では、粘性の低いモデルをもちいて、それとは異なる、より現実的な境界条件 -- コアの表面で一様な熱フラックスを課す条件 -- を考え、地球に似た磁場をモデルで再現できるかどうか考察した。われわれの結果によれば、表面温度が水平方向に一様な場合は、惑星スケールの流体の循環が抑制されるために、弱い磁場しか生成されなかった。いっぽう、水平方向に一様な熱フラックスをコア表面で課すと、大規模な対流が起こり、比較的強い双極子型の磁場が生成された。過去の研究とは相反して、低粘性の地球ダイナモモデルでは、コア表面における熱境界条件が重要な効果をもつことが示唆される。

A. Sakuraba and Y. Hamano, "Turbulent structure in Earth's fluid core inferred from time series of geomagnetic dipole moment", Geophys. Res. Lett. 34, L15308, 2007.

The physical grounds are discussed for assessing turbulent structures hidden inside the Earth's liquid core by using a time series of the geomagnetic dipole moment obtained from historical and paleomagnetic data. We propose the idea that the time-averaged wavenumber spectra of electric current density at the core-mantle boundary (CMB) and also velocity near the CMB have relation to the frequency spectrum of the dipole moment. We performed computer simulations of a magnetohydrodynamic spherical dynamo to verify this idea. We show that the frequency spectrum of the dipole moment in the simulation is similar to that inferred by paleomagnetic observations. The simulation results indicate that the underlying kinetic energy spectrum is proportional to m-5/3 in a high wavenumber range, where m is the azimuthal wavenumber. We speculate that a similar turbulent energy spectrum may exist in the Earth's core with a peak near m=5.


歴史データおよび古地磁気データによって復元された地磁気双極子モーメントの時系列をもちいて、地球の液体コア内に隠れている乱流構造を推定するために必要な物理的根拠について議論する。われわれは、コア・マントル境界(CMB)を流れる電流密度、およびそのすぐそばの流速の、時間平均された波数スペクトルが、双極子モーメントの周波数スペクトルと関係がある、という考えを提案する。この考えを裏付けるために、球領域での電磁流体力学的ダイナモの計算機シミュレーションをおこなった。シミュレーションにおける双極子モーメントの周波数スペクトルは、古地磁気学的に求められたものと似ていた。シミュレーション結果は、内部の運動エネルギースペクトルが、高波数領域において、m-5/3 に比例することを示した(m は方位角方向の波数)。われわれは、地球のコア内にも同様の乱流スペクトルが存在し、そのピーク波数は 5 であると推論する。

A. Sakuraba, "A jet-like structure revealed by a numerical simulation of rotating spherical-shell magnetoconvection", J. Fluid Mech. 573, 89-104, 2007.

Numerical results on thermally driven nonlinear magnetoconvection in a rapidly rotating fluid spherical shell are reported. A uniform magnetic field that is parallel to the rotation axis is imposed externally. The Ekman number is 2 x 10-6, representing a state of negligible viscosity, as in the Earth's core. The convection pattern is characterized by a few large-scale vortex columns superimposed on a fast westward (retrograde) zonal flow. In the equatorial region, an anticyclonic vortex is intensified, in which an induced axial magnetic field is stored. Interaction between the magnetized vortex and the zonal flow leads to a thin jet at the western side of the vortex. The jet is also characterized by a thin electric current sheet caused by a steep gradient of the axial magnetic field. Because of this structure, the jet region can be designated as a magnetic front by analogy with fronts in mid-latitude atmospheric cyclones. It can be estimated from an order-of-magnitude analysis that the jet width decreases in inverse proportion to the zonal flow speed, and that the jet speed and the sheet-like electric current are proportional to the square of the zonal flow speed.


温度差による浮力で駆動される、高速回転する球殻流体内の非線形磁気対流の数値計算結果を報告する。外部から、自転軸に平行な一様磁場を印加した。エクマン数は 2 x 10-6 で、地球のコアの場合と同様、粘性の効果が無視できるほど小さいような状態を実現している。対流パターンは、速い西向き(回転方向と逆方向)の帯状流と、いくつかのコラム状の大規模渦との重ね合わせで特徴付けられる。赤道域では、高気圧渦が強められ、その中に誘導磁場が閉じ込められる。この磁化した渦と、帯状流との相互作用により、渦の西側に、薄いジェットが生じる。このジェットは、自転軸方向の磁場の急な勾配の結果生じる、薄い電流シートによっても特徴付けられる。このような構造があるために、中緯度大気の低気圧にともなう前線との類推から、このジェット領域は、磁気前線とでも呼ぶべきものである。オーダーエスティメートをすると、ジェットの幅は、帯状流の速さに逆比例し、ジェットの流速とシート状の電流の強さは、ともに帯状流の速さの2乗に比例することがわかった。

A. Sakuraba, "Linear magnetoconvection in rotating fluid spheres permeated by a uniform axial magnetic field", Geophys. Astrophys. Fluid Dynam. 96, 291-318, 2002.

A linear analysis of thermally driven magnetoconvection is carried out with emphasis on its application to convection in the Earth's core. We consider a rotating and self-gravitating fluid sphere (or spherical shell) permeated by a uniform magnetic field parallel to the spin axis. In rapidly rotating cases, we find that five different convective modes appear as the uniform field is increased; namely, geostrophic, polar convective, magneto-geostrophic, fast magnetostrophic and slow magnetostrophic modes. The polar convective (P) and magneto-geostrophic (E) modes seem to be of geophysical interest. The P mode is characterized by such an axisymmetric meridional circulation that the fluid penetrates the equatorial plane, suggesting that generation of quadrapole from dipole fields could be explained by a linear process. The E mode is characterized by a few axially aligned columnar rolls which are almost two-dimensional due to a modified Proudman-Taylor theorem.



A. Sakuraba, "Effect of a uniform magnetic field on nonlinear magnetoconvection in a rotating fluid spherical shell", Geophys. Astrophys. Fluid Dynam. 92, 255-287, 2000.

Dynamic interaction between magnetic field and fluid motion is studied through a numerical experiment of nonlinear three-dimensional magnetoconvection in a rapidly rotating spherical fluid shell to which a uniform magnetic field parallel to its spin axis is applied. The fluid shell is heated by internal heat sources to maintain thermal convection. The mean value of the magnetic Reynolds number in the fluid shell is 22.4 and 10 pairs of axially aligned vortex rolls are stably developed. We found that confinement of magnetic flux into anti-cyclonic vortex rolls was crucial on an abrupt change of the mode of magnetoconvection which occurred at L = 1 to 2, where L is the Elsasser number. After the mode change, the fluid shell can store a large amount of magnetic flux in itself by changing its convection style, and the magnetostrophic balance among the Coriolis, Lorentz and pressure forces is established. Furthermore, the toroidal/poloidal ratio of the induced magnetic energy becomes less than unity, and the magnetized anti-cyclones are enlarged due to the effect of the magnetic force. Using these key ideas, we investigated the causes of the mode change of magnetoconvection. Considering relatively large magnetic Reynolds number and a rapid rotation rate of this model, we believe that these basic ideas used to interpret the present numerical experiment can be applied to the dynamics in the Earth's and other planetary cores.


自転軸に平行な一様磁場が印加された、高速回転流体球殻の非線形3次元磁気対流の数値実験を通して、磁場と流体運動とのあいだのダイナミックな相互作用を研究した。流体球殻は内部熱源により加熱され、熱対流を起こす。球殻内の平均的磁気レイノルズ数は 22.4 で、自転軸方向に整列した10対のロール状の渦が、安定的に生じた。エルサッサ数 L が 1 から 2 のあいだに起こった、突然の磁気対流のモード変化に関して、高気圧渦への磁束の閉じ込めが重要なはたらきをもっていることがわかった。モード変化が起こった後は、流体球殻は、対流の様式をみずから変えることにより、多くの磁束を内部に閉じ込めることができるようになり、そこではコリオリ力、ローレンツ力および圧力のあいだの磁気地衡流的バランスが成り立つ。さらに、生成する磁気エネルギーのトロイダル:ポロイダル比が1より小さくなり、磁気的な力により、磁化した高気圧渦は大きくなる。こうした事実をもとに、磁気対流のモード変化の原因について考察した。この実験における磁気レイノルズ数が比較的大きいこと、および回転速度が速いことを考慮すると、この数値実験を解釈するのにもちいた基本的な考えは、地球や他の惑星のコア内のダイナミクスに対しても、適用可能であると考える。

A. Sakuraba and M. Kono, "Effect of the inner core on the numerical solution of the magnetohydrodynamic dynamo", Phys. Earth Planet. Inter. 111, 105-121, 1999.

We report two simulation results of the magnetohydrodynamic dynamo applied to rapidly rotating spherical systems using fully nonlinear equations under Boussinesq approximation. Calculations were carried out under the same parameter conditions but for a spherical shell and a sphere. We assume that a uniform internal heat source distributed in the whole sphere drives the convection and dynamo and that the physical properties of the inner core are identical to those of the fluid outer core except for its rigidity. This treatment enables us to compare two cases under the same condition, except the existence of the inner core. Magnetic field is effectively generated by strong velocity shear and helicity of the fluid near the top and bottom boundaries. A stable axial dipole field develops in the case of the spherical shell because of the steady field generation at both the outer and inner boundaries, while the magnetic field in the sphere fluctuates with time from lack of the bottom boundary before it reaches the dipole dominant state at last. This result suggests that the Earth's magnetic field may be stabilized as the inner core grows, even though the total energy input is the same. This study provides a first step to interpret the paleointensity data from the Archaean when there was a transition due to the growth of the inner core.



Publication List