Constraints on the magnetic field within a stratified outer core. (arXiv:1912.02213v1 [physics.geo-ph])

<a href="http://arxiv.org/find/physics/1/au:+Hardy_C/0/1/0/all/0/1">Colin M Hardy</a>, <a href="http://arxiv.org/find/physics/1/au:+Livermore_P/0/1/0/all/0/1">Philip W Livermore</a>, <a href="http://arxiv.org/find/physics/1/au:+Niesen_J/0/1/0/all/0/1">Jitse Niesen</a>

Mounting evidence from both seismology and experiments on core composition

suggests the existence of a layer of stably stratified fluid at the top of

Earth’s outer core. In this work we examine the structure of the geomagnetic

field within such a layer, building on the important but little known work of

Malkus (1979). We assume (i) an idealised magnetostrophic spherical model of

the geodynamo neglecting inertia, viscosity and the solid inner core, and (ii)

a strongly stratified layer of constant depth immediately below the outer

boundary within which there is no spherically radial flow. Due to the

restricted dynamics, Malkus showed that the geomagnetic field must obey a

certain condition which is a more restrictive version of the condition of

Taylor (1963). The nonlinear nature of these constraints makes finding a

magnetic field that obeys them, here termed a Malkus state, a challenging task.

Nevertheless, such Malkus states when constrained further by geomagnetic

observations have the potential to probe the interior of the core. By focusing

on a particular class of magnetic fields for which the Malkus constraints are

linear, we describe a constructive method that turns any purely-poloidal field

into an exact Malkus state by adding a suitable toroidal field. We consider

poloidal fields following a prescribed smooth profile within the core that

match observation-derived models of the magnetic field in either epoch 2015 or

the 10000-yr time averaged field. Multiple possible solutions for the toroidal

field exist, hence we determine the Malkus state of miumum toroidal energy and

we find that it has a strong azimuthal toroidal field, larger than the observed

poloidal component at the core-mantle boundary. For the 2015 field for a layer

of depth 300 km, we estimate a root mean squared azimuthal toroidal field of 3

mT with a pointwise maximum of 8 mT occurring at a depth of about 70 km.

Mounting evidence from both seismology and experiments on core composition

suggests the existence of a layer of stably stratified fluid at the top of

Earth’s outer core. In this work we examine the structure of the geomagnetic

field within such a layer, building on the important but little known work of

Malkus (1979). We assume (i) an idealised magnetostrophic spherical model of

the geodynamo neglecting inertia, viscosity and the solid inner core, and (ii)

a strongly stratified layer of constant depth immediately below the outer

boundary within which there is no spherically radial flow. Due to the

restricted dynamics, Malkus showed that the geomagnetic field must obey a

certain condition which is a more restrictive version of the condition of

Taylor (1963). The nonlinear nature of these constraints makes finding a

magnetic field that obeys them, here termed a Malkus state, a challenging task.

Nevertheless, such Malkus states when constrained further by geomagnetic

observations have the potential to probe the interior of the core. By focusing

on a particular class of magnetic fields for which the Malkus constraints are

linear, we describe a constructive method that turns any purely-poloidal field

into an exact Malkus state by adding a suitable toroidal field. We consider

poloidal fields following a prescribed smooth profile within the core that

match observation-derived models of the magnetic field in either epoch 2015 or

the 10000-yr time averaged field. Multiple possible solutions for the toroidal

field exist, hence we determine the Malkus state of miumum toroidal energy and

we find that it has a strong azimuthal toroidal field, larger than the observed

poloidal component at the core-mantle boundary. For the 2015 field for a layer

of depth 300 km, we estimate a root mean squared azimuthal toroidal field of 3

mT with a pointwise maximum of 8 mT occurring at a depth of about 70 km.

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