Rotating magnetic shallow water waves and instabilities in a sphere

Márquez-Artavia, Xiomara; Jones, C. A.; Tobias, Steven M.

doi:10.1080/03091929.2017.1301937

Cited by 40 publications

(42 citation statements)

References 38 publications

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“…The goal of the extended beta-plane approximation is to provide a systematic way of retaining some of these higher order terms. To achieve this goal we transform the governing equations in Section 2 from spherical coordinates (r, θ, λ) to coordinates (z, y, λ), where the new meridional coordinate, y, is defined by The same choice is made for the meridional coordinate in the studies of Zaqarashvili et al (2007) and Marquez-Artavia et al (2017). The vertical coordinate, z = r − R, is referenced to the core-mantle boundary.…”

Section: E X T E N D E D B E Ta -P L a N E A P P Ro X I M At I O Nmentioning

confidence: 99%

Equatorially trapped waves in Earth’s core

Buffett

Matsui

2019

Geophysical Journal International

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Short-period fluctuations in geomagnetic acceleration are detected in recent satellite observations. A major component of this signal is confined to the equatorial region, suggesting the presence of equatorial waves, but the precise nature of these waves is not known. We explore the possibility that these waves arise from an interplay of magnetic, Archimedes and Coriolis forces in a stratified layer at the top of the core (sometimes called MAC waves). We adopt a beta-plane approximation and show that low-frequency MAC waves are not trapped near the equator when the root-mean-square (rms) radial magnetic field is constant over the surface of the core-mantle boundary. However, equatorial trapped MAC waves emerge when the rms radial magnetic field increases towards the poles. Further confinement of MAC waves occurs when we account for the leading-order effects of spherical geometry. The resulting MAC waves propagate to the east with phase velocities that depend strongly on the thickness of the stratified layer. Waves with periods less than 10 yr are predicted when the layer thickness is less than 30 km. These waves have low quality factors, Q ≈ 1, which means that they propagate only a few thousand kilometers before being dissipated by ohmic losses. Evidence for eastward and westward propagating disturbances in the observations may reflect a superposition of wave propagation and forced motion by an excitation source. Separation of the source from the wave propagation may be possible if the source is due mainly to westward drifting plumes in the equatorial region.

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Section: E X T E N D E D B E Ta -P L a N E A P P Ro X I M At I O Nmentioning

confidence: 99%

Equatorially trapped waves in Earth’s core

Buffett

Matsui

2019

Geophysical Journal International

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“…The observation of accretion-powered pulsations indicates that the source has a strong magnetic field (see Poutanen 2006). The presence of a magnetic field may significantly alter the mode (for instance, see calculations by Heng &Spitkovsky (2009) andMárquez-Artavia et al (2017)). The nature of TBOs observed from such sources, however, is quite different from those with no accretionpowered pulsations observed.…”

Section: Comparison With Observed Tbo Frequencies and Driftsmentioning

confidence: 99%

Relativistic ocean r-modes during type-I X-ray bursts

Chambers

Watts

2019

Monthly Notices of the Royal Astronomical Society

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Accreting neutron stars (NS) can exhibit high frequency modulations in their lightcurves during thermonuclear X-ray bursts, known as burst oscillations. These frequencies can be offset from the NS spin frequency by several Hz (where known independently) and can drift by 1 − 3 Hz. One plausible explanation is that a wave is present in the bursting ocean, the rotating frame frequency of which is the offset. The frequency of the wave should decrease (in the rotating frame) as the burst cools hence explaining the drift. A strong candidate is a buoyant r-mode. To date, models that calculated the frequency of this mode taking into account the radial structure neglected relativistic effects and predicted rotating frame frequencies of ∼ 4 Hz and frequency drifts of > 5 Hz; too large to be consistent with observations. We present a calculation that includes frame-dragging and gravitational redshift that reduces the rotating frame frequency by up to 30% and frequency drift by up to 20%. Updating previous models for the ocean cooling in the aftermath of the burst to a model more representative of detailed calculations of thermonuclear X-ray bursts reduces the frequency of the mode still further. This model, combined with relativistic effects, can reduce the rotating frequency of the mode to ∼ 2 Hz and frequency drift to ∼ 2 Hz, which is closer to the observed values.

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“…Las propiedades físicas de las ondas magnéticas de Rossby han sido predichas matemáticamente por varios autores (Márquez-Artavia et al, 2017, Gilman et al, 2002, Zaqarashvili et al, 2015. Márquez-Artavia et al (2017) han descrito exhaustivamente el comportamiento de las ondas magnéticas de Rossby en la presencia de un campo magnético tanto débil como fuerte y en un sistema tanto con rotación rápida como lenta, esto es un modelo que contempla un cascarón esférico de fluido conductor inmerso en un campo magnético de tipo toroidal, ver la Figura 2.…”

Section: Características De Las Ondas Magnéticas De Rossbyunclassified

“…El modelo matemático denominado "MHD ShallowWater" o la aproximación magnetohidrodinámica de la capa de fluido, (Márquez-Artavia et al, 2017, Zaqarashvili et al, 2015, ha predicho la presencia de ondas en capas delgadas de fluido, como la tacoclina, y recientemente se ha sugerido que si estas ondas se generan en la tacoclina su efecto puede manifestarse en la superficie solar, (Dikpati et al, 2017).…”

Section: Introductionunclassified

“…Como esta frecuencia es proporcional a la cuarta potencia del campo magnético, hace que su valor sea muy pequeño lo que provoca que la onda sea muy lenta, con periodos muy largos. Sin embargo si el campo magnético se incrementa, todas las ondas magnéticas de Rossby tienden a confinarse en los polos, para el caso de la cáscara esférica de fluido, este comportamiento ha sido notado por otros autores también, (Márquez-Artavia et al, 2017, Heng et al, 2009.…”

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Descifrando el clima espacial: ciclos solares y ondas magnéticas de Rossby

Márquez-Artavia¹

2019

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El objetivo de esta investigación es explorar si existe una relación entre las ondas magnéticas de Rossby rápidas o lentas y ciertas observaciones de la actividad solar de largo y muy largo plazo (meses, años, décadas…). El artículo intenta mostrar si los periodos de esas ondas y sus características corresponden a los valores de duración los ciclos de Rieger, Haly, o bien cuasiperiodos de llamaradas y eyecciones de masa coronal. Se inicia con una revisión bibliográfica y un resumen de los resultados de una tesis doctoral que resuelve completamente el modelo matemático en cuestión, con las ecuaciones derivadas de ese trabajo previo, se calcula los periodos de las ondas que serán comparados con las observaciones. Estos resultados teóricos sugieren que cierta actividad solar podría deberse a las ondas magnéticas de Rossby, originadas en el interior del Sol, específicamente en la tacoclina. Las ondas lentas se proponen ligadas a las periodicidades de largo y muy largo plazo y las ondas rápidas de Rossby se asocian con periodicidades de unos años a meses. El estudio de estas perturbaciones de Rossby y sus propiedades, sin duda, va a ayudar a comprender el origen y las características del campo magnético del Sol.

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Rotating magnetic shallow water waves and instabilities in a sphere

Abstract: This is a repository copy of Rotating magnetic shallow water waves and instabilities in a sphere.

Cited by 40 publications

References 38 publications

Equatorially trapped waves in Earth’s core

Equatorially trapped waves in Earth’s core

Relativistic ocean r-modes during type-I X-ray bursts

Descifrando el clima espacial: ciclos solares y ondas magnéticas de Rossby

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