Non-linear waves interactions in rotating shallow water magnetohydrodynamics

2020 ◽  
Author(s):  
Dmitry Klimachkov ◽  
Arakel Petrosyan
Keyword(s):  
Magnetic Field ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Plasma Layer ◽  
Vertical Component ◽  
Vertical Magnetic Field ◽  
Amplitude Equations ◽  
Horizontal Magnetic Field ◽  
Non Linear ◽  
Poincare Waves

<p>This study is devoted to the development of the nonlinear theory of the magneto-Poincare waves and magnetostrophic waves in rotating layers of astrophysical and space plasma in the shallow-water approximation. These waves determine the large-scale dynamics of the various astrophysical and space objects such as solar tachocline, as well as  magnetoactive atmospheres of exoplanets trapped by tides of a carrier star, neutron stars atmospheres and the flows in accretion disks of neutron stars. For this purpose we derived magnetohydrodynamic shallow water equations with a rotation and presence of an external vertical magnetic field. The system is obtained from conventional magnetohydrodynamic equations for incompressible inviscid heavy plasma layer with free surface in an external vertical magnetic field. The pressure is assumed to be hydrostatic, and the height of the plasma layer is considered to be much smaller than horizontal scales of the flow. The magnetohydrodynamic equations in the shallow-water approximation play equally important role in the space and astrophysical plasma flows like classical shallow-water equations in the fluid dynamics of a neutral fluid. The magnetohydrodynamic shallow water equations with an external vertical magnetic field are modified by supplementing them with the equation for the vertical component of the magnetic field and divergence-free condition for magnetic field contains its vertical component. Thus the velocity field remains two-dimensional while the magnetic field becomes three-dimensional. It is shown that the presence of a vertical magnetic field significantly changes the dynamics of the wave processes in astrophysical plasma compared to the neutral fluid and plasma layer in a horizontal magnetic field.  We have investigated the interaction of Magneto-Poincare waves and magnetostrophic waves in the magnetohydrodynamic shallow water flows in external vertical magnetic field and in horizontal (toroidal and poloidal) magnetic field. In the absence of the horizontal magnetic field the dynamics of plasma appears to be similar to the neutral fluid dynamics and it is shown that there are four-waves interactions in this case. Using the asymptotic multiscale method we obtained the non-linear amplitude equations for the three interacting Magneto-Poincare waves and magnetostrophic waves. The analysis of the amplitude equations shows that there are two types of instabilities for four different types of three-waves configurations. These instabilities occur in both cases: in the external vertical magnetic field and in the horizontal magnetic field. For all types of instabilities the growth rates are found. In the absence of the vertical magnetic field we obtained the non-linear amplitude equations for the four interacting waves. It is shown that the resulting system of equations has the first integrals that describe the mechanism of energy transfer among interacting waves of small amplitude. This work was supported by the Russian Foundation for Basic Research (project no. 19-02-00016).</p>

scholarly journals Properties of the inner penumbral boundary and temporal evolution of a decaying sunspot

2018 ◽  
Vol 620 ◽  
pp. A191 ◽  
Author(s):  
M. Benko ◽  
S. J. González Manrique ◽  
H. Balthasar ◽  
P. Gömöry ◽  
C. Kuckein ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Magnetic Flux ◽  
Temporal Evolution ◽  
Vertical Component ◽  
Field Vector ◽  
Linear Increase ◽  
Vertical Magnetic Field ◽  
Magnetic Diffusion ◽  
The Magnetic Field ◽  
Linear Decay

Context. It has been empirically determined that the umbra-penumbra boundaries of stable sunspots are characterized by a constant value of the vertical magnetic field. Aims. We analyzed the evolution of the photospheric magnetic field properties of a decaying sunspot belonging to NOAA 11277 between August 28–September 3, 2011. The observations were acquired with the spectropolarimeter on-board of the Hinode satellite. We aim to prove the validity of the constant vertical magnetic-field boundary between the umbra and penumbra in decaying sunspots. Methods. A spectral-line inversion technique was used to infer the magnetic field vector from the full-Stokes profiles. In total, eight maps were inverted and the variation of the magnetic properties in time were quantified using linear or quadratic fits. Results. We find a linear decay of the umbral vertical magnetic field, magnetic flux, and area. The penumbra showed a linear increase of the vertical magnetic field and a sharp decay of the magnetic flux. In addition, the penumbral area quadratically decayed. The vertical component of the magnetic field is weaker on the umbra-penumbra boundary of the studied decaying sunspot compared to stable sunspots. Its value seem to be steadily decreasing during the decay phase. Moreover, at any time of the sunspot decay shown, the inner penumbra boundary does not match with a constant value of the vertical magnetic field, contrary to what is seen in stable sunspots. Conclusions. During the decaying phase of the studied sunspot, the umbra does not have a sufficiently strong vertical component of the magnetic field and is thus unstable and prone to be disintegrated by convection or magnetic diffusion. No constant value of the vertical magnetic field is found for the inner penumbral boundary.

scholarly journals Multi-point ground-based ULF magnetic field observations in Europe during seismic active periods in 2004 and 2005

2008 ◽  
Vol 8 (3) ◽  
pp. 501-507 ◽  
Author(s):  
G. Prattes ◽  
K. Schwingenschuh ◽  
H. U. Eichelberger ◽  
W. Magnes ◽  
M. Boudjada ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Field Intensity ◽  
Seismic Activity ◽  
Magnetic Field Intensity ◽  
Field Measurements ◽  
Fluxgate Magnetometer ◽  
Vertical Magnetic Field ◽  
Earthquake Epicenter ◽  
Electromagnetic Noise ◽  
Horizontal Magnetic Field

Abstract. We present the results of ground-based Ultra Low Frequency (ULF) magnetic field measurements observed from June to August 2004 during the Bovec earthquake on 12 July 2004. Further we give information about the seismic activity in the local observatory region for an extended time span 2004 and 2005. ULF magnetic field data are provided by the South European Geomagnetic Array (SEGMA) where the experience and heritage from the CHInese MAGnetometer (CHIMAG) fluxgate magnetometer comes to application. The intensities of the horizontal H and vertical Z magnetic field and the polarization ratio R of the vertical and horizontal magnetic field intensity are analyzed taking into consideration three SEGMA observatories located at different close distances and directions from the earthquake epicenter. We observed a significant increase of high polarization ratios during strong seismic activity at the observatory nearest to the Bovec earthquake epicenter. Apart from indirect ionospheric effects electromagnetic noise could be emitted in the lithosphere due to tectonic effects in the earthquake focus region causing anomalies of the vertical magnetic field intensity. Assuming that the measured vertical magnetic field intensities are of lithospheric origin, we roughly estimate the amplitude of electromagnetic noise in the Earths crust considering an average electrical conductivity of <σ>=10−3 S/m and a certain distance of the observatory to the earthquake epicenter.

scholarly journals THE ADJOINT PROBLEM IN THE PRESENCE OF A DEFORMED SURFACE: THE EXAMPLE OF THE ROSENSWEIG INSTABILITY ON MAGNETIC FLUIDS

2002 ◽  
Vol 16 (08) ◽  
pp. 1155-1170 ◽  
Author(s):  
ADRIAN LANGE
Keyword(s):  
Magnetic Field ◽  
A Priori ◽  
Adjoint Operator ◽  
Horizontal Layer ◽  
Adjoint Problem ◽  
Vertical Magnetic Field ◽  
Amplitude Equations ◽  
Rosensweig Instability ◽  
Pattern Forming ◽  
Almost All

The Rosensweig instability is the phenomenon that above a certain threshold of a vertical magnetic field peaks appear on the free surface of a horizontal layer of magnetic fluid. In contrast to almost all classical hydrodynamical systems, the nonlinearities of the Rosensweig instability are entirely triggered by the properties of a deformed and a priori unknown surface. The resulting problems in defining an adjoint operator for such nonlinearities are illustrated. The implications concerning amplitude equations for pattern forming systems with a deformed surface are discussed.

THE EFFECT OF OVERBURDEN ON VERTICAL COMPONENT ANOMALIES IN AFMAG AND VLF EXPLORATION: A COMPUTER MODEL STUDY

Geophysics ◽  
1971 ◽  
Vol 36 (1) ◽  
pp. 53-57 ◽  
Author(s):  
K. Vozoff
Keyword(s):  
Magnetic Field ◽  
Computer Model ◽  
Field Component ◽  
Vertical Component ◽  
Vertical Magnetic Field ◽  
Model Study ◽  
Strike Direction ◽  
Overburden Thickness ◽  
Direction Model ◽  
Analog Models

New computer techniques permit the calculation of AFMAG and VLF anomalies in the vertical magnetic field component for situations which cannot be conveniently modeled with analog models. Conductivity and geometry of the “ore” zone, the overburden, and the bedrock can all be varied independently; although all must have the same strike direction. Model results accurate to about 10 percent can be obtained at negligible cost. One example shows how a decrease in overburden resistivity from 100 ohm‐m to 10 ohm‐m can obliterate a distinct AFMAG anomaly. An increase of overburden thickness from 20 m to 50 m has the same effect. This study shows the importance of obtaining some direct overburden resistivity data before ruling out areas which show no anomalies.

scholarly journals OSCILLATIONS OF SEMI-ENCLOSED WATER BODY INDUCED BY HURRICANES

2011 ◽  
Vol 1 (32) ◽  
pp. 41 ◽  
Author(s):  
Paul Yuan-Hung Tan ◽  
Jiin-Jen Lee
Keyword(s):  
Shallow Water ◽  
Hurricane Katrina ◽  
Water Body ◽  
Shallow Water Equations ◽  
Present Model ◽  
Storm Surges ◽  
Non Linear ◽  
Major Application ◽  
Primary Focus ◽  
Volume Method

The primary focus of this research is to study the oscillations of semi-enclosed water body induced by hurricanes. The physical mechanisms of the wind-induced oscillation (storm surge) in a semi-enclosed water body are analyzed by the depth-averaged, non-linear shallow-water equations. The numerical model using the finite-volume method (FVM) to solve the depth-averaged, non-linear shallow-water equations is developed and the present model is verified by the intensive field data reported by IPET. The present model is further applied to the investigation of the oscillations (storm surges) in Lake Pontchartrain induced by the winds generated by four synthetic hurricanes within the time-span of 00:00 UTC August 29 to 00:00 UTC August 30, 2005: 1.Hurricane Katrina tracking on its original route, 2.Hurricane Katrina tracking 36 km west of its original route, 3.Hurricane Katrina tracking 72 km west of its original route, and 4.Hurricane Katrina tracking on its original route with reduced forward speeds. The major application of the present model is to assist the design of the water-front structure surrounding the semi-enclosed water body that has been influenced by the oscillations induced by hurricanes. The numerical simulations generated by the present model can help the planners to determine a better strategy of the hurricane protection systems surrounding the communities of the semi-enclosed water body.

Rotating Shallow-Water Models with Full Coriolis Force

2018 ◽  
Author(s):  
Vladimir Zeitlin
Keyword(s):  
Shallow Water ◽  
Coriolis Force ◽  
Shallow Water Equations ◽  
Vertical Component ◽  
Tangent Plane ◽  
Water Model ◽  
Shallow Water Models ◽  
Water Models ◽  
Rotating Shallow Water ◽  
Rotating Shallow Water Equations

The derivation of the rotating shallow-water model by vertical averaging is carried on in the tangent plane approximation without neglecting the vertical component of the Coriolis force, and contributions of the vertical component of velocity in its horizontal component (‘non-traditional’ terms), leading to one- and two-layer ‘non-traditional’ rotating shallow-water models. A similar approach on the whole sphere encounters difficulties with conservation of angular momentum. Consistent ‘non-traditional’ rotating shallow-water equations in this case are obtained from the variational principle, which is first formulated for full primitive equations. It is shown that columnar motion hypothesis should be replaced by solid-angle motion one on the sphere. Two-layer non-traditional rotating shallow-water equations are used to analyse inertial instability of jets and compare the results with Chapter 10. It is shown that non-traditional terms can increase the growth rates up to 30% in some configurations and can also change the structure of the unstable modes.

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