Pub Date : 2019-11-15DOI: 10.1080/03091929.2020.1839896
Andrew D. Gilbert, J. Vanneste
ABSTRACT This paper considers magnetohydrodynamics (MHD) and some of its applications from the perspective of differential geometry, considering the dynamics of an ideal fluid flow and magnetic field on a general three-dimensional manifold, equipped with a metric and an induced volume form. The benefit of this level of abstraction is that it clarifies basic aspects of fluid dynamics such as how certain quantities are transported, how they transform under the action of mappings (e.g. the flow map between Lagrangian labels and Eulerian positions), how conservation laws arise, and the origin of certain approximations that preserve the mathematical structure of classical mechanics. First, the governing equations for ideal MHD are derived in a general setting by means of an action principle and making use of Lie derivatives. The way in which these equations transform under a pull back by the map taking the position of a fluid parcel to a background location is detailed. This is then used to parameterise Alfvén waves using concepts of pseudomomentum and pseudofield, in parallel with the development of Generalised Lagrangian Mean theory in hydrodynamics. Finally non-ideal MHD is considered with a sketch of the development of the Braginsky -dynamo in a general setting. Expressions for the α-tensor are obtained, including a novel geometric formulation in terms of connection coefficients, and related to formulae found elsewhere in the literature.
{"title":"A geometric look at MHD and the Braginsky dynamo","authors":"Andrew D. Gilbert, J. Vanneste","doi":"10.1080/03091929.2020.1839896","DOIUrl":"https://doi.org/10.1080/03091929.2020.1839896","url":null,"abstract":"ABSTRACT This paper considers magnetohydrodynamics (MHD) and some of its applications from the perspective of differential geometry, considering the dynamics of an ideal fluid flow and magnetic field on a general three-dimensional manifold, equipped with a metric and an induced volume form. The benefit of this level of abstraction is that it clarifies basic aspects of fluid dynamics such as how certain quantities are transported, how they transform under the action of mappings (e.g. the flow map between Lagrangian labels and Eulerian positions), how conservation laws arise, and the origin of certain approximations that preserve the mathematical structure of classical mechanics. First, the governing equations for ideal MHD are derived in a general setting by means of an action principle and making use of Lie derivatives. The way in which these equations transform under a pull back by the map taking the position of a fluid parcel to a background location is detailed. This is then used to parameterise Alfvén waves using concepts of pseudomomentum and pseudofield, in parallel with the development of Generalised Lagrangian Mean theory in hydrodynamics. Finally non-ideal MHD is considered with a sketch of the development of the Braginsky -dynamo in a general setting. Expressions for the α-tensor are obtained, including a novel geometric formulation in terms of connection coefficients, and related to formulae found elsewhere in the literature.","PeriodicalId":56132,"journal":{"name":"Geophysical and Astrophysical Fluid Dynamics","volume":"119 1","pages":"436 - 471"},"PeriodicalIF":1.3,"publicationDate":"2019-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77067145","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-11-05DOI: 10.1080/03091929.2019.1682568
Victoria Pereira, A. Fowler
ABSTRACT Oil wells contain two-phase liquid and gas mixtures driven upwards due to a pressure gradient. In this paper, we study a two-fluid model for vertical upwelling flow and explicitly account for the exsolution of the dissolved gas as the pressure decreases along the well. We find that the application of Henry's law for the dissolved gas concentration predicts a rapid transition to a foam, which runs counter to intuition. In order to study ways in which this rapid transition could be avoided, we examine rate limiting non-equilibrium dynamics by incorporating nucleation and bubble growth dynamics in the two-phase model.
{"title":"Exsolving two-phase flow in oil wells","authors":"Victoria Pereira, A. Fowler","doi":"10.1080/03091929.2019.1682568","DOIUrl":"https://doi.org/10.1080/03091929.2019.1682568","url":null,"abstract":"ABSTRACT Oil wells contain two-phase liquid and gas mixtures driven upwards due to a pressure gradient. In this paper, we study a two-fluid model for vertical upwelling flow and explicitly account for the exsolution of the dissolved gas as the pressure decreases along the well. We find that the application of Henry's law for the dissolved gas concentration predicts a rapid transition to a foam, which runs counter to intuition. In order to study ways in which this rapid transition could be avoided, we examine rate limiting non-equilibrium dynamics by incorporating nucleation and bubble growth dynamics in the two-phase model.","PeriodicalId":56132,"journal":{"name":"Geophysical and Astrophysical Fluid Dynamics","volume":"52 1","pages":"283 - 305"},"PeriodicalIF":1.3,"publicationDate":"2019-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75072629","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-10-09DOI: 10.1080/03091929.2019.1670827
J. Philidet, C. Gissinger, F. Lignières, L. Petitdemange
ABSTRACT Stably stratified layers are present in stellar interiors (radiative zones) as well as planetary interiors – recent observations and theoretical studies of the Earth's magnetic field seem to indicate the presence of a thin, stably stratified layer at the top of the liquid outer core. We present direct numerical simulations of this region, which is modelled as an axisymmetric spherical Couette flow for a stably stratified fluid embedded in a dipolar magnetic field. For strong magnetic fields, a super-rotating shear layer, rotating nearly 30% faster than the imposed rotation rate difference between the inner convective dynamo region and the outer boundary, is generated in the stably stratified region. In the Earth context, and contrary to what was previously believed, we show that this super-rotation may extend towards the Earth magnetostrophic regime if the density stratification is sufficiently large. The corresponding differential rotation triggers magnetohydrodynamic instabilities and waves in the stratified region, which feature growth rates comparable to the observed timescale for geomagnetic secular variations and jerks. In the stellar context, we perform a linear analysis which shows that similar instabilities are likely to arise, and we argue that it may play a role in explaining the observed magnetic dichotomy among intermediate-mass stars.
{"title":"Magnetohydrodynamics of stably stratified regions in planets and stars","authors":"J. Philidet, C. Gissinger, F. Lignières, L. Petitdemange","doi":"10.1080/03091929.2019.1670827","DOIUrl":"https://doi.org/10.1080/03091929.2019.1670827","url":null,"abstract":"ABSTRACT Stably stratified layers are present in stellar interiors (radiative zones) as well as planetary interiors – recent observations and theoretical studies of the Earth's magnetic field seem to indicate the presence of a thin, stably stratified layer at the top of the liquid outer core. We present direct numerical simulations of this region, which is modelled as an axisymmetric spherical Couette flow for a stably stratified fluid embedded in a dipolar magnetic field. For strong magnetic fields, a super-rotating shear layer, rotating nearly 30% faster than the imposed rotation rate difference between the inner convective dynamo region and the outer boundary, is generated in the stably stratified region. In the Earth context, and contrary to what was previously believed, we show that this super-rotation may extend towards the Earth magnetostrophic regime if the density stratification is sufficiently large. The corresponding differential rotation triggers magnetohydrodynamic instabilities and waves in the stratified region, which feature growth rates comparable to the observed timescale for geomagnetic secular variations and jerks. In the stellar context, we perform a linear analysis which shows that similar instabilities are likely to arise, and we argue that it may play a role in explaining the observed magnetic dichotomy among intermediate-mass stars.","PeriodicalId":56132,"journal":{"name":"Geophysical and Astrophysical Fluid Dynamics","volume":"76 1","pages":"336 - 355"},"PeriodicalIF":1.3,"publicationDate":"2019-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83038453","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-09-03DOI: 10.1080/03091929.2020.1740925
D. MacTaggart, C. Prior
Evidence for the emergence of twisted flux tubes into the solar atmosphere has, so far, come from indirect signatures. In this work, we investigate the topological input of twisted flux tube emergence directly by studying helicity and winding fluxes. In magnetohydrodynamic simulations with domains spanning from the top of the convection zone to the lower corona, we simulate the emergence of twisted flux tubes with a range of different initial field strengths. One important feature of this work is the inclusion of a convectively unstable layer beneath the photosphere. We find approximately self-similar behaviour in the helicity input for the different field strengths considered. As the tubes rise and reach the photosphere, there is a strong input of negative helicity since we consider left-handed twisted tubes. This phase is then followed by a reduction of the negative input and, for low initial field strengths, a net positive helicity input. This phase corresponds to the growing influence of convection on the field and the development of serpentine field structures during emergence. The winding flux can be used to detect when the twisted cores of the tubes reach the photosphere, giving clear information about the input of topologically complex magnetic field into the solar atmosphere. In short, the helicity and winding fluxes can provide much information about how a magnetic field emerges that is not directly available from other sources, such as magnetograms. In evaluating the helicity content of these simulations, we test numerous means for creating synthetic magnetograms, including methods which account for both the evolving geometry and the finite extent of the photosphere. Whilst the general qualitative behaviours are similar in each case, the different forms of averaging do affect the helicity and winding inputs quantitatively.
{"title":"Helicity and winding fluxes as indicators of twisted flux emergence","authors":"D. MacTaggart, C. Prior","doi":"10.1080/03091929.2020.1740925","DOIUrl":"https://doi.org/10.1080/03091929.2020.1740925","url":null,"abstract":"Evidence for the emergence of twisted flux tubes into the solar atmosphere has, so far, come from indirect signatures. In this work, we investigate the topological input of twisted flux tube emergence directly by studying helicity and winding fluxes. In magnetohydrodynamic simulations with domains spanning from the top of the convection zone to the lower corona, we simulate the emergence of twisted flux tubes with a range of different initial field strengths. One important feature of this work is the inclusion of a convectively unstable layer beneath the photosphere. We find approximately self-similar behaviour in the helicity input for the different field strengths considered. As the tubes rise and reach the photosphere, there is a strong input of negative helicity since we consider left-handed twisted tubes. This phase is then followed by a reduction of the negative input and, for low initial field strengths, a net positive helicity input. This phase corresponds to the growing influence of convection on the field and the development of serpentine field structures during emergence. The winding flux can be used to detect when the twisted cores of the tubes reach the photosphere, giving clear information about the input of topologically complex magnetic field into the solar atmosphere. In short, the helicity and winding fluxes can provide much information about how a magnetic field emerges that is not directly available from other sources, such as magnetograms. In evaluating the helicity content of these simulations, we test numerous means for creating synthetic magnetograms, including methods which account for both the evolving geometry and the finite extent of the photosphere. Whilst the general qualitative behaviours are similar in each case, the different forms of averaging do affect the helicity and winding inputs quantitatively.","PeriodicalId":56132,"journal":{"name":"Geophysical and Astrophysical Fluid Dynamics","volume":"37 1","pages":"85 - 124"},"PeriodicalIF":1.3,"publicationDate":"2019-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73479884","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-08-25DOI: 10.1080/03091929.2019.1653462
J. Reinaud, X. Carton
We consider the interaction between two quasi-geostrophic vortices of height-to-width aspect ratio h/r, lying at two different vertical levels. We investigate whether such structures naturally align. In the case the vortices occupy distinct yet contiguous vertical levels, such an alignment can contribute to the growth in volume of oceanic mesoscale vortices. The other growth mechanism is the merger of vortices sharing common vertical levels. We show that there exist titled equilibrium states where vortices nearly align slantwise. Most equilibria for prolate vortices ( ) are stable apart in a very narrow region of the parameter space. The instability is however normally non-destructive. Pairs of oblate vortices may also be in an unstable equilibria if they are moderately offset in the horizontal direction. In this case, the instability may result in the shedding of filamentary potentially vorticity away from the vortices. This shedding of potential vorticity may result in the further alignment of the main structures.
{"title":"The alignment of two three-dimensional quasi-geostrophic vortices","authors":"J. Reinaud, X. Carton","doi":"10.1080/03091929.2019.1653462","DOIUrl":"https://doi.org/10.1080/03091929.2019.1653462","url":null,"abstract":"We consider the interaction between two quasi-geostrophic vortices of height-to-width aspect ratio h/r, lying at two different vertical levels. We investigate whether such structures naturally align. In the case the vortices occupy distinct yet contiguous vertical levels, such an alignment can contribute to the growth in volume of oceanic mesoscale vortices. The other growth mechanism is the merger of vortices sharing common vertical levels. We show that there exist titled equilibrium states where vortices nearly align slantwise. Most equilibria for prolate vortices ( ) are stable apart in a very narrow region of the parameter space. The instability is however normally non-destructive. Pairs of oblate vortices may also be in an unstable equilibria if they are moderately offset in the horizontal direction. In this case, the instability may result in the shedding of filamentary potentially vorticity away from the vortices. This shedding of potential vorticity may result in the further alignment of the main structures.","PeriodicalId":56132,"journal":{"name":"Geophysical and Astrophysical Fluid Dynamics","volume":"49 1","pages":"524 - 560"},"PeriodicalIF":1.3,"publicationDate":"2019-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82917581","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-08-20DOI: 10.1080/03091929.2019.1654471
J. Boyd
ABSTRACT In an age of billion dollar particle accelerators and Mars rovers, it is surprising that solitary waves were first discovered by a man on horseback with no tools but his own eyes. A century and a half later, more complicated patterns of ridges, so-called hyperelliptic two-polycnoidal waves, were discovered in the ocean during a beach vacation. The inverse scattering method, which solves nonlinear partial differential equations through a sequence of solving purely linear equations, is a blend of quantum theory and hydrodynamics that arose from informal, unstructured conversations (i.e. goofing off) among a group of postdocs from different disciplines who were randomly assigned to the same office. The cnoidal wave in the lemniscate case is well-approximated by a nonlinear solitary wave and equally well approximated by a linear sine wave. It is always and exactly the superposition of solitary waves even in the limit in which it is an infinitesimal sine wave. The history and science of solitary waves has the disorienting quality of an M. C. Escher drawing. Here, we cannot give an understanding of these deep subjects in so brief an article; rather we strive to unveil the beauty and unexpectedness of these topics to give the reader a reason to pursue these in the much more comprehensive reviews and books we cite. Further, we stress the “scotomas” (blind spots), misconceptions and surprises, the sociology and epistemology of science. It is true that failed theories, scotomas, serendipity and cognitive saltation (progress in jumps) is characteristic of science. It is also true that the invention of the train was the invention of the train wreck. Engineering learns from each disaster and science should do the same. The highly nonlinear history of nonlinear waves is reported not to disrespect the past but to replace scientific fatalism with a constructive wariness. We are not smarter or more enlightened than Scott Russell or Stokes or Landau, but we can learn from their scotomas and misconceptions as much as from their triumphs.
{"title":"Miracles, misconceptions and scotomas in the theory of solitary waves","authors":"J. Boyd","doi":"10.1080/03091929.2019.1654471","DOIUrl":"https://doi.org/10.1080/03091929.2019.1654471","url":null,"abstract":"ABSTRACT In an age of billion dollar particle accelerators and Mars rovers, it is surprising that solitary waves were first discovered by a man on horseback with no tools but his own eyes. A century and a half later, more complicated patterns of ridges, so-called hyperelliptic two-polycnoidal waves, were discovered in the ocean during a beach vacation. The inverse scattering method, which solves nonlinear partial differential equations through a sequence of solving purely linear equations, is a blend of quantum theory and hydrodynamics that arose from informal, unstructured conversations (i.e. goofing off) among a group of postdocs from different disciplines who were randomly assigned to the same office. The cnoidal wave in the lemniscate case is well-approximated by a nonlinear solitary wave and equally well approximated by a linear sine wave. It is always and exactly the superposition of solitary waves even in the limit in which it is an infinitesimal sine wave. The history and science of solitary waves has the disorienting quality of an M. C. Escher drawing. Here, we cannot give an understanding of these deep subjects in so brief an article; rather we strive to unveil the beauty and unexpectedness of these topics to give the reader a reason to pursue these in the much more comprehensive reviews and books we cite. Further, we stress the “scotomas” (blind spots), misconceptions and surprises, the sociology and epistemology of science. It is true that failed theories, scotomas, serendipity and cognitive saltation (progress in jumps) is characteristic of science. It is also true that the invention of the train was the invention of the train wreck. Engineering learns from each disaster and science should do the same. The highly nonlinear history of nonlinear waves is reported not to disrespect the past but to replace scientific fatalism with a constructive wariness. We are not smarter or more enlightened than Scott Russell or Stokes or Landau, but we can learn from their scotomas and misconceptions as much as from their triumphs.","PeriodicalId":56132,"journal":{"name":"Geophysical and Astrophysical Fluid Dynamics","volume":"139 1","pages":"623 - 666"},"PeriodicalIF":1.3,"publicationDate":"2019-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86537165","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-07-29DOI: 10.1080/03091929.2019.1643849
P. Bourdin
ABSTRACT The quality of today's research is often tightly limited to the available computing power and scalability of codes to many processors. For example, tackling the problem of heating the solar corona requires a most realistic description of the plasma dynamics and the magnetic field. Numerically solving such a magneto-hydrodynamical (MHD) description of a small active region (AR) on the Sun requires millions of computation hours on current high-performance computing (HPC) hardware. The aim of this work is to describe methods for an efficient parallelisation of boundary conditions and data input/output (IO) strategies that allow for a better scaling towards thousands of processors (CPUs). The Pencil Code is tested before and after optimisation to compare the performance and scalability of a coronal MHD model above an AR. We present a novel boundary condition for non-vertical magnetic fields in the photosphere, where we approach the realistic pressure increase below the photosphere. With that, magnetic flux bundles become narrower with depth and the flux density increases accordingly. The scalability is improved by more than one order of magnitude through the HPC-friendly boundary conditions and IO strategies. This work describes also the necessary nudging methods to drive the MHD model with observed magnetic fields from the Sun's photosphere. In addition, we present the upper and lower atmospheric boundary conditions (photospheric and towards the outer corona), including swamp layers to diminish perturbations before they reach the boundaries. Altogether, these methods enable more realistic 3D MHD simulations than previous models regarding the coronal heating problem above an AR – simply because of the ability to use a large amount of CPUs efficiently in parallel.
{"title":"Driving solar coronal MHD simulations on high-performance computers","authors":"P. Bourdin","doi":"10.1080/03091929.2019.1643849","DOIUrl":"https://doi.org/10.1080/03091929.2019.1643849","url":null,"abstract":"ABSTRACT The quality of today's research is often tightly limited to the available computing power and scalability of codes to many processors. For example, tackling the problem of heating the solar corona requires a most realistic description of the plasma dynamics and the magnetic field. Numerically solving such a magneto-hydrodynamical (MHD) description of a small active region (AR) on the Sun requires millions of computation hours on current high-performance computing (HPC) hardware. The aim of this work is to describe methods for an efficient parallelisation of boundary conditions and data input/output (IO) strategies that allow for a better scaling towards thousands of processors (CPUs). The Pencil Code is tested before and after optimisation to compare the performance and scalability of a coronal MHD model above an AR. We present a novel boundary condition for non-vertical magnetic fields in the photosphere, where we approach the realistic pressure increase below the photosphere. With that, magnetic flux bundles become narrower with depth and the flux density increases accordingly. The scalability is improved by more than one order of magnitude through the HPC-friendly boundary conditions and IO strategies. This work describes also the necessary nudging methods to drive the MHD model with observed magnetic fields from the Sun's photosphere. In addition, we present the upper and lower atmospheric boundary conditions (photospheric and towards the outer corona), including swamp layers to diminish perturbations before they reach the boundaries. Altogether, these methods enable more realistic 3D MHD simulations than previous models regarding the coronal heating problem above an AR – simply because of the ability to use a large amount of CPUs efficiently in parallel.","PeriodicalId":56132,"journal":{"name":"Geophysical and Astrophysical Fluid Dynamics","volume":"100 1","pages":"235 - 260"},"PeriodicalIF":1.3,"publicationDate":"2019-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79307679","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-07-04DOI: 10.1080/03091929.2019.1636046
Zihua Liu, R. Grimshaw, E. Johnson
ABSTRACT In this study, we examine the transformation of a mode-1 internal solitary wave incident on a bottom step, and the consequent generation of mode-2 internal solitary waves. A linear long-wave theory of mode coupling in the vicinity of the step is used to estimate the mode-1 and mode-2 wave reflection and transmission coefficients, and hence the energy fluxes. Away from the step, the wave evolution of the transmitted and reflected waves is simulated by the Korteweg–de Vries equation. Specific calculations are made using a three-layer fluid model. Three different regimes based on the layer thicknesses are examined and discussed in detail for either depression or elevation mode-1 incident waves. The common features found are that the transmitted waves (mainly mode-1) are the dominant part; most of the incident energy is transmitted and only a small part is reflected. The amplitudes of the generated mode-2 waves and the reflected mode-1 waves increase when either the upper- or middle-layer thickness increases. When the lower layer is thin enough, the amplitude of the transmitted mode-2 wave can be larger than the mode-1 waves, and the reflected energy can increase considerably which we infer may be due to a blocking effect of the step on the lower layer. The evolution away from the step is either fission into several solitary waves, or the development of a rarefaction wave followed by an undular bore, depending on the relative signs of the wave amplitudes and the nonlinear coefficient in the Korteweg–de Vries equation.
{"title":"The interaction of a mode-1 internal solitary wave with a step and the generation of mode-2 waves","authors":"Zihua Liu, R. Grimshaw, E. Johnson","doi":"10.1080/03091929.2019.1636046","DOIUrl":"https://doi.org/10.1080/03091929.2019.1636046","url":null,"abstract":"ABSTRACT In this study, we examine the transformation of a mode-1 internal solitary wave incident on a bottom step, and the consequent generation of mode-2 internal solitary waves. A linear long-wave theory of mode coupling in the vicinity of the step is used to estimate the mode-1 and mode-2 wave reflection and transmission coefficients, and hence the energy fluxes. Away from the step, the wave evolution of the transmitted and reflected waves is simulated by the Korteweg–de Vries equation. Specific calculations are made using a three-layer fluid model. Three different regimes based on the layer thicknesses are examined and discussed in detail for either depression or elevation mode-1 incident waves. The common features found are that the transmitted waves (mainly mode-1) are the dominant part; most of the incident energy is transmitted and only a small part is reflected. The amplitudes of the generated mode-2 waves and the reflected mode-1 waves increase when either the upper- or middle-layer thickness increases. When the lower layer is thin enough, the amplitude of the transmitted mode-2 wave can be larger than the mode-1 waves, and the reflected energy can increase considerably which we infer may be due to a blocking effect of the step on the lower layer. The evolution away from the step is either fission into several solitary waves, or the development of a rarefaction wave followed by an undular bore, depending on the relative signs of the wave amplitudes and the nonlinear coefficient in the Korteweg–de Vries equation.","PeriodicalId":56132,"journal":{"name":"Geophysical and Astrophysical Fluid Dynamics","volume":"38 1","pages":"327 - 347"},"PeriodicalIF":1.3,"publicationDate":"2019-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80018171","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-07-04DOI: 10.1080/03091929.2019.1640876
D. Miller
ABSTRACT The Archontis dynamo is a rare example of an MHD dynamo within which forcing drives a dynamo where the flow and magnetic fields are almost perfectly aligned and the energies are approximately equal. In this paper, I expand upon our knowledge of the dynamo by showing that the intermediate steady states of the kinetic and magnetic energies observed by Cameron and Galloway are not a necessary feature of aligned dynamos. Furthermore, I show that the steady state into which the flow and magnetic fields eventually evolve is remarkably robust to the addition of time dependence and asymmetry to the forcing.
{"title":"Evolution of aligned states within nonlinear dynamos","authors":"D. Miller","doi":"10.1080/03091929.2019.1640876","DOIUrl":"https://doi.org/10.1080/03091929.2019.1640876","url":null,"abstract":"ABSTRACT The Archontis dynamo is a rare example of an MHD dynamo within which forcing drives a dynamo where the flow and magnetic fields are almost perfectly aligned and the energies are approximately equal. In this paper, I expand upon our knowledge of the dynamo by showing that the intermediate steady states of the kinetic and magnetic energies observed by Cameron and Galloway are not a necessary feature of aligned dynamos. Furthermore, I show that the steady state into which the flow and magnetic fields eventually evolve is remarkably robust to the addition of time dependence and asymmetry to the forcing.","PeriodicalId":56132,"journal":{"name":"Geophysical and Astrophysical Fluid Dynamics","volume":"59 1","pages":"405 - 423"},"PeriodicalIF":1.3,"publicationDate":"2019-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74056390","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-07-02DOI: 10.1080/03091929.2019.1640875
L. Silva, J. Mather, Radostin D Simitev
ABSTRACT Double-diffusive convection driven by both thermal and compositional buoyancy in a rotating spherical shell can exhibit a rather large number of behaviours often distinct from that of the single diffusive system. In order to understand how the differences in thermal and compositional molecular diffusivities determine the dynamics of thermo-compositional convection we investigate numerically the linear onset of convective instability in a double-diffusive setup. We construct an alternative equivalent formulation of the non-dimensional equations where the linearised double-diffusive problem is described by an effective Rayleigh number, , measuring the amplitude of the combined buoyancy driving, and a second parameter, α, measuring the mixing of the thermal and compositional contributions. This formulation is useful in that it allows for the analysis of several limiting cases and reveals dynamical similarities in the parameters space which are not obvious otherwise. We analyse the structure of the critical curves in this space, explaining asymptotic behaviours in α, transitions between inertial and diffusive regimes, and transitions between large-scale (fast drift) and small-scale (slow drift) convection. We perform this analysis for a variety of diffusivities, rotation rates and shell aspect ratios showing where and when new modes of convection take place.
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