Pub Date : 2020-05-13DOI: 10.1080/03091929.2020.1761350
Yufeng Lin, J. Noir
Several planetary bodies in our solar system undergo a forced libration owing to gravitational interactions with their orbital companions, leading to complex fluid motions in their metallic liquid cores or subsurface oceans. In this study, we numerically investigate flows in longitudinally librating spherical shells. We focus on the Ekman number dependencies of several shear layers when the libration frequency is less than twice of the rotation frequency and the libration amplitude is small. Time-dependent flows mainly consist of inertial waves excited at the critical latitudes due to the Ekman pumping singularities, forming conical shear layers. In particular, previous theoretical studies have proposed different scalings for the conical shear layers spawned from the critical latitudes at the inner boundary. Our numerical results favour the velocity amplitude scaling predicted by Le Dizès & Le Bars (J. Fluid Mech. 2017, 826, 653) over the scaling initially proposed by Kerswell (J. Fluid Mech. 1995, 298, 311), though the Ekman numbers in our calculations are not sufficiently small to pin down this scaling. Non-linear interactions in the boundary layers drive a mean zonal flow with several geostrophic shears. Our numerical results show that geostrophic shears associated with the critical latitudes at the inner and outer boundaries exhibit the same scalings, i.e. an amplitude of over a width of . Apart from the geostrophic shear associated with the critical latitude, our numerical results show that the reflection of inertial waves can induce a geostrophic shear with an amplitude of over a width of . As the amplitude of the geostrophic shears increases as reducing the Ekman number, the geostrophic shears in the mean flows may be significant in planetary cores and subsurface oceans given small Ekman numbers of these systems.
{"title":"Libration-driven inertial waves and mean zonal flows in spherical shells","authors":"Yufeng Lin, J. Noir","doi":"10.1080/03091929.2020.1761350","DOIUrl":"https://doi.org/10.1080/03091929.2020.1761350","url":null,"abstract":"Several planetary bodies in our solar system undergo a forced libration owing to gravitational interactions with their orbital companions, leading to complex fluid motions in their metallic liquid cores or subsurface oceans. In this study, we numerically investigate flows in longitudinally librating spherical shells. We focus on the Ekman number dependencies of several shear layers when the libration frequency is less than twice of the rotation frequency and the libration amplitude is small. Time-dependent flows mainly consist of inertial waves excited at the critical latitudes due to the Ekman pumping singularities, forming conical shear layers. In particular, previous theoretical studies have proposed different scalings for the conical shear layers spawned from the critical latitudes at the inner boundary. Our numerical results favour the velocity amplitude scaling predicted by Le Dizès & Le Bars (J. Fluid Mech. 2017, 826, 653) over the scaling initially proposed by Kerswell (J. Fluid Mech. 1995, 298, 311), though the Ekman numbers in our calculations are not sufficiently small to pin down this scaling. Non-linear interactions in the boundary layers drive a mean zonal flow with several geostrophic shears. Our numerical results show that geostrophic shears associated with the critical latitudes at the inner and outer boundaries exhibit the same scalings, i.e. an amplitude of over a width of . Apart from the geostrophic shear associated with the critical latitude, our numerical results show that the reflection of inertial waves can induce a geostrophic shear with an amplitude of over a width of . As the amplitude of the geostrophic shears increases as reducing the Ekman number, the geostrophic shears in the mean flows may be significant in planetary cores and subsurface oceans given small Ekman numbers of these systems.","PeriodicalId":56132,"journal":{"name":"Geophysical and Astrophysical Fluid Dynamics","volume":"1 1","pages":"258 - 279"},"PeriodicalIF":1.3,"publicationDate":"2020-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75989568","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 : 2020-05-03DOI: 10.1080/03091929.2019.1680660
Chen Sun
ABSTRACT Geometric stability theory is developed as an analogue of structural stability in physical space. Two steady flows are said to be geometrically equivalent if they have the same streamline pattern with velocities satisfying . A stationary solution to the Euler equations is non-unique if there exists a geometrically equivalent solution with horizontally varying F, in which case its geometric structure is stable and permits non-proportional velocity change. An Euler flow without such an equivalent solution is unique and geometrically unstable. Analysis of pseudo-plane flows shows that only constant-speed flows, specifically straightline jet and vertical-aligned circular vortex, are geometrically stable. The only stable flow with closed streamlines is vertical-aligned circular vortex, which provides a stability explanation for the phenomenon of vortex alignment and axisymmetrisation. A series of polynomial and nonpolynomial Euler solutions is used to validate the generic instability of pseudo-plane ideal flows. The quadratic solutions indicate that the pressure field has dynamic multiplicity and cannot be used as a proxy for geometric analysis.
{"title":"Geometric stability of stationary Euler flows","authors":"Chen Sun","doi":"10.1080/03091929.2019.1680660","DOIUrl":"https://doi.org/10.1080/03091929.2019.1680660","url":null,"abstract":"ABSTRACT Geometric stability theory is developed as an analogue of structural stability in physical space. Two steady flows are said to be geometrically equivalent if they have the same streamline pattern with velocities satisfying . A stationary solution to the Euler equations is non-unique if there exists a geometrically equivalent solution with horizontally varying F, in which case its geometric structure is stable and permits non-proportional velocity change. An Euler flow without such an equivalent solution is unique and geometrically unstable. Analysis of pseudo-plane flows shows that only constant-speed flows, specifically straightline jet and vertical-aligned circular vortex, are geometrically stable. The only stable flow with closed streamlines is vertical-aligned circular vortex, which provides a stability explanation for the phenomenon of vortex alignment and axisymmetrisation. A series of polynomial and nonpolynomial Euler solutions is used to validate the generic instability of pseudo-plane ideal flows. The quadratic solutions indicate that the pressure field has dynamic multiplicity and cannot be used as a proxy for geometric analysis.","PeriodicalId":56132,"journal":{"name":"Geophysical and Astrophysical Fluid Dynamics","volume":"56 1","pages":"317 - 335"},"PeriodicalIF":1.3,"publicationDate":"2020-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83287095","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 : 2020-04-27DOI: 10.1080/03091929.2020.1753723
M. McIntyre
Abstract Three examples of wave–vortex interaction are studied, in analytically tractable weak refraction regimes with attention to the mean recoil forces, local and remote, that are associated with refractive changes in wave pseudomomentum fluxes. Wave-induced mean forces of this kind can be persistent, with cumulative effects, even in the absence of wave dissipation. In each example, a single wavetrain propagates past a single vortex. In the first two examples, in a two-dimensional, non-rotating acoustic or shallow-water setting, the focus is on whether or not the wavetrain overlaps the vortex core. In the overlapping case, the recoil has a local contribution given by the Craik–Leibovich force on the vortex core, the vector product of Stokes drift and mean vorticity. (For a quantum vortex this contribution is called the Iordanskii force arising from the Aharonov–Bohm effect on a phonon current.) However, in all except one special limiting case there are additional “remote” contributions, mediated by Stokes-drift-induced return flows that can intersect the vortex core well away from locations where the waves are refracted. The third example is a non-overlapping, remote-recoil-only example in a rapidly rotating frame, in which the waves are deep-water gravity waves and the mean flow obeys shallow-water quasigeostrophic dynamics. Contrary to what might at first be thought, the Ursell “anti-Stokes flow” induced by the rotation – an Eulerian-mean flow tending to cancel the Stokes drift – fails to suppress remote recoil. There are nontrivial open questions about extending these results to regimes of stronger refraction, especially regarding the scope of the “pseudomomentum rule” for the wave-induced recoil forces.
{"title":"Wave–vortex interactions and effective mean forces: three basic problems","authors":"M. McIntyre","doi":"10.1080/03091929.2020.1753723","DOIUrl":"https://doi.org/10.1080/03091929.2020.1753723","url":null,"abstract":"Abstract Three examples of wave–vortex interaction are studied, in analytically tractable weak refraction regimes with attention to the mean recoil forces, local and remote, that are associated with refractive changes in wave pseudomomentum fluxes. Wave-induced mean forces of this kind can be persistent, with cumulative effects, even in the absence of wave dissipation. In each example, a single wavetrain propagates past a single vortex. In the first two examples, in a two-dimensional, non-rotating acoustic or shallow-water setting, the focus is on whether or not the wavetrain overlaps the vortex core. In the overlapping case, the recoil has a local contribution given by the Craik–Leibovich force on the vortex core, the vector product of Stokes drift and mean vorticity. (For a quantum vortex this contribution is called the Iordanskii force arising from the Aharonov–Bohm effect on a phonon current.) However, in all except one special limiting case there are additional “remote” contributions, mediated by Stokes-drift-induced return flows that can intersect the vortex core well away from locations where the waves are refracted. The third example is a non-overlapping, remote-recoil-only example in a rapidly rotating frame, in which the waves are deep-water gravity waves and the mean flow obeys shallow-water quasigeostrophic dynamics. Contrary to what might at first be thought, the Ursell “anti-Stokes flow” induced by the rotation – an Eulerian-mean flow tending to cancel the Stokes drift – fails to suppress remote recoil. There are nontrivial open questions about extending these results to regimes of stronger refraction, especially regarding the scope of the “pseudomomentum rule” for the wave-induced recoil forces.","PeriodicalId":56132,"journal":{"name":"Geophysical and Astrophysical Fluid Dynamics","volume":"81 1","pages":"414 - 428"},"PeriodicalIF":1.3,"publicationDate":"2020-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85586203","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 : 2020-04-25DOI: 10.1080/03091929.2020.1762875
J. Mather, Radostin D Simitev
Convection and magnetic field generation in the Earth and planetary interiors are driven by both thermal and compositional gradients. In this work numerical simulations of finite-amplitude double-diffusive convection and dynamo action in rapidly rotating spherical shells full of incompressible two-component electrically-conducting fluid are reported. Four distinct regimes of rotating double-diffusive convection identified in a recent linear analysis (Silva, Mather and Simitev, Geophys. Astrophys. Fluid Dyn. 2019, 113, 377) are found to persist significantly beyond the onset of instability while their regime transitions remain abrupt. In the semi-convecting and the fingering regimes characteristic flow velocities are small compared to those in the thermally- and compositionally-dominated overturning regimes, while zonal flows remain weak in all regimes apart from the thermally-dominated one. Compositionally-dominated overturning convection exhibits significantly narrower azimuthal structures compared to all other regimes while differential rotation becomes the dominant flow component in the thermally-dominated case as driving is increased. Dynamo action occurs in all regimes apart from the regime of fingering convection. While dynamos persist in the semi-convective regime they are very much impaired by small flow intensities and very weak differential rotation in this regime which makes poloidal to toroidal field conversion problematic. The dynamos in the thermally-dominated regime include oscillating dipolar, quadrupolar and multipolar cases similar to the ones known from earlier parameter studies. Dynamos in the compositionally-dominated regime exhibit subdued temporal variation and remain predominantly dipolar due to weak zonal flow in this regime. These results significantly enhance our understanding of the primary drivers of planetary core flows and magnetic fields.
{"title":"Regimes of thermo-compositional convection and related dynamos in rotating spherical shells","authors":"J. Mather, Radostin D Simitev","doi":"10.1080/03091929.2020.1762875","DOIUrl":"https://doi.org/10.1080/03091929.2020.1762875","url":null,"abstract":"Convection and magnetic field generation in the Earth and planetary interiors are driven by both thermal and compositional gradients. In this work numerical simulations of finite-amplitude double-diffusive convection and dynamo action in rapidly rotating spherical shells full of incompressible two-component electrically-conducting fluid are reported. Four distinct regimes of rotating double-diffusive convection identified in a recent linear analysis (Silva, Mather and Simitev, Geophys. Astrophys. Fluid Dyn. 2019, 113, 377) are found to persist significantly beyond the onset of instability while their regime transitions remain abrupt. In the semi-convecting and the fingering regimes characteristic flow velocities are small compared to those in the thermally- and compositionally-dominated overturning regimes, while zonal flows remain weak in all regimes apart from the thermally-dominated one. Compositionally-dominated overturning convection exhibits significantly narrower azimuthal structures compared to all other regimes while differential rotation becomes the dominant flow component in the thermally-dominated case as driving is increased. Dynamo action occurs in all regimes apart from the regime of fingering convection. While dynamos persist in the semi-convective regime they are very much impaired by small flow intensities and very weak differential rotation in this regime which makes poloidal to toroidal field conversion problematic. The dynamos in the thermally-dominated regime include oscillating dipolar, quadrupolar and multipolar cases similar to the ones known from earlier parameter studies. Dynamos in the compositionally-dominated regime exhibit subdued temporal variation and remain predominantly dipolar due to weak zonal flow in this regime. These results significantly enhance our understanding of the primary drivers of planetary core flows and magnetic fields.","PeriodicalId":56132,"journal":{"name":"Geophysical and Astrophysical Fluid Dynamics","volume":"1 1","pages":"61 - 84"},"PeriodicalIF":1.3,"publicationDate":"2020-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85528792","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 : 2020-04-16DOI: 10.1080/03091929.2020.1748614
A. Constantin
Surface ocean currents have a significant influence on the climate and their dynamics depend to a large extent on the behaviour of the vertical eddy viscosity. We present an analytic study of wind-driven surface currents for general depth-dependent vertical eddy viscosities. A novel formulation for Ekman-type flows, that relies of a transformation to polar coordinates, enables us to show that in the Northern Hemisphere the horizontal current profile decays in magnitude and turns clockwise with increasing depth, irrespective of the vertical variations in diffusivity. Using a perturbation approach, we also derive a formula for the deflection angle of the current at the surface from the wind direction and discuss its implications.
{"title":"Frictional effects in wind-driven ocean currents","authors":"A. Constantin","doi":"10.1080/03091929.2020.1748614","DOIUrl":"https://doi.org/10.1080/03091929.2020.1748614","url":null,"abstract":"Surface ocean currents have a significant influence on the climate and their dynamics depend to a large extent on the behaviour of the vertical eddy viscosity. We present an analytic study of wind-driven surface currents for general depth-dependent vertical eddy viscosities. A novel formulation for Ekman-type flows, that relies of a transformation to polar coordinates, enables us to show that in the Northern Hemisphere the horizontal current profile decays in magnitude and turns clockwise with increasing depth, irrespective of the vertical variations in diffusivity. Using a perturbation approach, we also derive a formula for the deflection angle of the current at the surface from the wind direction and discuss its implications.","PeriodicalId":56132,"journal":{"name":"Geophysical and Astrophysical Fluid Dynamics","volume":"2 1","pages":"1 - 14"},"PeriodicalIF":1.3,"publicationDate":"2020-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87522733","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 : 2020-04-15DOI: 10.1080/03091929.2020.1795647
G. Meletti, S. Abide, S. Viazzo, A. Krebs, U. Harlander
The present paper describes a combined experimental and high-performance computing study of new specific behaviours of the Strato-Rotational Instability (SRI). The SRI is a purely hydrodynamical instability that consists of a classical Taylor–Couette (TC) system under stable axial density stratification. The density stratification causes a change on the marginal instability transition when compared to classical non-stratified TC systems, making the flow unstable in regions where – without stratification – it would be stable. This characteristic makes the SRI a relevant phenomenon in planetary and astrophysical applications, particularly in accretion disk theory. In spite of many advances in the understanding of strato-rotational flows, the confrontation of experimental data with non-linear numerical simulations remains relevant, since involved linear aspects and non-linear interactions of SRI modes still need to be better understood. These comparisons also reveal new non-linear phenomena and patterns not yet observed in the SRI that can contribute for our understanding of geophysical flows. The experiment designed to investigate these SRI-related phenomena consists of two cylinders that can rotate independently, with the space between these two vertical cylinders filled with a silicon oil. For obtaining a stable density stratification along the cylinder axis, the bottom lid of the setup is cooled, and its top part is heated, with temperature differences varying between , establishing an axial linear gradient, leading to Froude numbers between 1.5
{"title":"Experiments and long-term high-performance computations on amplitude modulations of strato-rotational flows","authors":"G. Meletti, S. Abide, S. Viazzo, A. Krebs, U. Harlander","doi":"10.1080/03091929.2020.1795647","DOIUrl":"https://doi.org/10.1080/03091929.2020.1795647","url":null,"abstract":"The present paper describes a combined experimental and high-performance computing study of new specific behaviours of the Strato-Rotational Instability (SRI). The SRI is a purely hydrodynamical instability that consists of a classical Taylor–Couette (TC) system under stable axial density stratification. The density stratification causes a change on the marginal instability transition when compared to classical non-stratified TC systems, making the flow unstable in regions where – without stratification – it would be stable. This characteristic makes the SRI a relevant phenomenon in planetary and astrophysical applications, particularly in accretion disk theory. In spite of many advances in the understanding of strato-rotational flows, the confrontation of experimental data with non-linear numerical simulations remains relevant, since involved linear aspects and non-linear interactions of SRI modes still need to be better understood. These comparisons also reveal new non-linear phenomena and patterns not yet observed in the SRI that can contribute for our understanding of geophysical flows. The experiment designed to investigate these SRI-related phenomena consists of two cylinders that can rotate independently, with the space between these two vertical cylinders filled with a silicon oil. For obtaining a stable density stratification along the cylinder axis, the bottom lid of the setup is cooled, and its top part is heated, with temperature differences varying between , establishing an axial linear gradient, leading to Froude numbers between 1.5<Fr<4.5, where is the inner cylinder rotation and N is the buoyancy frequency. The flow field resulting from the cylinders rotation interacting with the stable density stratification is measured using low frequency Particle Image Velocimetry (PIV). In the present investigation, we focus on cases of moderate Reynolds numbers ( , based on the inner cylinder radius and angular velocities), varying between and , and rotation ratio between outer and inner cylinders fixed at , a value slightly smaller than the Keplerian velocity profile, but beyond the Rayleigh limit. The same experimental configuration is also investigated by performing several Direct Numerical Simulations using a parallel high-order compact schemes incompressible code that solves the Boussinesq equations combining a 2d-pencil decomposition and the reduced Parallel Diagonal Dominant for an efficient parallelization. Both simulations and experiments reveal, in agreement with recent linear stability analyses, the occurrence of a return to stable flows with respect to the SRI when the Reynolds numbers increase. Low frequency velocity amplitude modulations related to two competing spiral wave modes, not yet reported, are observed both numerically and experimentally.","PeriodicalId":56132,"journal":{"name":"Geophysical and Astrophysical Fluid Dynamics","volume":"92 1","pages":"297 - 321"},"PeriodicalIF":1.3,"publicationDate":"2020-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85403948","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 : 2020-04-08DOI: 10.1080/03091929.2020.1747058
Mathieu Morvan, X. Carton, P. L’Hégaret, Charly de Marez, Stéphanie Corréard, S. Louazel
The Red Sea Water enters the Gulf of Aden through the Strait of Bab El Mandeb as a density current. The Red Sea Water subsequently spreads into the Gulf of Aden under the influence of surface mesoscale eddies, which dominate the surface flow, of topographic features such as rift and capes, and of the monsoon regimes. The dynamics of a bottom density current overflowing in a semi-enclosed basin, as the Red Sea Water outflows in the Gulf of Aden, is investigated by performing idealised numerical simulations, at submesoscale resolution, in which we progressively add topographic and dynamical elements. The rift and cape play an important role, respectively, on the vertical and the horizontal mixing as well as baroclinic and barotropic instabilities undergone by the bottom density current. Mesoscale and submesoscale eddies are generated depending on the model configuration. In the presence of surface mesoscale eddies, the bottom density current water is mainly advected at their periphery. In winter, both mesoscale and submesoscale eddies are generated, while in summer only submesoscale eddies are present. Finally, to put our results based on idealised numerical simulations and Lagrangian experiments in perspective, we analyse the trajectories of three Argo floats, deployed in the Rift of Tadjurah. Clues of submesoscale eddies generation at capes are observed which is in agreement with our idealised numerical simulations.
{"title":"On the dynamics of an idealised bottom density current overflowing in a semi-enclosed basin: mesoscale and submesoscale eddies generation","authors":"Mathieu Morvan, X. Carton, P. L’Hégaret, Charly de Marez, Stéphanie Corréard, S. Louazel","doi":"10.1080/03091929.2020.1747058","DOIUrl":"https://doi.org/10.1080/03091929.2020.1747058","url":null,"abstract":"The Red Sea Water enters the Gulf of Aden through the Strait of Bab El Mandeb as a density current. The Red Sea Water subsequently spreads into the Gulf of Aden under the influence of surface mesoscale eddies, which dominate the surface flow, of topographic features such as rift and capes, and of the monsoon regimes. The dynamics of a bottom density current overflowing in a semi-enclosed basin, as the Red Sea Water outflows in the Gulf of Aden, is investigated by performing idealised numerical simulations, at submesoscale resolution, in which we progressively add topographic and dynamical elements. The rift and cape play an important role, respectively, on the vertical and the horizontal mixing as well as baroclinic and barotropic instabilities undergone by the bottom density current. Mesoscale and submesoscale eddies are generated depending on the model configuration. In the presence of surface mesoscale eddies, the bottom density current water is mainly advected at their periphery. In winter, both mesoscale and submesoscale eddies are generated, while in summer only submesoscale eddies are present. Finally, to put our results based on idealised numerical simulations and Lagrangian experiments in perspective, we analyse the trajectories of three Argo floats, deployed in the Rift of Tadjurah. Clues of submesoscale eddies generation at capes are observed which is in agreement with our idealised numerical simulations.","PeriodicalId":56132,"journal":{"name":"Geophysical and Astrophysical Fluid Dynamics","volume":"11 1","pages":"607 - 630"},"PeriodicalIF":1.3,"publicationDate":"2020-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91300363","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 : 2020-04-02DOI: 10.1080/03091929.2020.1745789
Gökce Tuba Masur, M. Oliver
ABSTRACT Optimal balance is a near-optimal computational algorithm for nonlinear mode decomposition of geophysical flows into balanced and unbalanced components. It was first proposed as “optimal potential vorticity balance” by Viúdez and Dritschel [J. Fluid Mech., 2004, 521, 343] in the specific setting of semi-Lagrangian potential vorticity-based numerical codes. Later, it was recognised as an instance of the more general principle of adiabatic invariance of fast degrees of motion under slow perturbations. From this point of view, the system is slowly deformed from a linearised configuration to the full nonlinear dynamics. In the former, linear analysis yields an exact separation of balanced and unbalanced flow. In the latter, a given base-point coordinate, e.g. the height or potential vorticity field, can be matched. This formulation leads to a boundary value problem in time. In this paper, we show that this more general viewpoint leads to practical implementations of optimal balance on top of a primitive variables (here, velocity-height variables) numerical code. We identify preferred choices for several design parameters. The most critical choices concern the linear projector onto the slow modes at the linear-end boundary and the choice of base-point coordinate at the nonlinear end. We find that, even though the evolutionary model is formulated in primitive variables, potential vorticity based end-point conditions are advantageous. In particular, the only universally robust linear projector is the oblique projector onto the Rossby modes along the gravity-wave modes, which can be interpreted as the distinct non-orthogonal projector onto the Rossby modes that preserves the linear potential vorticity. Hence, the projector can be formulated as an elliptic partial differential equation which holds promise for using the method to produce an accurate nonlinear mode decomposition for more general models without the need to resort to asymptotic analysis.
{"title":"Optimal balance for rotating shallow water in primitive variables","authors":"Gökce Tuba Masur, M. Oliver","doi":"10.1080/03091929.2020.1745789","DOIUrl":"https://doi.org/10.1080/03091929.2020.1745789","url":null,"abstract":"ABSTRACT Optimal balance is a near-optimal computational algorithm for nonlinear mode decomposition of geophysical flows into balanced and unbalanced components. It was first proposed as “optimal potential vorticity balance” by Viúdez and Dritschel [J. Fluid Mech., 2004, 521, 343] in the specific setting of semi-Lagrangian potential vorticity-based numerical codes. Later, it was recognised as an instance of the more general principle of adiabatic invariance of fast degrees of motion under slow perturbations. From this point of view, the system is slowly deformed from a linearised configuration to the full nonlinear dynamics. In the former, linear analysis yields an exact separation of balanced and unbalanced flow. In the latter, a given base-point coordinate, e.g. the height or potential vorticity field, can be matched. This formulation leads to a boundary value problem in time. In this paper, we show that this more general viewpoint leads to practical implementations of optimal balance on top of a primitive variables (here, velocity-height variables) numerical code. We identify preferred choices for several design parameters. The most critical choices concern the linear projector onto the slow modes at the linear-end boundary and the choice of base-point coordinate at the nonlinear end. We find that, even though the evolutionary model is formulated in primitive variables, potential vorticity based end-point conditions are advantageous. In particular, the only universally robust linear projector is the oblique projector onto the Rossby modes along the gravity-wave modes, which can be interpreted as the distinct non-orthogonal projector onto the Rossby modes that preserves the linear potential vorticity. Hence, the projector can be formulated as an elliptic partial differential equation which holds promise for using the method to produce an accurate nonlinear mode decomposition for more general models without the need to resort to asymptotic analysis.","PeriodicalId":56132,"journal":{"name":"Geophysical and Astrophysical Fluid Dynamics","volume":"54 1","pages":"429 - 452"},"PeriodicalIF":1.3,"publicationDate":"2020-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84734929","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 : 2020-04-02DOI: 10.1080/03091929.2020.1743989
A. Choudhary, S. Koley, S. C. Martha
Wave structure interaction problem having thick vertical barrier over an arbitrary seabed is analysed for its solution. The associated boundary value problem is handled using a coupled eigenfunction expansion–boundary element method. This method converts the boundary value problem into integral equation over the physical boundaries. The physical boundaries are discretised into a finite number of elements and hence the integral equation give rise to a system of linear algebraic equations. Finally, the system of equations is solved to obtain the physical quantities, namely, the reflection and transmission coefficients. For ensuring the correctness of these physical quantities, the energy balance relation is derived and verified. The present results are also verified by comparing the results available in the literature. The present study reveals that the width and height of the structure along with the undulated seabed play an important role to construct an effective wave barrier to protect various marine facilities from wave attack and also helpful to create the tranquility zone on the lee side of the structure.
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Pub Date : 2020-03-20DOI: 10.1080/03091929.2019.1690203
P. Roberts
This is the book everyone interested in dynamo theory has been waiting for, the second and greatly expanded edition of Magnetic Field Generation in Electrically Conducting Fluids by Keith Moffatt. ...
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