Pub Date : 2022-01-14DOI: 10.1080/03091929.2021.2021197
A. Yeates
The magneto-frictional method is used in solar physics to compute both static and quasi-static models of the Sun's coronal magnetic field. Here, we examine how accurately magneto-friction (without fluid pressure) is able to predict the relaxed state in a one-dimensional test case containing two magnetic null points. Firstly, we show that relaxation under the full ideal magnetohydrodynamic equations in the presence of nulls leads necessarily to a non-force-free state, which could not be reached exactly by magneto-friction. Secondly, the magneto-frictional solutions are shown to lead to breakdown of magnetic flux conservation, whether or not the friction coefficient is scaled with magnetic field strength. When this coefficient is constant, flux is initially conserved, but only until discontinuous current sheets form at the null points. In the ensuing weak solution, we show that magnetic flux is dissipated at these current sheets. The breakdown of flux conservation does not occur for an alternative viscous relaxation scheme.
{"title":"On the limitations of magneto-frictional relaxation","authors":"A. Yeates","doi":"10.1080/03091929.2021.2021197","DOIUrl":"https://doi.org/10.1080/03091929.2021.2021197","url":null,"abstract":"The magneto-frictional method is used in solar physics to compute both static and quasi-static models of the Sun's coronal magnetic field. Here, we examine how accurately magneto-friction (without fluid pressure) is able to predict the relaxed state in a one-dimensional test case containing two magnetic null points. Firstly, we show that relaxation under the full ideal magnetohydrodynamic equations in the presence of nulls leads necessarily to a non-force-free state, which could not be reached exactly by magneto-friction. Secondly, the magneto-frictional solutions are shown to lead to breakdown of magnetic flux conservation, whether or not the friction coefficient is scaled with magnetic field strength. When this coefficient is constant, flux is initially conserved, but only until discontinuous current sheets form at the null points. In the ensuing weak solution, we show that magnetic flux is dissipated at these current sheets. The breakdown of flux conservation does not occur for an alternative viscous relaxation scheme.","PeriodicalId":56132,"journal":{"name":"Geophysical and Astrophysical Fluid Dynamics","volume":"1 1","pages":"305 - 320"},"PeriodicalIF":1.3,"publicationDate":"2022-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77274070","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 : 2021-12-31DOI: 10.1080/03091929.2021.1987427
P. Kundu, B. Mandal
The generation of two-dimensional surface waves due to various types of bottom disturbances such as underwater explosions, earthquakes, or volcanic eruptions is investigated here. Assuming linear theory the present problem is formulated as an initial value problem for the wave potential function ϕ and Stokes stream function ψ. Viscosity is considered. The physical model is illustrated by a sketch. Fourier and Laplace transform techniques are applied in the mathematical analysis to obtain the form of the free surface in terms of a multiple infinite integral. This integral is evaluated asymptotically by the method of steepest descent. The asymptotic form of the free surface is depicted graphically in some figures for different values of the viscosity and different types of ground disturbances. Appropriate conclusions are made.
{"title":"Generation of waves due to bottom disturbances in a viscous fluid","authors":"P. Kundu, B. Mandal","doi":"10.1080/03091929.2021.1987427","DOIUrl":"https://doi.org/10.1080/03091929.2021.1987427","url":null,"abstract":"The generation of two-dimensional surface waves due to various types of bottom disturbances such as underwater explosions, earthquakes, or volcanic eruptions is investigated here. Assuming linear theory the present problem is formulated as an initial value problem for the wave potential function ϕ and Stokes stream function ψ. Viscosity is considered. The physical model is illustrated by a sketch. Fourier and Laplace transform techniques are applied in the mathematical analysis to obtain the form of the free surface in terms of a multiple infinite integral. This integral is evaluated asymptotically by the method of steepest descent. The asymptotic form of the free surface is depicted graphically in some figures for different values of the viscosity and different types of ground disturbances. Appropriate conclusions are made.","PeriodicalId":56132,"journal":{"name":"Geophysical and Astrophysical Fluid Dynamics","volume":"58 1","pages":"122 - 139"},"PeriodicalIF":1.3,"publicationDate":"2021-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80237062","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 : 2021-11-08DOI: 10.1080/03091929.2021.1981307
A. Constantin
We rely on the f-plane approximation to derive the nonlinear governing equations for arctic wind-drift flow in regions that are not in the vicinity of the North Pole. An exact solution is derived in the material (Lagrangian) framework, a setting suitable for the accurate description of the particle paths. This approach facilitates the identification of oscillations superimposed on a mean spiralling Ekman current.
{"title":"Nonlinear wind-drift ocean currents in arctic regions","authors":"A. Constantin","doi":"10.1080/03091929.2021.1981307","DOIUrl":"https://doi.org/10.1080/03091929.2021.1981307","url":null,"abstract":"We rely on the f-plane approximation to derive the nonlinear governing equations for arctic wind-drift flow in regions that are not in the vicinity of the North Pole. An exact solution is derived in the material (Lagrangian) framework, a setting suitable for the accurate description of the particle paths. This approach facilitates the identification of oscillations superimposed on a mean spiralling Ekman current.","PeriodicalId":56132,"journal":{"name":"Geophysical and Astrophysical Fluid Dynamics","volume":"31 1","pages":"101 - 115"},"PeriodicalIF":1.3,"publicationDate":"2021-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80750577","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 : 2021-09-17DOI: 10.1080/03091929.2021.1959574
M. Rostami, V. Zeitlin
A simple two-layer model, the moist-convective rotating shallow water, which allows for low-cost high-resolution numerical simulations of the dynamics of the moist atmosphere in the presence of topography, is used to identify and understand dynamical processes governing the evolution of easterly waves propagating on the background of a low-latitude easterly jet crossing a land-sea boundary, a setup crudely representing the African Easterly Jet over the West-African plateau and the Atlantic ocean. We perform a thorough linear stability analysis and identify the unstable modes of the jet, which we use then for initialisation of fully nonlinear numerical simulations. In this way, we determine nonlinear evolution of unstable perturbations of the jet, both in the “dry” and moist-convective environments and highlight essential differences between the two cases. We identify a mechanism of formation of intense lower-layer cyclonic vortices at the northern flank of the jet and determine the influence of the land-sea contrast upon this process.
{"title":"Instabilities of low-latitude easterly jets in the presence of moist convection and topography and related cyclogenesis, in a simple atmospheric model","authors":"M. Rostami, V. Zeitlin","doi":"10.1080/03091929.2021.1959574","DOIUrl":"https://doi.org/10.1080/03091929.2021.1959574","url":null,"abstract":"A simple two-layer model, the moist-convective rotating shallow water, which allows for low-cost high-resolution numerical simulations of the dynamics of the moist atmosphere in the presence of topography, is used to identify and understand dynamical processes governing the evolution of easterly waves propagating on the background of a low-latitude easterly jet crossing a land-sea boundary, a setup crudely representing the African Easterly Jet over the West-African plateau and the Atlantic ocean. We perform a thorough linear stability analysis and identify the unstable modes of the jet, which we use then for initialisation of fully nonlinear numerical simulations. In this way, we determine nonlinear evolution of unstable perturbations of the jet, both in the “dry” and moist-convective environments and highlight essential differences between the two cases. We identify a mechanism of formation of intense lower-layer cyclonic vortices at the northern flank of the jet and determine the influence of the land-sea contrast upon this process.","PeriodicalId":56132,"journal":{"name":"Geophysical and Astrophysical Fluid Dynamics","volume":"8 4 1","pages":"56 - 77"},"PeriodicalIF":1.3,"publicationDate":"2021-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78357243","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 : 2021-09-17DOI: 10.1080/03091929.2021.1946802
M. Kopp, A. Tur, V. Yanovsky
In this paper we have studied the large-scale instability in a rotating stratified moist atmosphere with a small-scale turbulence. The axis of rotation of the medium is deviated from the vertical direction. The turbulence is excited by an external small-scale force with zero helicity and a low Reynolds number. The nonlinear equations of a vortex dynamo were obtained on the basis of the method of multiscale asymptotic expansions. The linear instability and stationary nonlinear modes were studied. The solutions in a form of localized vortex structures were obtained.
{"title":"Hydrodynamic α-effect in a rotating stratified moist atmosphere driven by small-scale non-helical force","authors":"M. Kopp, A. Tur, V. Yanovsky","doi":"10.1080/03091929.2021.1946802","DOIUrl":"https://doi.org/10.1080/03091929.2021.1946802","url":null,"abstract":"In this paper we have studied the large-scale instability in a rotating stratified moist atmosphere with a small-scale turbulence. The axis of rotation of the medium is deviated from the vertical direction. The turbulence is excited by an external small-scale force with zero helicity and a low Reynolds number. The nonlinear equations of a vortex dynamo were obtained on the basis of the method of multiscale asymptotic expansions. The linear instability and stationary nonlinear modes were studied. The solutions in a form of localized vortex structures were obtained.","PeriodicalId":56132,"journal":{"name":"Geophysical and Astrophysical Fluid Dynamics","volume":"56 1","pages":"551 - 576"},"PeriodicalIF":1.3,"publicationDate":"2021-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79346201","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 : 2021-09-13DOI: 10.1080/03091929.2021.1939326
Yang Zhang, Y. Afanasyev
The surface dynamics of the rotating thermal convection are examined in finely resolved laboratory flows. Deep rotating convection creates geostrophic turbulent flow at the surface, the regime of convection relevant to flows observed in deep convection sites in the ocean or in the atmospheres of the gas giants Jupiter and Saturn. Spectral analyses reveal a dual energy cascade of the surface kinetic energy and a downscale cascade of surface buoyancy. The spectral slopes of these quantities are found to be very similar to each other. This property is further confirmed theoretically; it was showed in particular that buoyancy is proportional to velocity in the subsurface thermal boundary layer.
{"title":"Rotating thermal convection: surface turbulence observed with altimetry and thermal radiometry","authors":"Yang Zhang, Y. Afanasyev","doi":"10.1080/03091929.2021.1939326","DOIUrl":"https://doi.org/10.1080/03091929.2021.1939326","url":null,"abstract":"The surface dynamics of the rotating thermal convection are examined in finely resolved laboratory flows. Deep rotating convection creates geostrophic turbulent flow at the surface, the regime of convection relevant to flows observed in deep convection sites in the ocean or in the atmospheres of the gas giants Jupiter and Saturn. Spectral analyses reveal a dual energy cascade of the surface kinetic energy and a downscale cascade of surface buoyancy. The spectral slopes of these quantities are found to be very similar to each other. This property is further confirmed theoretically; it was showed in particular that buoyancy is proportional to velocity in the subsurface thermal boundary layer.","PeriodicalId":56132,"journal":{"name":"Geophysical and Astrophysical Fluid Dynamics","volume":"26 1","pages":"499 - 522"},"PeriodicalIF":1.3,"publicationDate":"2021-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84083445","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 : 2021-09-06DOI: 10.1080/03091929.2021.1954631
Madeleine Cockerill, A. Bassom, Andrew J. Willmott
This study is concerned with properties of freely propagating barotropic Rossby waves in a circular polar cap, a prototype model for the Arctic Ocean. The linearised shallow-water equations are used to derive an amplitude equation for the waves in which full spherical geometry is retained. Almost by definition, polar basin dynamics are confined to regions of limited latitudinal extent and this provides a natural small scale which can underpin a rational asymptotic analysis of the amplitude equation. The coefficients of this equation depend on the topography of the basin and, as a simple model of the Arctic basin, we assume that the basin interior is characterised by a constant depth, surrounded by a continental shelf-slope the depth of which has algebraic dependence on co-latitude. Isobaths are therefore a family of concentric circles with centre at the pole. On the shelf and slope regions the leading order amplitude equation is of straightforward Euler type. Asymptotic values of the wave frequencies are derived and these are compared to values computed directly from the full amplitude equation. It is shown that the analytic results are in very good accord with the numerical predictions. Further simulations show that the properties of the waves are not particularly sensitive to the precise details of the underlying topography; this is reassuring as it is difficult to faithfully represent the shelf topography using simple mathematical functions.
{"title":"Modelling topographic waves in a polar basin","authors":"Madeleine Cockerill, A. Bassom, Andrew J. Willmott","doi":"10.1080/03091929.2021.1954631","DOIUrl":"https://doi.org/10.1080/03091929.2021.1954631","url":null,"abstract":"This study is concerned with properties of freely propagating barotropic Rossby waves in a circular polar cap, a prototype model for the Arctic Ocean. The linearised shallow-water equations are used to derive an amplitude equation for the waves in which full spherical geometry is retained. Almost by definition, polar basin dynamics are confined to regions of limited latitudinal extent and this provides a natural small scale which can underpin a rational asymptotic analysis of the amplitude equation. The coefficients of this equation depend on the topography of the basin and, as a simple model of the Arctic basin, we assume that the basin interior is characterised by a constant depth, surrounded by a continental shelf-slope the depth of which has algebraic dependence on co-latitude. Isobaths are therefore a family of concentric circles with centre at the pole. On the shelf and slope regions the leading order amplitude equation is of straightforward Euler type. Asymptotic values of the wave frequencies are derived and these are compared to values computed directly from the full amplitude equation. It is shown that the analytic results are in very good accord with the numerical predictions. Further simulations show that the properties of the waves are not particularly sensitive to the precise details of the underlying topography; this is reassuring as it is difficult to faithfully represent the shelf topography using simple mathematical functions.","PeriodicalId":56132,"journal":{"name":"Geophysical and Astrophysical Fluid Dynamics","volume":"35 1","pages":"1 - 19"},"PeriodicalIF":1.3,"publicationDate":"2021-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82295563","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 : 2021-09-06DOI: 10.1080/03091929.2021.1954630
A. A. Bachtiar, R. W. James
Bachtiar, Ivers and James [Planar velocity dynamos in a sphere. Proc. R. Soc. Lond. 2006, A462, 2439–2456] showed that a planar fluid velocity v can support dynamo action in a conducting sphere, however their model p1Y22DM12 exhibited slow convergence. Seeking more planar flow dynamos, they also considered converting some historical flows to planar flows by a process they termed ‘planarising‘. In particular they studied one of many flows considered by Pekeris, Accad and Shkoller [Kinematic dynamos and the earth's magnetic field. Phil. Trans. R. Soc. Lond. 1973, A275, 425–461]. This PAS flow was chosen because it produced a dynamo at low truncation levels and low critical magnetic Reynolds number R c, properties enhanced by the flow being a helical Beltrami flow. The original aim of the present project was to find a planar flow dynamo with faster convergence than p1Y22DM12. Whilst the PAS flow can only be partly planarised, we have constructed two modifications, labelled biPAS and quasiPAS, which can be fully planarised. We have studied 128 models using the PAS, biPAS, quasiPAS flows, and their part and full planarisations. We have verified 12 known dynamos, found 84 new dynamos, but found no dynamos with fully planar flows. The partly-planarised PAS, and the biPAS- and quasiPAS-based flows are not Beltrami. But 20 (normalised using rms( v ), or 22 using max | v |) of the associated dynamos have lower R c than the original Beltrami PAS dynamos from which they were derived, showing that the Beltrami property is not essential for low R c. A comparison is also made herein with optimal enstrophy-normalised dynamos.
{"title":"Dynamos driven by modified Beltrami flows, and a search for related planar flow dynamos","authors":"A. A. Bachtiar, R. W. James","doi":"10.1080/03091929.2021.1954630","DOIUrl":"https://doi.org/10.1080/03091929.2021.1954630","url":null,"abstract":"Bachtiar, Ivers and James [Planar velocity dynamos in a sphere. Proc. R. Soc. Lond. 2006, A462, 2439–2456] showed that a planar fluid velocity v can support dynamo action in a conducting sphere, however their model p1Y22DM12 exhibited slow convergence. Seeking more planar flow dynamos, they also considered converting some historical flows to planar flows by a process they termed ‘planarising‘. In particular they studied one of many flows considered by Pekeris, Accad and Shkoller [Kinematic dynamos and the earth's magnetic field. Phil. Trans. R. Soc. Lond. 1973, A275, 425–461]. This PAS flow was chosen because it produced a dynamo at low truncation levels and low critical magnetic Reynolds number R c, properties enhanced by the flow being a helical Beltrami flow. The original aim of the present project was to find a planar flow dynamo with faster convergence than p1Y22DM12. Whilst the PAS flow can only be partly planarised, we have constructed two modifications, labelled biPAS and quasiPAS, which can be fully planarised. We have studied 128 models using the PAS, biPAS, quasiPAS flows, and their part and full planarisations. We have verified 12 known dynamos, found 84 new dynamos, but found no dynamos with fully planar flows. The partly-planarised PAS, and the biPAS- and quasiPAS-based flows are not Beltrami. But 20 (normalised using rms( v ), or 22 using max | v |) of the associated dynamos have lower R c than the original Beltrami PAS dynamos from which they were derived, showing that the Beltrami property is not essential for low R c. A comparison is also made herein with optimal enstrophy-normalised dynamos.","PeriodicalId":56132,"journal":{"name":"Geophysical and Astrophysical Fluid Dynamics","volume":"32 1","pages":"140 - 157"},"PeriodicalIF":1.3,"publicationDate":"2021-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90497262","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 : 2021-08-27DOI: 10.1080/03091929.2021.1962851
S. Hariri
In this paper, we report on the mixing structures and transport properties of the Adriatic Sea surface, as a semi-enclosed basin of the Mediterranean Sea, from October 2006 until December 2011. Lagrangian transport models were used to simulate synthetic trajectories from the mean flow fields obtained by the Massachusetts Institute of Technology general circulation model implemented for the Adriatic. We examine the dispersion properties of numerical pair particles, through the calculation of time-averaged finite-size Lyapunov exponents (FSLEs) in the Adriatic Sea during selected months in each year. The results show the significant effects of river runoff and wind forcing, especially the Bora wind field, on the mixing activities of numerical pair particles by the generation of vortices, which appear as a tangle of filaments on the FSLE maps. The stretch/compression lines, which contain high values of the FSLEs, work as robust transport barriers, most having been detected along boundary currents on the eastern and western flanks of the Adriatic, particularly during winter. Numerical experiments have indicated that stable flows, with less mixing activity, occur in the northern part of the Adriatic in June and September of each year, while the Southern Adriatic Pit has flows with larger seasonal fluctuations and high values of eddy kinetic energy because of the influence of wind and energetic currents entering from the Ionian Sea.
{"title":"Analysis of mixing structures in the Adriatic Sea using finite-size Lyapunov exponents","authors":"S. Hariri","doi":"10.1080/03091929.2021.1962851","DOIUrl":"https://doi.org/10.1080/03091929.2021.1962851","url":null,"abstract":"In this paper, we report on the mixing structures and transport properties of the Adriatic Sea surface, as a semi-enclosed basin of the Mediterranean Sea, from October 2006 until December 2011. Lagrangian transport models were used to simulate synthetic trajectories from the mean flow fields obtained by the Massachusetts Institute of Technology general circulation model implemented for the Adriatic. We examine the dispersion properties of numerical pair particles, through the calculation of time-averaged finite-size Lyapunov exponents (FSLEs) in the Adriatic Sea during selected months in each year. The results show the significant effects of river runoff and wind forcing, especially the Bora wind field, on the mixing activities of numerical pair particles by the generation of vortices, which appear as a tangle of filaments on the FSLE maps. The stretch/compression lines, which contain high values of the FSLEs, work as robust transport barriers, most having been detected along boundary currents on the eastern and western flanks of the Adriatic, particularly during winter. Numerical experiments have indicated that stable flows, with less mixing activity, occur in the northern part of the Adriatic in June and September of each year, while the Southern Adriatic Pit has flows with larger seasonal fluctuations and high values of eddy kinetic energy because of the influence of wind and energetic currents entering from the Ionian Sea.","PeriodicalId":56132,"journal":{"name":"Geophysical and Astrophysical Fluid Dynamics","volume":"27 1","pages":"20 - 37"},"PeriodicalIF":1.3,"publicationDate":"2021-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80428025","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 : 2021-08-04DOI: 10.1080/03091929.2021.1943379
U. Harlander, M. Kurgansky
The instability of propagating internal gravity waves (IGWs) is of long-standing interest in geophysical fluid dynamics since breaking IGWs exchange energy and momentum with the large-scale flow and hence they support the large-scale circulation. In this study a low-order IGW beam model is used to delineate both linear and so called non-modal transient instability. In the first part of the study, linear normal mode instability of a wave beam consisting of two finite-amplitude plane monochromatic IGWs with the same frequency and parallel wave vectors of different magnitude is investigated using the Galerkin method. It is concluded that the wave beam is linearly more unstable than its constituent plane waves, taken separately. The degree of instability increases with the separation of the constituent waves in the wave number space, that is, with the wave beam concentration in the physical space. The narrower a wave beam is, the more linearly unstable it is. In its turn, transient instability typically occurs for linearly stable flows or before linear instability can set in (subcritical instability) if the governing system matrix is non-normal. In the second part of the paper, first the non-normality of the linear system matrix of the wave beam model is examined by computing measures like the Henrici number, the pseudospectrum, and the range of the matrix. Subsequently, the robustness of the transient growth is studied when the initial condition for optimal growth is randomly perturbed. It is concluded that for full randomisation, in particular, shallow wave beams can show subcritical growth when entering a turbulent background field. Such growing and eventually breaking wave beams might add turbulence to existing background turbulence that originates from other sources of instability. However, the robustness of transient growth for wave beam perturbations depends strongly on the strength of randomisation of the initial conditions, the beam angle and the perturbation wavelength.
{"title":"Two-dimensional internal gravity wave beam instability. Linear theory and subcritical instability","authors":"U. Harlander, M. Kurgansky","doi":"10.1080/03091929.2021.1943379","DOIUrl":"https://doi.org/10.1080/03091929.2021.1943379","url":null,"abstract":"The instability of propagating internal gravity waves (IGWs) is of long-standing interest in geophysical fluid dynamics since breaking IGWs exchange energy and momentum with the large-scale flow and hence they support the large-scale circulation. In this study a low-order IGW beam model is used to delineate both linear and so called non-modal transient instability. In the first part of the study, linear normal mode instability of a wave beam consisting of two finite-amplitude plane monochromatic IGWs with the same frequency and parallel wave vectors of different magnitude is investigated using the Galerkin method. It is concluded that the wave beam is linearly more unstable than its constituent plane waves, taken separately. The degree of instability increases with the separation of the constituent waves in the wave number space, that is, with the wave beam concentration in the physical space. The narrower a wave beam is, the more linearly unstable it is. In its turn, transient instability typically occurs for linearly stable flows or before linear instability can set in (subcritical instability) if the governing system matrix is non-normal. In the second part of the paper, first the non-normality of the linear system matrix of the wave beam model is examined by computing measures like the Henrici number, the pseudospectrum, and the range of the matrix. Subsequently, the robustness of the transient growth is studied when the initial condition for optimal growth is randomly perturbed. It is concluded that for full randomisation, in particular, shallow wave beams can show subcritical growth when entering a turbulent background field. Such growing and eventually breaking wave beams might add turbulence to existing background turbulence that originates from other sources of instability. However, the robustness of transient growth for wave beam perturbations depends strongly on the strength of randomisation of the initial conditions, the beam angle and the perturbation wavelength.","PeriodicalId":56132,"journal":{"name":"Geophysical and Astrophysical Fluid Dynamics","volume":"24 1","pages":"612 - 647"},"PeriodicalIF":1.3,"publicationDate":"2021-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79126747","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}
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