Pub Date : 2023-03-04DOI: 10.1080/03091929.2023.2199454
N. Kumar, Amandeep Kaur, S. C. Martha
In this paper, water waves interaction with two thin vertical barriers over shelf bottom topography is analysed using linearised wave theory. The associated mixed boundary value problem is solved with the aid of method involving eigenfunction expansions of the velocity potential and orthogonality relation of the eigenfunctions. Further, the resulting system of algebraic equations is solved using the least square method to find the physical quantities, that is, reflection and transmission coefficients, free surface elevation and non-dimensional horizontal force experienced by the barriers. The energy balance relation is derived from Green's identity which ensures the correctness of the present results. The obtained results are also compared with the results available in the literature for validation purpose. With the help of different plots, the effect of depth ratios, length of the barriers, angle of incidence and gap between the barriers is investigated for various values of physical parameters. The study reveals that the phenomena of zero reflection, that is, full transmission can be avoided by using non-identical barriers or asymmetric shelf bottom topography. Also, it is highlighted that the presence of two barriers instead of a single barrier over shelf topography will help to reduce the transmitted wave energy near the seashore. A generalisation of number of surface piercing barriers over the shelf bottom topography is also demonstrated.
{"title":"Scattering of water waves by two thin vertical barriers over shelf bottom topography","authors":"N. Kumar, Amandeep Kaur, S. C. Martha","doi":"10.1080/03091929.2023.2199454","DOIUrl":"https://doi.org/10.1080/03091929.2023.2199454","url":null,"abstract":"In this paper, water waves interaction with two thin vertical barriers over shelf bottom topography is analysed using linearised wave theory. The associated mixed boundary value problem is solved with the aid of method involving eigenfunction expansions of the velocity potential and orthogonality relation of the eigenfunctions. Further, the resulting system of algebraic equations is solved using the least square method to find the physical quantities, that is, reflection and transmission coefficients, free surface elevation and non-dimensional horizontal force experienced by the barriers. The energy balance relation is derived from Green's identity which ensures the correctness of the present results. The obtained results are also compared with the results available in the literature for validation purpose. With the help of different plots, the effect of depth ratios, length of the barriers, angle of incidence and gap between the barriers is investigated for various values of physical parameters. The study reveals that the phenomena of zero reflection, that is, full transmission can be avoided by using non-identical barriers or asymmetric shelf bottom topography. Also, it is highlighted that the presence of two barriers instead of a single barrier over shelf topography will help to reduce the transmitted wave energy near the seashore. A generalisation of number of surface piercing barriers over the shelf bottom topography is also demonstrated.","PeriodicalId":56132,"journal":{"name":"Geophysical and Astrophysical Fluid Dynamics","volume":"146 1","pages":"130 - 154"},"PeriodicalIF":1.3,"publicationDate":"2023-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76083111","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 : 2023-03-04DOI: 10.1080/03091929.2023.2204430
Chang Liu, A. Clark
Analysing the impact of bottom friction on shallow water waves over bottom terrains is important in areas including environmental and coastal engineering as well as the oceanic and atmospheric sciences. However, current theoretical developments rely on making certain limiting assumptions about these flows and thus more development is needed to be able to further generalise this behaviour. This work uses Adomian decomposition method (ADM) to not only develop semi-analytical formulations describing this behaviour, for flat terrains, but also as reverse-engineering mechanisms to develop new closed-form solutions describing this type of phenomena. Specifically, we respectively focus on inertial geostrophic oscillations and anticyclonic vortices with finite escape times in which our results directly demonstrate the direct correlation between the constant Coriolis force, the constant bottom friction, and the overall dynamics. Additionally, we illustrate elements of dissipation-induced instability with respect to constant bottom friction in these types of flows where we also demonstrate the connection to the initial dynamics for certain cases.
{"title":"Analysing the impact of bottom friction on shallow water waves over idealised bottom topographies","authors":"Chang Liu, A. Clark","doi":"10.1080/03091929.2023.2204430","DOIUrl":"https://doi.org/10.1080/03091929.2023.2204430","url":null,"abstract":"Analysing the impact of bottom friction on shallow water waves over bottom terrains is important in areas including environmental and coastal engineering as well as the oceanic and atmospheric sciences. However, current theoretical developments rely on making certain limiting assumptions about these flows and thus more development is needed to be able to further generalise this behaviour. This work uses Adomian decomposition method (ADM) to not only develop semi-analytical formulations describing this behaviour, for flat terrains, but also as reverse-engineering mechanisms to develop new closed-form solutions describing this type of phenomena. Specifically, we respectively focus on inertial geostrophic oscillations and anticyclonic vortices with finite escape times in which our results directly demonstrate the direct correlation between the constant Coriolis force, the constant bottom friction, and the overall dynamics. Additionally, we illustrate elements of dissipation-induced instability with respect to constant bottom friction in these types of flows where we also demonstrate the connection to the initial dynamics for certain cases.","PeriodicalId":56132,"journal":{"name":"Geophysical and Astrophysical Fluid Dynamics","volume":"53 1","pages":"107 - 129"},"PeriodicalIF":1.3,"publicationDate":"2023-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91375555","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 : 2023-01-02DOI: 10.1080/03091929.2023.2176849
Minakshi Ghosh, D. Das
To construct cylindrical structures like circular pipe bridges or tunnels submerged in the almost still density-stratified ocean or seawater, the study of waves radiated by the cylinder is essential. This research solves the wave radiation problem by calculating non-dimensionalized added mass and damping coefficients to the mass of the fluid displaced by the submerged horizontal cylinder in either layer of a three-layer fluid, which is still otherwise. Under the linear theory of water waves, we investigate the circular cylinder's hydrodynamic forces by its swaying and heaving motion. The time-harmonic wave propagates with three distinct wavenumbers for a given frequency. The method of multipoles has been employed due to its rapid converging solutions by increasing the truncation limit. Potential functions are expressed into systems of linear algebraic equations, which are solved numerically for two sets of unknowns in each case by truncation. Then, the added mass and damping coefficients are obtained from the non-dimensionalized hydrodynamic forces when the horizontal circular cylinder is submerged in the lower, middle and upper layers, respectively. The obtained results are depicted graphically against wavenumber in numerous figures and analysed.
{"title":"Wave radiation by a horizontal circular cylinder in a three-layer fluid","authors":"Minakshi Ghosh, D. Das","doi":"10.1080/03091929.2023.2176849","DOIUrl":"https://doi.org/10.1080/03091929.2023.2176849","url":null,"abstract":"To construct cylindrical structures like circular pipe bridges or tunnels submerged in the almost still density-stratified ocean or seawater, the study of waves radiated by the cylinder is essential. This research solves the wave radiation problem by calculating non-dimensionalized added mass and damping coefficients to the mass of the fluid displaced by the submerged horizontal cylinder in either layer of a three-layer fluid, which is still otherwise. Under the linear theory of water waves, we investigate the circular cylinder's hydrodynamic forces by its swaying and heaving motion. The time-harmonic wave propagates with three distinct wavenumbers for a given frequency. The method of multipoles has been employed due to its rapid converging solutions by increasing the truncation limit. Potential functions are expressed into systems of linear algebraic equations, which are solved numerically for two sets of unknowns in each case by truncation. Then, the added mass and damping coefficients are obtained from the non-dimensionalized hydrodynamic forces when the horizontal circular cylinder is submerged in the lower, middle and upper layers, respectively. The obtained results are depicted graphically against wavenumber in numerous figures and analysed.","PeriodicalId":56132,"journal":{"name":"Geophysical and Astrophysical Fluid Dynamics","volume":"66 1","pages":"59 - 77"},"PeriodicalIF":1.3,"publicationDate":"2023-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84037463","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 : 2023-01-02DOI: 10.1080/03091929.2023.2175822
R. S. Selim
We consider the nonlinear interaction system of waves to identify discrete clusters of resonant triads, which are classified on the basis of the resonance condition. This study is conducted to investigate the coherent structure of incompressible fluid flow in the turbulent boundary layer. The discrete wave turbulence is characterised by weakly nonlinear interaction modes for amplitude Tollmien Schlichting in a single-mode approximation. Within the framework of multiple-scale analysis, the coherent part of the amplitude equation is defined in the case of multiple three-wave resonance. The resonance condition is defined from the dispersion relation of these amplitudes, which are determined from solving the spectral problem of Orr–Sommerfeld equation by the Chebyshev collocation method. The spectral characteristics of these amplitudes are investigated to define the condition of multiple three-wave resonance. This condition is also defined for a resonant cluster made out of triads sharing a common mode, where all triads satisfy the resonance condition. The coherent amplitudes are represented dynamically by an autonomous system of ordinary differential equations. Non-integrable system of a single triad and a cluster of triads is noted, where the interaction coefficients in the given system do not have the same complex phase. The obtained dynamical system admits a number of invariants, similar to the classical Manley–Rowe invariants but of a different nature. One of these invariants is called the energy invariant manifold that represents the sum of modules square amplitudes of the dynamical system, this invariant is normalised to be defined on the unit sphere. Therefore, Birkhoff–Khinchin theory is applied to calculate the time average of square harmonic and sub harmonic amplitudes. Moreover, this paper is also focused on studying the numerical solutions of both simple and complex structure of the dynamical system by using Runge–Kutta method with random initial conditions. The solution of the dynamical system is examined at different signs of the weight factors, where the bounded solutions of this system are found at both positive and negative signs. However, in another study of a dynamical system, an explosive instability is noted at a negative sign for only one of the weight factors, where all study cases are related to the choice of wave vectors. The random initial conditions are applied to both simple and complex dynamical system to study the behaviour of system solutions. The coupling different triads within the dynamical system lead to chaotic turbulence regime.
{"title":"Dynamics of the coherent structure for incompressible fluid flow in turbulent boundary layers","authors":"R. S. Selim","doi":"10.1080/03091929.2023.2175822","DOIUrl":"https://doi.org/10.1080/03091929.2023.2175822","url":null,"abstract":"We consider the nonlinear interaction system of waves to identify discrete clusters of resonant triads, which are classified on the basis of the resonance condition. This study is conducted to investigate the coherent structure of incompressible fluid flow in the turbulent boundary layer. The discrete wave turbulence is characterised by weakly nonlinear interaction modes for amplitude Tollmien Schlichting in a single-mode approximation. Within the framework of multiple-scale analysis, the coherent part of the amplitude equation is defined in the case of multiple three-wave resonance. The resonance condition is defined from the dispersion relation of these amplitudes, which are determined from solving the spectral problem of Orr–Sommerfeld equation by the Chebyshev collocation method. The spectral characteristics of these amplitudes are investigated to define the condition of multiple three-wave resonance. This condition is also defined for a resonant cluster made out of triads sharing a common mode, where all triads satisfy the resonance condition. The coherent amplitudes are represented dynamically by an autonomous system of ordinary differential equations. Non-integrable system of a single triad and a cluster of triads is noted, where the interaction coefficients in the given system do not have the same complex phase. The obtained dynamical system admits a number of invariants, similar to the classical Manley–Rowe invariants but of a different nature. One of these invariants is called the energy invariant manifold that represents the sum of modules square amplitudes of the dynamical system, this invariant is normalised to be defined on the unit sphere. Therefore, Birkhoff–Khinchin theory is applied to calculate the time average of square harmonic and sub harmonic amplitudes. Moreover, this paper is also focused on studying the numerical solutions of both simple and complex structure of the dynamical system by using Runge–Kutta method with random initial conditions. The solution of the dynamical system is examined at different signs of the weight factors, where the bounded solutions of this system are found at both positive and negative signs. However, in another study of a dynamical system, an explosive instability is noted at a negative sign for only one of the weight factors, where all study cases are related to the choice of wave vectors. The random initial conditions are applied to both simple and complex dynamical system to study the behaviour of system solutions. The coupling different triads within the dynamical system lead to chaotic turbulence regime.","PeriodicalId":56132,"journal":{"name":"Geophysical and Astrophysical Fluid Dynamics","volume":"143 1","pages":"1 - 34"},"PeriodicalIF":1.3,"publicationDate":"2023-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86636521","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 : 2023-01-02DOI: 10.1080/03091929.2023.2169283
Chang-ming Liu, A. Clark
Analysing two-dimensional shallow water equations with idealised bottom topographies have many applications in the atmospheric and oceanic sciences; however, restrictive flow pattern assumptions have been made to achieve explicit solutions. This work employs the Adomian decomposition method (ADM) to develop semi-analytical formulations of these problems that preserve the direct correlation of the physical parameters while capturing the nonlinear phenomenon. Furthermore, we exploit these techniques as reverse engineering mechanisms to develop key connections between some prevalent ansatz formulations in the open literature as well as derive new families of exact solutions describing geostrophic inertial oscillations and anticyclonic vortices with finite escape times. Our semi-analytical evaluations show the promise of this approach in terms of providing robust approximations against several oceanic variations and bottom topographies while also preserving the direct correlation between the physical parameters such as the Froude number, the bottom topography, the Coriolis parameter, as well as the flow and free surface behaviours. Our numerical validations provide additional confirmations of this approach while also illustrating that ADM can also be used to provide insight and deduce novel solutions that have not been explored, which can be used to characterise various types of geophysical flows.
{"title":"Semi-analytical solutions of shallow water waves with idealised bottom topographies","authors":"Chang-ming Liu, A. Clark","doi":"10.1080/03091929.2023.2169283","DOIUrl":"https://doi.org/10.1080/03091929.2023.2169283","url":null,"abstract":"Analysing two-dimensional shallow water equations with idealised bottom topographies have many applications in the atmospheric and oceanic sciences; however, restrictive flow pattern assumptions have been made to achieve explicit solutions. This work employs the Adomian decomposition method (ADM) to develop semi-analytical formulations of these problems that preserve the direct correlation of the physical parameters while capturing the nonlinear phenomenon. Furthermore, we exploit these techniques as reverse engineering mechanisms to develop key connections between some prevalent ansatz formulations in the open literature as well as derive new families of exact solutions describing geostrophic inertial oscillations and anticyclonic vortices with finite escape times. Our semi-analytical evaluations show the promise of this approach in terms of providing robust approximations against several oceanic variations and bottom topographies while also preserving the direct correlation between the physical parameters such as the Froude number, the bottom topography, the Coriolis parameter, as well as the flow and free surface behaviours. Our numerical validations provide additional confirmations of this approach while also illustrating that ADM can also be used to provide insight and deduce novel solutions that have not been explored, which can be used to characterise various types of geophysical flows.","PeriodicalId":56132,"journal":{"name":"Geophysical and Astrophysical Fluid Dynamics","volume":"47 1","pages":"35 - 58"},"PeriodicalIF":1.3,"publicationDate":"2023-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86827257","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 : 2022-11-02DOI: 10.1080/03091929.2022.2156188
A. Brandenburg
{"title":"Astrophysical magnetic fields: from galaxies to the early universe","authors":"A. Brandenburg","doi":"10.1080/03091929.2022.2156188","DOIUrl":"https://doi.org/10.1080/03091929.2022.2156188","url":null,"abstract":"","PeriodicalId":56132,"journal":{"name":"Geophysical and Astrophysical Fluid Dynamics","volume":"1 1","pages":"537 - 539"},"PeriodicalIF":1.3,"publicationDate":"2022-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89219494","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 : 2022-11-02DOI: 10.1080/03091929.2022.2148666
Colin M. Hardy, P. Livermore, Jitse Niesen
Recent studies have demonstrated the possibility of constructing magnetostrophic dynamo models, which describe the slowly evolving background state of Earth's magnetic field when inertia and viscosity are negligible. Here we explore the properties of steady, stable magnetostrophic states as a leading order approximation to the slow dynamics within Earth's core. For the case of an axisymmetric magnetostrophic system driven by a prescribed α-effect, we confirmed the existence of four known steady states: , , where is purely dipolar and is purely quadrupolar. Importantly, here we show that in all but the most weakly driven cases, an initial magnetic field that is not purely dipolar or quadrapolar never converges to these states. Despite this instability, we also show that there are a plethora of instantaneous solutions that are quasi-steady, but nevertheless unstable. If the dynamics in Earth's core are reasonably modelled by a strongly driven α-effect, this work suggests that the background state can never be steady. We discuss the difficulties in comparing our magnetostrophic models with geomagnetic timeseries.
{"title":"The inherent instability of axisymmetric magnetostrophic dynamo models","authors":"Colin M. Hardy, P. Livermore, Jitse Niesen","doi":"10.1080/03091929.2022.2148666","DOIUrl":"https://doi.org/10.1080/03091929.2022.2148666","url":null,"abstract":"Recent studies have demonstrated the possibility of constructing magnetostrophic dynamo models, which describe the slowly evolving background state of Earth's magnetic field when inertia and viscosity are negligible. Here we explore the properties of steady, stable magnetostrophic states as a leading order approximation to the slow dynamics within Earth's core. For the case of an axisymmetric magnetostrophic system driven by a prescribed α-effect, we confirmed the existence of four known steady states: , , where is purely dipolar and is purely quadrupolar. Importantly, here we show that in all but the most weakly driven cases, an initial magnetic field that is not purely dipolar or quadrapolar never converges to these states. Despite this instability, we also show that there are a plethora of instantaneous solutions that are quasi-steady, but nevertheless unstable. If the dynamics in Earth's core are reasonably modelled by a strongly driven α-effect, this work suggests that the background state can never be steady. We discuss the difficulties in comparing our magnetostrophic models with geomagnetic timeseries.","PeriodicalId":56132,"journal":{"name":"Geophysical and Astrophysical Fluid Dynamics","volume":"20 1","pages":"499 - 520"},"PeriodicalIF":1.3,"publicationDate":"2022-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87916455","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 : 2022-11-02DOI: 10.1080/03091929.2022.2137501
G. Riccardi
ABSTRACT The existence of an integral relation between self-induced velocity of a uniform, planar vortex and Schwarz function of its boundary opens the way to understand the kinematics of the vortex by analysing the internal singularities of that function. In general, they are branch cuts and form the so-called “mother body” of the vortex, because they generate the same external velocities of the vortex, by means of a relation identical to the Biot–Savart law for a vortex sheet. The jump of the Schwarz function across the cuts plays the role of the (complex) density of circulation. This paper investigates the singularities of polygonal vortices, which are highly nontrivial steady vortices widely present in Nature, and having fascinating properties, some of them still not well understood. By means of the equation of the dynamics of the Schwarz function specialised for steady vortices, a numerical tool based on elementary properties of the holomorphic functions is used for detecting the internal singularities and evaluating their strengths. In this way, it is shown that an nagonal vortex possesses n internal branch cuts. In a reference system having origin on the centre of vorticity of the vortex and real axis crossing one of its vertices, these cuts start from the origin and are directed along the n roots of the unity, so that they are aligned with the vertices. The positions of the branch points and the values assumed by the Schwarz function in these points are calculated by evaluating this function just outside the vortex boundary. Once the conditions on the branch points are defined, a power series representation of the Schwarz function is proposed, that is able to explain the behaviour of its real and imaginary parts in neighbourhoods of these points. Some conjectures about the external singularities are also discussed.
{"title":"On the mother bodies of steady polygonal uniform vortices. Part I: numerical experiments","authors":"G. Riccardi","doi":"10.1080/03091929.2022.2137501","DOIUrl":"https://doi.org/10.1080/03091929.2022.2137501","url":null,"abstract":"ABSTRACT The existence of an integral relation between self-induced velocity of a uniform, planar vortex and Schwarz function of its boundary opens the way to understand the kinematics of the vortex by analysing the internal singularities of that function. In general, they are branch cuts and form the so-called “mother body” of the vortex, because they generate the same external velocities of the vortex, by means of a relation identical to the Biot–Savart law for a vortex sheet. The jump of the Schwarz function across the cuts plays the role of the (complex) density of circulation. This paper investigates the singularities of polygonal vortices, which are highly nontrivial steady vortices widely present in Nature, and having fascinating properties, some of them still not well understood. By means of the equation of the dynamics of the Schwarz function specialised for steady vortices, a numerical tool based on elementary properties of the holomorphic functions is used for detecting the internal singularities and evaluating their strengths. In this way, it is shown that an nagonal vortex possesses n internal branch cuts. In a reference system having origin on the centre of vorticity of the vortex and real axis crossing one of its vertices, these cuts start from the origin and are directed along the n roots of the unity, so that they are aligned with the vertices. The positions of the branch points and the values assumed by the Schwarz function in these points are calculated by evaluating this function just outside the vortex boundary. Once the conditions on the branch points are defined, a power series representation of the Schwarz function is proposed, that is able to explain the behaviour of its real and imaginary parts in neighbourhoods of these points. Some conjectures about the external singularities are also discussed.","PeriodicalId":56132,"journal":{"name":"Geophysical and Astrophysical Fluid Dynamics","volume":"78 1","pages":"433 - 457"},"PeriodicalIF":1.3,"publicationDate":"2022-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88129037","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 : 2022-11-02DOI: 10.1080/03091929.2022.2137878
Parag Gupta, Radostin D Simitev, D. MacTaggart
ABSTRACT Magnetic helicity is a fundamental constraint in both ideal and resistive magnetohydrodynamics. Measurements of magnetic helicity density on the Sun and other stars are used to interpret the internal behaviour of the dynamo generating the global magnetic field. In this note, we study the behaviour of the global relative magnetic helicity in three self-consistent spherical dynamo solutions of increasing complexity. Magnetic helicity describes the global linkage of the poloidal and toroidal magnetic fields (weighted by magnetic flux), and our results indicate that there are preferred states of this linkage. This leads us to propose that global magnetic reversals are, perhaps, a means of preserving this linkage, since, when only one of the poloidal or toroidal fields reverses, the preferred state of linkage is lost. It is shown that magnetic helicity indicates the onset of reversals and that this signature may be observed at the outer surface.
{"title":"A study of global magnetic helicity in self-consistent spherical dynamos","authors":"Parag Gupta, Radostin D Simitev, D. MacTaggart","doi":"10.1080/03091929.2022.2137878","DOIUrl":"https://doi.org/10.1080/03091929.2022.2137878","url":null,"abstract":"ABSTRACT Magnetic helicity is a fundamental constraint in both ideal and resistive magnetohydrodynamics. Measurements of magnetic helicity density on the Sun and other stars are used to interpret the internal behaviour of the dynamo generating the global magnetic field. In this note, we study the behaviour of the global relative magnetic helicity in three self-consistent spherical dynamo solutions of increasing complexity. Magnetic helicity describes the global linkage of the poloidal and toroidal magnetic fields (weighted by magnetic flux), and our results indicate that there are preferred states of this linkage. This leads us to propose that global magnetic reversals are, perhaps, a means of preserving this linkage, since, when only one of the poloidal or toroidal fields reverses, the preferred state of linkage is lost. It is shown that magnetic helicity indicates the onset of reversals and that this signature may be observed at the outer surface.","PeriodicalId":56132,"journal":{"name":"Geophysical and Astrophysical Fluid Dynamics","volume":"92 1","pages":"521 - 536"},"PeriodicalIF":1.3,"publicationDate":"2022-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74995905","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 : 2022-11-02DOI: 10.1080/03091929.2022.2138865
Pierre Labreuche, C. Staquet, J. Le Sommer
The interactions between inertial oscillations (IO) and lee waves (LW) close to the bottom of the ocean and the role of IO in energy dissipation are addressed for a range of physical parameters typical of Southern Ocean conditions. Idealized numerical simulations in a vertical plane and resonant interaction theory are combined for this purpose. The lee waves are emitted by a uniform geostrophic flow over a sinusoidal topography for a constant buoyancy frequency at mid-latitude. We show that IO can grow by triadic resonant interactions with the LW. Two triads are dominant, which involve waves with frequency , f and , where is the intrinsic frequency of the LW and f the Coriolis frequency (assumed positive). These triads differ by the sign and value of the IO vertical wavenumber. Results from the numerical simulations show that the triad associated with the upward phase propagation of the IO is selected, consistent with oceanic observations, that a good agreement is obtained with the IO growth rate predicted theoretically and that the IO develop in a bottom layer of height less than 1000 m. A quasi-steady flow regime is eventually reached, with the IO amplitude being of the same order as the geostrophic flow speed. During this regime, depending upon the flow parameters, the IO kinetic energy is equal to 30–70% of the LW energy flux during one inertial period. This large range of values is not reflected in the turbulent kinetic energy (TKE) dissipation rate, which is comprised between 10 and 30% of the LW energy flux, whatever the IO amplitude, even if vanishingly small. Therefore, for the set of parameters we consider, the TKE dissipation rate cannot be inferred from the IO amplitude. Yet, the nonlinear interactions between the lee waves and the IO are critical in setting the energy spectrum, and similarly for the internal tide and the IO at low latitudes according to the literature. This implies that IO should be taken into account in the parameterisation of mixing in the ocean.
{"title":"Resonant growth of inertial oscillations from lee waves in the deep ocean","authors":"Pierre Labreuche, C. Staquet, J. Le Sommer","doi":"10.1080/03091929.2022.2138865","DOIUrl":"https://doi.org/10.1080/03091929.2022.2138865","url":null,"abstract":"The interactions between inertial oscillations (IO) and lee waves (LW) close to the bottom of the ocean and the role of IO in energy dissipation are addressed for a range of physical parameters typical of Southern Ocean conditions. Idealized numerical simulations in a vertical plane and resonant interaction theory are combined for this purpose. The lee waves are emitted by a uniform geostrophic flow over a sinusoidal topography for a constant buoyancy frequency at mid-latitude. We show that IO can grow by triadic resonant interactions with the LW. Two triads are dominant, which involve waves with frequency , f and , where is the intrinsic frequency of the LW and f the Coriolis frequency (assumed positive). These triads differ by the sign and value of the IO vertical wavenumber. Results from the numerical simulations show that the triad associated with the upward phase propagation of the IO is selected, consistent with oceanic observations, that a good agreement is obtained with the IO growth rate predicted theoretically and that the IO develop in a bottom layer of height less than 1000 m. A quasi-steady flow regime is eventually reached, with the IO amplitude being of the same order as the geostrophic flow speed. During this regime, depending upon the flow parameters, the IO kinetic energy is equal to 30–70% of the LW energy flux during one inertial period. This large range of values is not reflected in the turbulent kinetic energy (TKE) dissipation rate, which is comprised between 10 and 30% of the LW energy flux, whatever the IO amplitude, even if vanishingly small. Therefore, for the set of parameters we consider, the TKE dissipation rate cannot be inferred from the IO amplitude. Yet, the nonlinear interactions between the lee waves and the IO are critical in setting the energy spectrum, and similarly for the internal tide and the IO at low latitudes according to the literature. This implies that IO should be taken into account in the parameterisation of mixing in the ocean.","PeriodicalId":56132,"journal":{"name":"Geophysical and Astrophysical Fluid Dynamics","volume":"35 1","pages":"351 - 373"},"PeriodicalIF":1.3,"publicationDate":"2022-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86584834","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：