Search Results
You are looking at 1 - 4 of 4 items for
- Author or Editor: Georgi G. Sutyrin x
- Refine by Access: All Content x
Abstract
An analytical theory is presented for the self-induced translation of an intense vortex relative to a uniform background flow on the β plane. The equivalent barotropic approximation is used to formulate the initial value problem within a polar coordinate frame translating with the vortex center. A contour dynamical model of the vortex is melded with the regular beta-plane model of the residual flow. Evolution of vortex asymmetries for azimuthal mode number one, the so-called beta gyres, which are responsible for the relative vortex motion, is considered for a period of time while the Rossby wave radiation is not important.
It is shown for an initially axisymmetric vortex that the beta gyres and corresponding vortex translational velocity consist of two parts. The first one is generated by advection of the background potential vorticity gradient and rotates differentially because of the symmetric vortex circulation. The second part arises due to distortion in the vortex shape represented by displacements of the piecewise constant potential vorticity contours relative to the vortex center. The distortion of the vortex shape is described by the sum of normal modes generated by the first part. Explicit solutions for both parts are obtained, and approximate expressions for different stages of the vortex motion are presented.
For a vortex with a uniform potential vorticity core (single contour), the beta gyres are found to consist only of the first part so that the vortex translation depends on the ratio of the core size to the radius of deformation. A small core corresponds to the geostrophic point vortex limit with initially predominantly meridional motion. Asymptotically, after a large number of fluid revolutions at a radial distance on the order of the radius of deformation, the westward translation dominates: the meridional velocity and the deviation of zonal velocity from the maximum linear Rossby wave speed decay linearly with time. This tendency is explained to be a result of effective symmetrization of the potential vorticity due to differential rotation of fluid around the vortex. The period of initial predominantly meridional motion is negligible when the core size is on the order of the deformation radius.
For the vortex with two steps in the potential vorticity, the normal mode rotates faster than the fluid if the potential vorticities in the core and at the periphery have different signs. The effect of the distortion in the vortex shape on the vortex translation increases with increasing deformation radius relative to the vortex size. In a stationary beta gyre, for a finite vortex, the relative contour shift contributes to the westward translation just up to the long Rossby wave speed.
In the nondivergent limit a universal approximate trajectory has been found for large outer contour radius. The center of a finite vortex moves northwestward with permanent meridional acceleration due to degeneracy of a zero-frequency normal mode. The zonal translational velocity approaches a limit proportional to the vortex area. The effect of the distortion in the vortex shape in this nondivergent limit results in decreasing the westward translation and increasing the meridional one.
Applications of the theory to hurricanes in the atmosphere and rings in the ocean are discussed.
Abstract
An analytical theory is presented for the self-induced translation of an intense vortex relative to a uniform background flow on the β plane. The equivalent barotropic approximation is used to formulate the initial value problem within a polar coordinate frame translating with the vortex center. A contour dynamical model of the vortex is melded with the regular beta-plane model of the residual flow. Evolution of vortex asymmetries for azimuthal mode number one, the so-called beta gyres, which are responsible for the relative vortex motion, is considered for a period of time while the Rossby wave radiation is not important.
It is shown for an initially axisymmetric vortex that the beta gyres and corresponding vortex translational velocity consist of two parts. The first one is generated by advection of the background potential vorticity gradient and rotates differentially because of the symmetric vortex circulation. The second part arises due to distortion in the vortex shape represented by displacements of the piecewise constant potential vorticity contours relative to the vortex center. The distortion of the vortex shape is described by the sum of normal modes generated by the first part. Explicit solutions for both parts are obtained, and approximate expressions for different stages of the vortex motion are presented.
For a vortex with a uniform potential vorticity core (single contour), the beta gyres are found to consist only of the first part so that the vortex translation depends on the ratio of the core size to the radius of deformation. A small core corresponds to the geostrophic point vortex limit with initially predominantly meridional motion. Asymptotically, after a large number of fluid revolutions at a radial distance on the order of the radius of deformation, the westward translation dominates: the meridional velocity and the deviation of zonal velocity from the maximum linear Rossby wave speed decay linearly with time. This tendency is explained to be a result of effective symmetrization of the potential vorticity due to differential rotation of fluid around the vortex. The period of initial predominantly meridional motion is negligible when the core size is on the order of the deformation radius.
For the vortex with two steps in the potential vorticity, the normal mode rotates faster than the fluid if the potential vorticities in the core and at the periphery have different signs. The effect of the distortion in the vortex shape on the vortex translation increases with increasing deformation radius relative to the vortex size. In a stationary beta gyre, for a finite vortex, the relative contour shift contributes to the westward translation just up to the long Rossby wave speed.
In the nondivergent limit a universal approximate trajectory has been found for large outer contour radius. The center of a finite vortex moves northwestward with permanent meridional acceleration due to degeneracy of a zero-frequency normal mode. The zonal translational velocity approaches a limit proportional to the vortex area. The effect of the distortion in the vortex shape in this nondivergent limit results in decreasing the westward translation and increasing the meridional one.
Applications of the theory to hurricanes in the atmosphere and rings in the ocean are discussed.
Abstract
The symmetry properties of the Gulf Stream–type jet equilibrated over topographic slope are investigated in a series of idealized numerical experiments. A baroclinically unstable zonal jet equilibrates over a sloping bottom through the process of potential vorticity (PV) homogenization underneath the main thermocline by the bottom-intensified eddy activity associated with the stream meandering. Potential vorticity homogenization underneath the main thermocline leads to formation of recirculation gyres on both sides of the jet. The magnitude of the northern recirculation gyre, as measured by its westward transport, is larger than the magnitude of the southern recirculation gyre. This asymmetry in recirculations is shown to be the result of an asymmetric PV mixing underneath the thermocline produced by an asymmetric jet. In particular, the lateral shift of the velocity maximum near the surface relative to the velocity maximum at depth is shown to be responsible for the asymmetry. The results are related to the Gulf Stream data between 73° and 65°W.
Abstract
The symmetry properties of the Gulf Stream–type jet equilibrated over topographic slope are investigated in a series of idealized numerical experiments. A baroclinically unstable zonal jet equilibrates over a sloping bottom through the process of potential vorticity (PV) homogenization underneath the main thermocline by the bottom-intensified eddy activity associated with the stream meandering. Potential vorticity homogenization underneath the main thermocline leads to formation of recirculation gyres on both sides of the jet. The magnitude of the northern recirculation gyre, as measured by its westward transport, is larger than the magnitude of the southern recirculation gyre. This asymmetry in recirculations is shown to be the result of an asymmetric PV mixing underneath the thermocline produced by an asymmetric jet. In particular, the lateral shift of the velocity maximum near the surface relative to the velocity maximum at depth is shown to be responsible for the asymmetry. The results are related to the Gulf Stream data between 73° and 65°W.
Abstract
Spatiotemporal evolution of a small localized meander on a Gulf Stream–type baroclinically unstable jet over a topographic slope is investigated numerically using a three-dimensional, primitive equation model. An unperturbed jet is prescribed by a potential vorticity front in the upper thermocline overlaying intermediate layers with weak isentropic potential vorticity gradients and a quiscent bottom layer over a positive (same sense as isopycnal tilt) cross-stream continental slope. A series of numerical experiments with the same initial conditions over a slope and flat bottom on the β plane and on the f plane has been carried out.
An initially localized meander evolves into a wave packet and generates deep eddies that provide a positive feedback for the meander growth. Meanders found growing over a flat bottom are able to pinch off resembling warm and cold core rings, while in the presence of a weak bottom slope such as 0.002, the maximum amplitudes of meanders and associated deep eddies saturate with no eddy shedding. In the flat bottom case, the growth rate is only 10% larger than in the weak slope case. Nevertheless, the bottom slope efficiently controls nonlinear saturation of meander growth via constraining the development of deep eddies. The topographic slope modifies the evolution of deep eddies and causes the phase displacement of deep eddies in the direction of the upper layer troughs/crests, thus limiting growth of the meanders. Behind the wave packet peak deep eddies form a nearly zonal circulation that stabilizes the jet in an equilibrated state. The main equilibration mechanism is a homogenization of the lower-layer potential vorticity by deep eddies. The width of the homogenized zone is narrower for a larger slope and/or on the β plane.
These results have the following implications to the Gulf Stream dynamics: 1) maximum of the meander amplitudes increase as the topographic slope relaxes in qualitative agreement with observed behavior of the Gulf Stream, 2) the phase locking of the meanders with deep eddies underneath at the nonlinear stage agrees qualitatively with the observed structure of large amplitude cyclonic troughs at the central array, and 3) the increase of the barotropic transport on the warm side of the jet and the generation of the recirculation on the cold side of the jet is consistent with observations in the Gulf Stream system downstream of Cape Hatteras.
Abstract
Spatiotemporal evolution of a small localized meander on a Gulf Stream–type baroclinically unstable jet over a topographic slope is investigated numerically using a three-dimensional, primitive equation model. An unperturbed jet is prescribed by a potential vorticity front in the upper thermocline overlaying intermediate layers with weak isentropic potential vorticity gradients and a quiscent bottom layer over a positive (same sense as isopycnal tilt) cross-stream continental slope. A series of numerical experiments with the same initial conditions over a slope and flat bottom on the β plane and on the f plane has been carried out.
An initially localized meander evolves into a wave packet and generates deep eddies that provide a positive feedback for the meander growth. Meanders found growing over a flat bottom are able to pinch off resembling warm and cold core rings, while in the presence of a weak bottom slope such as 0.002, the maximum amplitudes of meanders and associated deep eddies saturate with no eddy shedding. In the flat bottom case, the growth rate is only 10% larger than in the weak slope case. Nevertheless, the bottom slope efficiently controls nonlinear saturation of meander growth via constraining the development of deep eddies. The topographic slope modifies the evolution of deep eddies and causes the phase displacement of deep eddies in the direction of the upper layer troughs/crests, thus limiting growth of the meanders. Behind the wave packet peak deep eddies form a nearly zonal circulation that stabilizes the jet in an equilibrated state. The main equilibration mechanism is a homogenization of the lower-layer potential vorticity by deep eddies. The width of the homogenized zone is narrower for a larger slope and/or on the β plane.
These results have the following implications to the Gulf Stream dynamics: 1) maximum of the meander amplitudes increase as the topographic slope relaxes in qualitative agreement with observed behavior of the Gulf Stream, 2) the phase locking of the meanders with deep eddies underneath at the nonlinear stage agrees qualitatively with the observed structure of large amplitude cyclonic troughs at the central array, and 3) the increase of the barotropic transport on the warm side of the jet and the generation of the recirculation on the cold side of the jet is consistent with observations in the Gulf Stream system downstream of Cape Hatteras.
Abstract
We explore the dynamics of baroclinic instability in westward flows using an asymptotic weakly nonlinear model. The proposed theory is based on the multilayer quasigeostrophic framework, which is reduced to a system governed by a single nonlinear prognostic equation for the upper layer. The dynamics of deeper layers are represented by linear diagnostic relations. A major role in the statistical equilibration of baroclinic instability is played by the latent zonally elongated modes. These structures form spontaneously in baroclinically unstable systems and effectively suppress the amplification of primary unstable modes. Special attention is given to the effects of bottom friction, which is shown to control both linear and nonlinear properties of baroclinic instability. The reduced-dynamics model is validated by a series of numerical simulations.
Abstract
We explore the dynamics of baroclinic instability in westward flows using an asymptotic weakly nonlinear model. The proposed theory is based on the multilayer quasigeostrophic framework, which is reduced to a system governed by a single nonlinear prognostic equation for the upper layer. The dynamics of deeper layers are represented by linear diagnostic relations. A major role in the statistical equilibration of baroclinic instability is played by the latent zonally elongated modes. These structures form spontaneously in baroclinically unstable systems and effectively suppress the amplification of primary unstable modes. Special attention is given to the effects of bottom friction, which is shown to control both linear and nonlinear properties of baroclinic instability. The reduced-dynamics model is validated by a series of numerical simulations.
