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- Author or Editor: P. G. Drazin x
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Abstract
The weakly nonlinear dynamics of quasi-geostrophic Perturbations of various basic states is investigated. The basic states differ slightly from Eady's, i.e., from an inviscid zonal flow of a fluid of uniform Brunt–Väisälä frequency in which the velocity varies linearly with height. Such differences lead to weak critical layers which may, in a certain region of parameter space where the Eady basic state is neutrally stable, render the flows unstable to some modes: the Green modes. Weak dissipation may balance the growth of these modes. In accord with the numerical results of Lindzen, Farrell and Jacqmin, it is found asymptotically that, in that region of parameter space, two modes with the same wavenumbers may grow. The weakly nonlinear interactions of these unstable modes and the basic state am examined in detail. It is found that the modes may equilibrate. Amplitude vacillation is identified as the physical manifestation of this equilibration, because the two finite amplitude waves with different vertical structures alternately reinforce and cancel one another by interference as they propagate zonally with different velocities. The results for a special case are found to illustrate the theory and are compared with experimental observations of a differentially heated rotating annulus.
Abstract
The weakly nonlinear dynamics of quasi-geostrophic Perturbations of various basic states is investigated. The basic states differ slightly from Eady's, i.e., from an inviscid zonal flow of a fluid of uniform Brunt–Väisälä frequency in which the velocity varies linearly with height. Such differences lead to weak critical layers which may, in a certain region of parameter space where the Eady basic state is neutrally stable, render the flows unstable to some modes: the Green modes. Weak dissipation may balance the growth of these modes. In accord with the numerical results of Lindzen, Farrell and Jacqmin, it is found asymptotically that, in that region of parameter space, two modes with the same wavenumbers may grow. The weakly nonlinear interactions of these unstable modes and the basic state am examined in detail. It is found that the modes may equilibrate. Amplitude vacillation is identified as the physical manifestation of this equilibration, because the two finite amplitude waves with different vertical structures alternately reinforce and cancel one another by interference as they propagate zonally with different velocities. The results for a special case are found to illustrate the theory and are compared with experimental observations of a differentially heated rotating annulus.
Abstract
Under the assumptions of small perturbation, long wavelength and two dimensionality, it is shown that the effects of the atmospheric structure and the mountain profile on a lee wave problem can be calculated separately. The flow field is then given entirely by a composite formula.
Abstract
Under the assumptions of small perturbation, long wavelength and two dimensionality, it is shown that the effects of the atmospheric structure and the mountain profile on a lee wave problem can be calculated separately. The flow field is then given entirely by a composite formula.
Abstract
A simple, zonally and annually averaged, energy-balance climatological model with diffusive heat transport and nonlinear albedo feedback is solved numerically. Some parameters of the model are varied, one by one, to find the resultant effects on the steady solution representing the climate. In particular, the outward radiation flux, the insulation distribution and the albedo parameterization are varied. We have found an accurate yet simple analytic expression for the mean annual insolation as a function of latitude and the obliquity of the Earth's rotation axis; this has enabled us to consider the effects of the oscillation of the obliquity. We have used a continuous albedo function which fits the observed values; it considerably reduces the sensitivity of the model. Climatic cycles, calculated by solving the time-dependent equation when parameters change slowly and periodically, are compared qualitatively with paleoclimatic records.
Abstract
A simple, zonally and annually averaged, energy-balance climatological model with diffusive heat transport and nonlinear albedo feedback is solved numerically. Some parameters of the model are varied, one by one, to find the resultant effects on the steady solution representing the climate. In particular, the outward radiation flux, the insulation distribution and the albedo parameterization are varied. We have found an accurate yet simple analytic expression for the mean annual insolation as a function of latitude and the obliquity of the Earth's rotation axis; this has enabled us to consider the effects of the oscillation of the obliquity. We have used a continuous albedo function which fits the observed values; it considerably reduces the sensitivity of the model. Climatic cycles, calculated by solving the time-dependent equation when parameters change slowly and periodically, are compared qualitatively with paleoclimatic records.
Abstract
We consider the general structure of the equilibrium solutions of simple, zonally averaged, energy-balance climatological models with diffusive heat transport and a nonlinear ice albedo feedback. The relation between the appearance of unstable modes and the bifurcation of equilibrium solutions is elucidated, in particular the relation between antisymmetric modes and bifurcation of asymmetric equilibrium solutions. Numerical solution of a specific model, which has been shown by others to possess an equilibrium solution similar to the present climate of the earth, shows that as well as the several previously known symmetric equilibrium solutions, it possesses asymmetric solutions, including ones with an ice cap at only one pole. One of these types of asymmetric solutions is shown to be stable for values of parameters which represent present conditions on earth.
Abstract
We consider the general structure of the equilibrium solutions of simple, zonally averaged, energy-balance climatological models with diffusive heat transport and a nonlinear ice albedo feedback. The relation between the appearance of unstable modes and the bifurcation of equilibrium solutions is elucidated, in particular the relation between antisymmetric modes and bifurcation of asymmetric equilibrium solutions. Numerical solution of a specific model, which has been shown by others to possess an equilibrium solution similar to the present climate of the earth, shows that as well as the several previously known symmetric equilibrium solutions, it possesses asymmetric solutions, including ones with an ice cap at only one pole. One of these types of asymmetric solutions is shown to be stable for values of parameters which represent present conditions on earth.
