Structural Determinism of Linear Baroclinic Waves and Simple Nonlinear Equilibration

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  • 1 Department of Meteorology, University of Stockholm, Arrhenius Laboratory, S-106 91 Stockholm, Sweden
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Abstract

The linear evolution of arbitrarily specified perturbations in a zonally homogeneous, two-layer model is analyzed in a dynamical system which describes the disturbances in terms of the phase difference and amplitude ratio between the temperature and streamfunction components. The stationary equilibria of this system are equivalent to the individual eigenmodes of normal mode analysis and in the inviscid case, simple analytical expressions for these equilibria are possible. These expressions allow us to quantitatively examine the physical processes that determine the normal mode structures in the inviscid case and how the processes of friction then affect them. The advantage to this approach is that a conceptual understanding for the processes determining the so-called “preferred structure” and their characteristics (e.g., growth rates) of normal mode analysis is obtained in terms of the basic Quid flow properties of advection, dispersion and dissipation. But the most important conceptual property we find is that in the presence of dissipation the normal modes are indeed “preferred structure” or deterministic, in the sense that any arbitrarily specified initial perturbation evolves asymptotically to that structure. This is not always the case in the inviscid problem or certain cases of symmetrically applied dissipation. However, the occurrence of determinism in this simple case allows us to conceptually investigate and understand the equilibrated truncated nonlinear state in terms of the linear solution.

Abstract

The linear evolution of arbitrarily specified perturbations in a zonally homogeneous, two-layer model is analyzed in a dynamical system which describes the disturbances in terms of the phase difference and amplitude ratio between the temperature and streamfunction components. The stationary equilibria of this system are equivalent to the individual eigenmodes of normal mode analysis and in the inviscid case, simple analytical expressions for these equilibria are possible. These expressions allow us to quantitatively examine the physical processes that determine the normal mode structures in the inviscid case and how the processes of friction then affect them. The advantage to this approach is that a conceptual understanding for the processes determining the so-called “preferred structure” and their characteristics (e.g., growth rates) of normal mode analysis is obtained in terms of the basic Quid flow properties of advection, dispersion and dissipation. But the most important conceptual property we find is that in the presence of dissipation the normal modes are indeed “preferred structure” or deterministic, in the sense that any arbitrarily specified initial perturbation evolves asymptotically to that structure. This is not always the case in the inviscid problem or certain cases of symmetrically applied dissipation. However, the occurrence of determinism in this simple case allows us to conceptually investigate and understand the equilibrated truncated nonlinear state in terms of the linear solution.

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