Farrell, B. F., & Ioannou, P. J. (1995).
Stochastic dynamics of the mid-latitude atmospheric jet. In (Vol. 52, pp. 1642-1656) . J. Atmos. Sci.
AbstractThe innate tendency of the background straining field of the midlatitude atmospheric jet to preferentially amplify a subset of disturbances produces a characteristic response to stochastic perturbation whether the perturbations are internally generated by non linear processes or externally imposed. This physical property of enhances response to a subset of perturbations is expressed analytically through the nonnormality of t he linearized dynamical operator, which can be studied to determine the transient growth of particular disturbances over time through solution of the initial value problem or, alternatively, to determine the stationary response to continual excitation through solution of the related stochastic problem. Making use of the fact that the background flow dominates the strain rate field, a theory for the turbulent state can be constructed based on the nonormality of the dynamical operator linearized about the background flow. While the initial value problem provides an explanation for the individual cyclogenesis events, solution of the stochastic problem provides a theory for the statistics of the ensemble of all cyclones including structure, frequency, intensity, and resulting fluxes of heat and momentum, which together constitute the synoptic-scale influence on midlatitude climate. Moreover, the observed climate can be identified with the background thermal and velocity structure that is in self-consistent equilibrium with both its own induced fluxes and imposed large-scale thermal forcing. In order to approach the problem of determining the self-consistent statistical equilibrium of the midlatitude jet it is first necessary to solve the stochastic problem for the mixed baroclinic/barotropic jet because fluxes of both heat and momentum are involved in this balance.
In this work the response to stochastic forcing of a linearized nonseparable quasigeostrophic model of the midlatitude jet is solved. The observed distribution of transient eddy variance with frequency and wavenumber, the observed vertical structures, and the observed heat and momentum flux distributions are obtained. Associated energetics and implications for maintenance of the climatological jet are discussed.
.pdf DelSole, T. M., & Farrell, B. F. (1995).
A stochastically excited linear system as a model for quasigeostrophic turbulence: analytic results for one- and two-layer fluids. In (Vol. 52, pp. 2531-2547) . J. Atmos. Sci.
AbstractThe authors explore the hypothesis that nonlinear eddy interactions in quasigeosptrophic turbulence can be parameterized as a stochastic excitation plus an augmented dissipation in a statistically stationary equilibrium. The focus primarily on models sufficiently simple to be solves analytically a In particular, closed form solutions are obtained for the linear response to stochastic excitation of horizontally uniform barotropic and two-layer baroclinic flow. The response of the barotrophoic model is very simple to understand because the governing equations are mathematically normal. In contrast, the two-layer model is non-normal in the presence of vertical shear and/or vertically asymmetric dissipation and yields rather complicated results. The space-time spectra of the streamfunction and the hear fluxes derived from the two lyer model are in quantative agreement with the corresponding observed quantities at 50N. The velocity variance predicted from the parameterication is a weaker function of the temperature gradient than indicated by observations. For strong thermal forcing, the parameterized fluxes vary inversely with the difference between a critical temperature gradient and the ambient gradient. This parameterization yields behavior suggestive of baroclinic adjustment but operates by mechanisms fundamentally different from those conventionally associated with instability theory.
.pdf