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Dean G. Duffy

Abstract

In this paper the tropospheric-stratospheric system is modeled as a two-layer, quasigeostrophic atmosphere, and the modal and nonmodal solutions that arise from an impulse forcing within the troposphere are found. Regardless of the nature of the zonal flow, the troposphere can support disturbances over a broad range of wavenumbers, whereas the stratosphere solutions have significant amplitudes only at low wavenumbers. The results are applied to observational data given by a tropospheric-stratospheric analysis. It is shown that explosive baroclinic disturbances within the troposphere can generate transient waves within the stratosphere.

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Dean G. Duffy

Abstract

The split explicit integration scheme for numerical weather prediction models is employed in a version of the regional numerical weather prediction model of the Japan Meteorological Agency. The finite-difference scheme of the model is designed in the manner proposed by Okamura (1975). The horizontal advection terms in the governing equations are integrated with a time step limited by the wind speed while the terms which describe inertial-gravity oscillations are integrated in a succession of shorter time steps. The physical processes included within the model are precipitation, small-scale convection, surface exchanges of sensible and latent beat, and radiative heating and cooling.

An example of a surface pressure forecast over Europe is shown for initial data observed at 0000 GMT 29 December 1979. Quantitative precipitation forecasts over Europe and North America for the 24 h period beginning at 0000 GMT 30 December 1979 are also shown. It is concluded that the model is capable of realistically depicting the evolution of synoptic-scale systems.

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Dean G. Duffy

Abstract

The stability of the classical Norwegian polar front model is reinvestigated, using a numerical technique to supplement the precise conclusions which are possible in the limiting case of zero density difference or zero wavenumber. Instead of using the primitive equations, a system of filtered momentum equations which neglects the substantial derivative of the ageostrophic put of the horizontal wind is used to test the applicability to meteorological problems. For Rossby numbers ≪0.4, the agreement between the primitive and the semigeostrophic equations is found to he good provided that the Richardson number is not ton small. Unstable waves are found only at Rossby numbers less than a critical value; large-scale shear instability exists at small Richardson number and quasigeostrophic baroclinic instability occurs at larger Richardson number.

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Dean G. Duffy

Abstract

The barotropic instability of a stationary Rossby wave to arbitrarily small-amplitude perturbations is investigated primarily by analytical means. The flow is found to be unstable; in addition to the unstable and neutral Rossby waves found by Lorenz, the author finds additional modes corresponding to stable inertial-gravity waves. The amplifying disturbances receive their energy from the eddy kinetic energy of the basic flow.

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Dean G. Duffy

Abstract

Lorenz's stability analysis of a finite-amplitude, barotropic Rossby wave is extended to a nonlinear, finite-amplitude, neutrally stable Eady wave with a vertical phase shift. For disturbances with a meridional wave-number less than the zonal wavenumber of the Eady wave, instability results from baroclinic and barotropic instability. For disturbances with a meridional wavenumber greater than the zonal wavenumber of the Eady wave, instability also occurs but results only from baroclinic instability. The most unstable mode occurs when the meridional wavelength of the perturbation is approximately twice the zonal wavelength of the Eady wave.

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Dean G. Duffy

Abstract

The classical geostrophic adjustment problem is reexamined in a baroclinically unstable atmosphere. After the geostrophic balance is disturbed by either adding mass or momentum to the atmosphere, the resulting evolution of the mass and momentum fields is found by using Laplace and Fourier transforms. In general, the results from classical geostrophic theory hold in the baroclinically unstable atmosphere. Although the most unstable modes eventually dominate, in certain situations the perturbations may actually decay before they begin to grow. This may be a key mechanism which explains a portion of the spinup problem commonly encountered in numerical models.

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Dean G. Duffy

Abstract

The nonlinear dynamics of inertial-gravity and Rossby waves are studied via the asymptotic method of multiple scales. Two important parameters which enter the problem are the conventional Rossby number ε and a nondimensional measure of the northward variation of the Coriolis parameter μ. Restricted to the weakly nonlinear limit (ε≪1), this paper examines three possible nonlinear wave motions: weakly non-linear interactions on an f-plane (μ=0), very weakly interacting disturbances in a quiescent atmosphere [ε=O(μ2)], and nonlinear interactions of finite-amplitude disturbances [ε=O(μ)]. In particular, resonant interactions are studied and the slow modulations of the linear solutions due to the nonlinearity are found. Some of these nonlinear solutions are unstable, being able to feed their energy into a resonantly interacting pair of disturbances.

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Dean G. Duffy

Abstract

The ability of various numerical techniques used in compressible, nonhydrostatic models to handlehydrostatic adjustment is intercompared. The exact solution of a linearized model of an isothermal, compressible, nonrotating atmosphere is compared against those from finite-differenced versions of the samemodel. For the semi-implicit scheme, the scheme traps acoustic waves near the point of excitation but haslittle effect on gravity waves. The time-splitting scheme captures hydrostatic adjustment well.

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Dean G. Duffy

Abstract

The author examines hydrostatic adjustment due to heating in two nonisothermal atmospheres. In the first case both the temperature and lapse rate decrease with height; in the second case the atmosphere consists of a troposphere with constant lapse rate and a colder, isothermal, semi-infinitely deep stratosphere. In both cases hydrostatic adjustment, to a good approximation, follows the pattern found in the Lamb problem: initially the Eulerian available potential energy remains essentially constant so that an increase (a decrease) in the kinetic energy occurs with a corresponding decrease (increase) of Eulerian available elastic energy. After this initial period the acoustic–gravity waves disperse and all three forms of energy—Eulerian kinetic, Eulerian available potential, and available elastic—interact with each other. Relaxation to hydrostatic balance occurs rapidly, within the first acoustic cutoff period 4πH S/c, where c is the speed of sound and H S is the scale height. In the Lagrangian description, the available potential energy remains constant with time. The kinetic energy is coupled to the Lagrangian available elastic energy so that an increase (a decrease) in the kinetic energy always occurs with a corresponding decrease (increase) of Lagrangian available elastic energy.

The primary effect of a positive lapse rate is a decrease in the percentage of the total perturbation energy available for wave motions. In the two-layer atmosphere, the discontinuity in the static stability at the tropopause results in imperfect ducting of the acoustic–gravity waves within the troposphere.

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Dean G. Duffy

Abstract

Recently a new spectral technique has been developed for the analysis of aperiodic signals from nonlinear systems—the Hilbert–Huang transform. It is shown how this transform can be used to discover synoptic and climatic features: For sea level data, the transforms capture the oceanic tides as well as variations in precipitation patterns. In the case of solar radiation, variations in the diurnal and seasonal cycles are observed. Finally, from barographic data, the Hilbert–Huang transform reveals the passage of extratropical cyclones, fronts, and troughs. Thus, this technique can detect signals on synoptic to interannual time scales.

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