Quasi-geostrophic Potential Vorticity Equation Research Articles

Note on simplified forms of the quasi-geostrophic potential vorticity equation

Note on simplified forms of the quasi-geostrophic potential vorticity equation

Note on simplified forms of the quasi-geostrophic potential vorticity equation

Different approximations of the general quasi-geostrophic potential vorticity equation under high Richardson number condition are obtained for different types of large-scale disturbances in the atmosphere. It is found that the complete equation is needed for the long waves in middle latitudes, but that the barotropic and non-divergent approximation is adequate for ordinary long waves in low latitude, whereas for disturbances with ultra-long horizontal length-scale in both zonal and meridional directions, the potential vorticity can be approximated by the thermal portion alone. On the other hand, for the EW-elongated ultra-long waves in the tropics, the uy term in the potential vorticity must be included. DOI: 10.1111/j.1600-0870.1984.tb00239.x

Simulations of an observed stratospheric warming with quasigeostrophic refractive index as a model diagnostic

A three-dimensional primitive equation model of the stratosphere and mesosphere is described. The model was forced at its lower boundary by observed 100 mb height fields for the wavenumber 2 stratospheric warming period of February 1979, and correctly simulated the reversal of the high latitude circulation. This behaviour contrasts with earlier model simulations of wavenumber 2 warmings in which forcing of a climatological zonally symmetric initial circulation by a stationary wave perturbation led to an initial reversal of the circulation in low latitudes. In a series of idealized experiments we show that wave-wave interaction played no essential role in this simulation and that the ingredients leading to its success were firstly the non-climatological initial wind structure and secondly an imposed longitudinal phase speed for the upward propagating planetary wave at the lower boundary. These studies also demonstrate that in the prewarming period the direction of propagation of planetary wave activity, as represented by integral curves of the so-called Eliassen-Palm flux, may be qualitatively described by the WKBJ limit of the quasi-geostrophic potential vorticity equation. In this limit, the Eliassen-Palm flux is simply related to the zonal mean refractive index, leading to two complementary diagnostics for studying wave, mean-flow interaction.

A parameter study of the mixed instability of idealized ocean currents

We investigate the nature of linear instabilities that can arise on eastward-flowing baroclinic currents similar to those found to serve as sites of strong eddy-mean flow interaction in certain mesoscale-resolution ocean circulation studies. The intent is to deduce the dependence of the linear instability mechanism — thought to be operative in some form in these simulations — on the internal parameters characterizing them. Following conventional practice, we adopt as our physical model the two-level quasigeostrophic potential vorticity equations which, in their linearized form, are solved numerically to yield the properties of the most unstable linear waves under a variety of mean flow and environmental conditions. The kinematic and dynamic features of the growing perturbations — preferred wavelength, growth rate and frequency, eddy-mean field energy transfers and vertical distribution of wave amplitude — are shown to be sensitive functions of our nondimensional parameters: (i) α = (U3U1), the ratio of lower to upper level velocity scale amplitude; (ii) X = (RdL), the ratio of the first baroclinic deformation radius to the meridional width of the jet; (iii) δ = (H1H3), the resting layer depth ratio; and (iv) ϵ = (βL2U), an (inverse) Rossby number based on the northward gradient of the planetary vorticity (β). Viscous effects, although included in the analysis, are shown to be unimportant for values of frictional coefficients typical of recent eddy-resolving ocean model studies. Despite a strong dependence of the details of the linear instability mechanism on environmental factors, the associated unstable eigenmodes do have important structural similarities which are intimately connected with their ability to extract energy from the mean flow.

A Mechanistic Model of Ozone Transport by Planetary Waves in the Stratosphere

Abstract The role of planetary-scale waves in the transport of ozone in middle and high latitudes is studied with a linearized model which takes into account the coupling between radiation, chemistry and dynamics. The governing equations are a quasi-geostrophic potential vorticity equation and a continuity equation for perturbations of the O3 mixing ratio. These equations include the effects of absorption of solar radiation by O3, temperature-dependent O3 photochemistry and advection of O3 by wave motions. Model runs show that, with a basic state representative of winter conditions, ultralong waves can produce O3 perturbation which exhibit a phase shift of nearly 180° between the lower stratosphere (where the O3 perturbations are controlled by advection) and the upper stratosphere (where they are controlled by photochemical processes). This phase shift brings the O3 perturbation into phase with the eddy meridional velocity (and 180° out of phase with the eddy vertical velocity) at ∼45 km, giving rise to l...

Characteristics of disturbances in the atmosphere and oceans

The characteristics of the disturbances in the atmosphere and oceans and in other stably stratified and rotating fluids are analyzed according to their phase and group velocities. It is shown that both stable stratification and rotation augment the velocity of the sound waves, and that the internal gravity waves and inertial waves are mutually exclusive when the Brunt-Vaisala frequency is different from the Coriolis parameter. It is also shown that both the barotropic and the internal Rossby waves are well separated from the gravity waves and that they can be represented accurately by the quasi-geostrophic potential vorticity equation, even close to the equator, except for the one member withn=0 which is coupled with an eastward propagating gravity wave.

Deep-ocean dynamics for environmental acoustics models

A hydrodynamic model for flows in the deep ocean is developed in order to determine the velocity field and sound-speed distribution for use in acoustic transmission problems. A scaling of the governing equations is constructed that explicitly includes sound speed. A subsequent perturbation expansion yields a set of approximate equations for motions nearly in geostrophic and hydrostatic balance, such as large-scale, quasisteady currents and Rossby waves. The quasigeostrophic potential vorticity equation or a simpler limiting case of this equation arises from the perturbation scheme to govern higher-order dynamics of the stream function for these flows. The results of the analysis are used to obtain a significant simplification of the ray equations of geometrical acoustics for moving media. For the particular class of flows considered here, the model equations are applicable if the ocean depth is about 1 km or greater and if the spatial and temporal scales of variation of the motions are of the order of 100 km and 10 days, respectively. A solution for a flow such as the Antilles current is derived. Isospeed curves for this solution are shown in a plane perpendicular to the current, and specific features of the curves are discussed and interpreted. Subject Classification: [43]30.25, [43]30.20; [43]28.60.

The effect of side walls on homogeneous rotating flow over two-dimensional obstacles

We consider the flow of a slightly viscous homogeneous fluid over a small two-dimensional obstacle perpendicular to the vertical side walls in a channel rotating about a vertical axis. The flow in the channel is obtained from the solution of the quasi-geostrophic potential vorticity equation in the limit ε = D/L→ 0, where D is the obstacle width and L the channel width. The lowest order, interior flow is shown to be a combination of three effects: a rotational flow caused by vortex stretching and Ekman boundary-layer pumping; a significant irrotational flow induced by the magnitude of the former flow at the vertical boundaries; and the interior Ekman drift due to the basic current. The maximum streamline displacement is calculated and compares very well with recent experiments in the identical parameter range by Boyer (1971a, b). This theory explains how the side walls are responsible for the dependence of the maximum streamline displacement on Rossby number.