Baroclinic stationary waves in aquaplanet models

An aquaplanet model is used to study the nature of the highly persistent low-frequency waves that have been observed in models forced by zonally symmetric boundary conditions. Using the Hayashi spectral analysis of the extratropical waves, the authors find that a quasi-stationary wave 5 belongs to a wave packet obeying a well-defined dispersion relation with eastward group velocity. The components of the dispersion relation with k ≥ 5 baroclinically convert eddy available potential energy into eddy kinetic energy, whereas those with k < 5 are baroclinically neutral. In agreement with Green’s model of baroclinic instability, wave 5 is weakly unstable, and the inverse energy cascade, which had been previously proposed as a main forcing for this type of wave, only acts as a positive feedback on its predominantly baroclinic energetics. The quasi-stationary wave is reinforced by a phase lock to an analogous pattern in the tropical convection, which provides further amplification to the wave. It is also found that the Pedlosky bounds on the phase speed of unstable waves provide guidance in explaining the latitudinal structure of the energy conversion, which is shown to be more enhanced where the zonal westerly surface wind is weaker. The wave’s energy is then trapped in the waveguide created by the upper tropospheric jet stream. In agreement with Green’s theory, as the equator-to-pole SST difference is reduced, the stationary marginally stable component shifts toward higher wavenumbers, while wave 5 becomes neutral and westward propagating. Some properties of the aquaplanet quasi-stationary waves are found to be in interesting agreement with a low frequency wave observed by Salby during December–February in the Southern Hemisphere so that this perspective on low frequency variability, apart from its value in terms of basic geophysical fluid dynamics, might be of specific interest for studying the earth’s atmosphere.

Classification of instability modes in a model of aluminium reduction cells with a uniform magnetic field

A unified view on the interfacial instability in a model of aluminium reduction cells in the presence of a uniform, vertical, background magnetic field is presented. The classification of instability modes is based on the asymptotic theory for high values of parameter β, which characterises the ratio of the Lorentz force based on the disturbance current, and gravity. It is shown that the spectrum of the travelling waves consists of two parts independent of the horizontal cross-section of the cell: highly unstable wall modes and stable or weakly unstable centre, or Sele’s modes. The wall modes with the disturbance of the interface being localised at the sidewalls of the cell dominate the dynamics of instability. Sele’s modes are characterised by a distributed disturbance over the whole horizontal extent of the cell. As β increases these modes are stabilized by the field.

Baroclinic waves with parameterized effects of moisture interpreted using Rossby wave components

A theoretical framework is developed for the evolution of baroclinic waves with latent heat release parameterized in terms of vertical velocity. Both wave–conditional instability of the second kind (CISK) and large-scale rain approaches are included. The new quasigeostrophic framework covers evolution from general initial conditions on zonal flows with vertical shear, planetary vorticity gradient, a lower boundary, and a tropopause. The formulation is given completely in terms of potential vorticity, enabling the partition of perturbations into Rossby wave components, just as for the dry problem. Both modal and nonmodal development can be understood to a good approximation in terms of propagation and interaction between these components alone. The key change with moisture is that growing normal modes are described in terms of four counterpropagating Rossby wave (CRW) components rather than two. Moist CRWs exist above and below the maximum in latent heating, in addition to the upper- and lower-level CRWs of dry theory. Four classifications of baroclinic development are defined by quantifying the strength of interaction between the four components and identifying the dominant pairs, which range from essentially dry instability to instability in the limit of strong heating far from boundaries, with type-C cyclogenesis and diabatic Rossby waves being intermediate types. General initial conditions must also include passively advected residual PV, as in the dry problem.

Sensitivity of GCM tropical middle atmosphere variability and climate to ozone and parametrized gravity wave changes

This paper describes the impact of changing the current imposed ozone climatology upon the tropical Quasi-Biennial Oscillation (QBO) in a high top climate configuration of the Met Office U.K. general circulation model. The aim is to help distinguish between QBO changes in chemistry climate models that result from temperature-ozone feedbacks and those that might be forced by differences in climatology between previously fixed and newly interactive ozone distributions. Different representations of zonal mean ozone climatology under present-day conditions are taken to represent the level of change expected between acceptable model realizations of the global ozone distribution and thus indicate whether more detailed investigation of such climatology issues might be required when assessing ozone feedbacks. Tropical stratospheric ozone concentrations are enhanced relative to the control climatology between 20–30 km, reduced from 30–40 km and enhanced above, impacting the model profile of clear-sky radiative heating, in particular warming the tropical stratosphere between 15–35 km. The outcome is consistent with a localized equilibrium response in the tropical stratosphere that generates increased upwelling between 100 and 4 hPa, sufficient to account for a 12 month increase of modeled mean QBO period. This response has implications for analysis of the tropical circulation in models with interactive ozone chemistry because it highlights the possibility that plausible changes in the ozone climatology could have a sizable impact upon the tropical upwelling and QBO period that ought to be distinguished from other dynamical responses such as ozone-temperature feedbacks.

Equatorial waves in opposite QBO phases

A methodology for identifying equatorial waves is used to analyze the multilevel 40-yr ECMWF Re-Analysis (ERA-40) data for two different years (1992 and 1993) to investigate the behavior of the equatorial waves under opposite phases of the quasi-biennial oscillation (QBO). A comprehensive view of 3D structures and of zonal and vertical propagation of equatorial Kelvin, westward-moving mixed Rossby–gravity (WMRG), and n = 1 Rossby (R1) waves in different QBO phases is presented. Consistent with expectation based on theory, upward-propagating Kelvin waves occur more frequently during the easterly QBO phase than during the westerly QBO phase. However, the westward-moving WMRG and R1 waves show the opposite behavior. The presence of vertically propagating equatorial waves in the stratosphere also depends on the upper tropospheric winds and tropospheric forcing. Typical propagation parameters such as the zonal wavenumber, zonal phase speed, period, vertical wavelength, and vertical group velocity are found. In general, waves in the lower stratosphere have a smaller zonal wavenumber, shorter period, faster phase speed, and shorter vertical wavelength than those in the upper troposphere. All of the waves in the lower stratosphere show an upward group velocity and downward phase speed. When the phase of the QBO is not favorable for waves to propagate, their phase speed in the lower stratosphere is larger and their period is shorter than in the favorable phase, suggesting Doppler shifting by the ambient flow and a filtering of the slow waves. Tropospheric WMRG and R1 waves in the Western Hemisphere also show upward phase speed and downward group velocity, with an indication of their forcing from middle latitudes. Although the waves observed in the lower stratosphere are dominated by “free” waves, there is evidence of some connection with previous tropical convection in the favorable year for the Kelvin waves in the warm water hemisphere and WMRG and R1 waves in the Western Hemisphere, which is suggestive of the importance of convective forcing for the existence of propagating coupled Kelvin waves and midlatitude forcing for the existence of coupled WMRG and R1 waves.

Equivalence of weak formulations of the steady water waves equations

We prove the equivalence of three weak formulations of the steady water waves equations, namely: the velocity formulation, the stream function formulation and the Dubreil-Jacotin formulation, under weak Hölder regularity assumptions on their solutions.

Gravity well visibility in haptic interfaces for motion-impaired

Haptic computer interfaces provide users with feedback through the sense of touch, thereby allowing users to feel a graphical user interface. Force feedback gravity wells, i.e. attractive basins that can pull the cursor toward a target, are one type of haptic effect that have been shown to provide improvements in "point and click" tasks. For motion-impaired users, gravity wells could improve times by as much as 50%. It has been reported that the presentation of information to multiple sensory modalities, e.g. haptics and vision, can provide performance benefits. However, previous studies investigating the use of force feedback gravity wells have generally not provided visual representations of the haptic effect. Where force fields extend beyond clickable targets, the addition of visual cues may affect performance. This paper investigates how the performance of motion-impaired computer users is affected by having visual representations of force feedback gravity wells presented on-screen. Results indicate that the visual representation does not affect times and errors in a "point and click" task involving multiple targets.