Is the Coefficient of Eddy Potential Vorticity Diffusion Positive? Part I: Barotropic Zonal Channel

The question of whether the coefficient of diffusivity of potential vorticity by mesoscale eddies is positive is studied for a zonally reentrant barotropic channel using the quasigeostrophic approach. The topography is limited to the first mode in the meridional direction but is unlimited in the zonal direction. We derive an analytic solution for the stationary (time independent) solution. New terms associated with parameterized eddy fluxes of potential vorticity appear both in the equations for the mean zonal momentum balance and in the kinetic energy balance. These terms are linked with the topographic form stress exerted by parameterized eddies. It is demonstrated that in regimes with zonal flow (analogous to the Antarctic Circumpolar Current), the coefficient of eddy potential vorticity diffusivity must be positive.

Tuning of a convective gravity wave source scheme based on HIRDLS observations

Convection as one dominant source of atmospheric gravity waves (GWs) has been in focus of investigation over recent years. However, its spatial and temporal forcing scales are not well known. In this work we address this open issue by a systematic verification of free parameters of the Yonsei convective GW source scheme based on observations from the High Resolution Dynamics Limb Sounder (HIRDLS). Observational constraints are taken into account by applying a comprehensive observational filter on the simulated GWs. By this approach, only long horizontal scale convective GWs are addressed. Results show that effects of long horizontal scale convective GWs can be successfully simulated by the superposition of three or four combinations of parameter sets reproducing the observed GW spectrum. These selected parameter sets are different for northern and southern summer. Although long horizontal scale waves are only part of the full spectrum of convective GWs, the momentum flux of these waves are found to be significant and relevant for the driving of the QBO. The zonal momentum balance is considered in vertical cross sections of GW momentum flux (GWMF) and GW drag (GWD). Global maps of the horizontal distribution of GWMF are considered and consistency between simulated results and HIRDLS observations is found. The latitude dependence of the zonal phase speed spectrum of GWMF and its change with altitude is discussed.

First experimental verification of summertime mesospheric momentum balance based on radar wind measurements at 69° N

Gravity waves (GWs) greatly influence the background state of the middle atmosphere by imposing their momentum on the mean flow upon breaking and by thus driving, e.g., the upper mesospheric summer zonal wind reversal. In this situation momentum is conserved by a balance between the vertical divergence of GW momentum flux (the so-called GW drag) and the Coriolis acceleration of the mean meridional wind. In this study, we present first quantitative mean annual cycles of these two balancing quantities from the medium frequency Doppler radar at the polar site Saura (SMF radar, 69° N, 16° E). Three-year means for 2009 through 2011 clearly show that the observed zonal momentum balance between 70 and 100 km with contributions from GWs only is fulfilled during summer when GW activity is strongest and more stable than in winter. During winter, the balance between GW drag and Coriolis acceleration of the mean meridional wind is not existent, which is likely due to the additional contribution from planetary waves, which are not considered by the present investigation. The differences in the momentum balance between summer and winter conditions are additionally clarified by 3-month mean vertical profiles for summer 2010 and winter 2010/2011.

Acceleration of the Antarctic Circumpolar Current by Wind Stress along the Coast of Antarctica

The influence of wind forcing on variability of the Antarctic Circumpolar Current (ACC) is investigated using a series of eddy-permitting ocean–sea ice models. At interannual and decadal time scales the ACC transport is sensitive to both the mean strength of westerly winds along the ACC circumpolar path, consistent with zonal momentum balance theories, and sensitive to the wind stresses along the coast of Antarctica, consistent with the “free mode” theory of Hughes et al. A linear combination of the two factors explains differences in ACC transport across 11 regional quasi-equilibrium experiments. Repeated single-year global experiments show that the ACC can be robustly accelerated by both processes. Across an ensemble of simulations with realistic forcing over the second half of the twentieth century, interannual ACC transport variability owing to the free-mode mechanism exceeds that due to the zonal momentum balance mechanism by a factor of between 3.5 and 5 to one. While the ACC transport may not accelerate significantly owing to projected increases in along-ACC winds in future decades, significant changes in transport could still occur because of changes in the stress along the coast of Antarctica.

Hadley Cell Dynamics in a Virtually Dry Snowball Earth Atmosphere

The Hadley cell of a virtually dry snowball Earth atmosphere under equinox insolation is studied in a comprehensive atmospheric general circulation model. In contrast to the Hadley cell of modern Earth, momentum transport by dry convection, which is modeled as vertical diffusion of momentum, is important in the upper branch of the snowball Earth Hadley cell. In the zonal momentum balance, mean meridional advection of mean absolute vorticity is not only balanced by eddies but also by vertical diffusion of zonal momentum. Vertical diffusion also contributes to the meridional momentum balance by decelerating the Hadley cell through downgradient mixing of meridional momentum between its upper and lower branches. When vertical diffusion of momentum is suppressed in the upper branch, the Hadley cell strengthens by a factor of about 2. This is in line with the effect of vertical diffusion in the meridional momentum balance but in contrast with its effect in the zonal momentum balance. Neither axisymmetric Hadley cell theories based on angular momentum conservation nor eddy-permitting Hadley cell theories that neglect vertical diffusion of momentum are applicable to the snowball Earth Hadley cell. Because the snowball Earth Hadley cell is a particular realization of a dry Hadley cell, these results show that an appropriate description of dry Hadley cells should take into account vertical transport of momentum by dry convection.

On the Steadiness of Separating Meandering Currents

The existence of inertial steady currents that separate from a coast and meander afterward is investigated. By integrating the zonal momentum equation over a suitable area, it is shown that retroflecting currents cannot be steady in a reduced gravity or in a barotropic model of the ocean. Even friction cannot negate this conclusion. Previous literature on this subject, notably the discrepancy between several articles by Nof and Pichevin on the unsteadiness of retroflecting currents and steady solutions presented in other papers, is critically discussed. For more general separating current systems, a local analysis of the zonal momentum balance shows that given a coastal current with a specific zonal momentum structure, an inertial, steady, separating current is unlikely, and the only analytical solution provided in the literature is shown to be inconsistent. In a basin-wide view of these separating current systems, a scaling analysis reveals that steady separation is impossible when the interior flow is nondissipative (e.g., linear Sverdrup-like). These findings point to the possibility that a large part of the variability in the world’s oceans is due to the separation process rather than to instability of a free jet.

A finite-difference convective model for Jupiter's equatorial jet

We present results of a numerical model for studying the dynamics of Jupiter's equatorial jet. The computed domain is a piece of spherical shell around the equator. The bulk of the region is convective, with a thin radiative layer at the top. The shell is spinning fast, with a Coriolis number = ΩL/V on the order of 50. A prominent super-rotating equatorial jet is generated, and secondary alternating jets appear in the higher latitudes. The roles of terms in the zonal momentum equation are analyzed. Since both the Reynolds number and the Taylor number are large, the viscous terms are small. The zonal momentum balance is primarily between the Coriolis and the Reynolds stress terms.

Tropical Zonal Momentum Balance in the NCEP Reanalyses

The seasonal cycle of the zonal-mean zonal momentum balance in the Tropics is investigated using NCEP reanalysis data. It is found that the climatological stationary waves in the tropical upper troposphere, which are dominated by the equatorial Rossby wave response to tropical heating, produce an equatorward eddy flux of westerly momentum in the equatorial belt. The resulting westerly acceleration in the tropical upper troposphere is balanced by the advection of easterly momentum associated with the cross-equatorial mean meridional circulation. The eddy momentum fluxes and the cross-equatorial flow both tend to be strongest during the monsoon seasons, when the maximum diabatic heating is off the equator, and weakest during April–May, the season of strongest equatorial symmetry of the heating. The upper-level Rossby wave pattern exhibits a surprising degree of equatorial symmetry and follows a similar seasonal progression. Solutions of the nonlinear shallow water wave equation also show a predominantly equatorially symmetric response to a heat source centered off the equator.

Zonal Momentum Balance, Potential Vorticity Dynamics, and Mass Fluxes on Near-Surface Isentropes

While it has been recognized for some time that isentropic coordinates provide a convenient framework for theories of the global circulation of the atmosphere, the role of boundary effects in the zonal momentum balance and in potential vorticity dynamics on isentropes that intersect the surface has remained unclear. Here, a balance equation is derived that describes the temporal and zonal mean balance of zonal momentum and of potential vorticity on isentropes, including the near-surface isentropes that sometimes intersect the surface. Integrated vertically, the mean zonal momentum or potential vorticity balance leads to a balance condition that relates the mean meridional mass flux along isentropes to eddy fluxes of potential vorticity and surface potential temperature. The isentropic-coordinate balance condition formally resembles balance conditions well known in quasigeostrophic theory, but on near-surface isentropes it generally differs from the quasigeostrophic balance conditions. Not taking the intersection of isentropes with the surface into account, quasigeostrophic theory does not adequately represent the potential vorticity dynamics and mass fluxes on near-surface isentropes—a shortcoming that calls into question the relevance of quasigeostrophic theories for the macroturbulence and global circulation of the atmosphere.