Rossby waves and α\alpha-effect

Rossby waves drifting in the azimuthal direction are a common feature at the onset of thermal convective instability in a rapidly rotating spherical shell. They can also result from the destabilization of a Stewartson shear layer produced by differential rotation as expected in the liquid sodium experiment (DTS) working in Grenoble, France. A usual way to explain why Rossby waves can participate to the dynamo process goes back to Busse (1975). In his picture, the flow geometry is a cylindrical array of parallel rolls aligned with the rotation axis. The axial flow component (the component parallel to the rotation axis) is (i) maximum in the middle of each roll and changes its sign from one roll to the next. It is produced by the Ekman pumping at the fluid containing shell boundary. The corresponding dynamo mechanism can be explained in terms of an $\alpha$-tensor with non-zero coefficients on the diagonal. In rapidly rotating objects like the Earth's core (or in a fast rotating experiment), Rossby waves occur in the limit of small Ekman number ($\approx 10^{-15}$). In that case, the main source of the axial flow component is not the Ekman pumping but rather the ``geometrical slope effect'' due to the spherical shape of the fluid containing shell. This implies that the axial flow component is (ii) maximum at the borders of the rolls and not at the centers. If assumed to be stationary, such rolls would lead to zero coefficients on the diagonal of the $\alpha$-tensor, making the dynamo probably less efficient if possible at all. Actually, the rolls are drifting as a wave, and we show that this drift implies non--zero coefficients on the diagonal of the $\alpha$-tensor. These new coefficients are in essence very different from the ones obtained in case (i) and cannot be interpreted in terms of the heuristic picture of Busse (1975)

Topical cyclone rainfall characteristics as determined from a satellite passive microwave radiometer

Data from the Nimbus-5 Electrically Scanning Microwave Radiometer (ESMR-5) were used to calculate latent heat release and other rainfall parameters for over 70 satellite observations of 21 tropical cyclones in the tropical North Pacific Ocean. The results indicate that the ESMR-5 measurements can be useful in determining the rainfall characteristics of these storms and appear to be potentially useful in monitoring as well as predicting their intensity. The ESMR-5 derived total tropical cyclone rainfall estimates agree favorably with previous estimates for both the disturbance and typhoon stages. The mean typhoon rainfall rate (1.9 mm h(-1)) is approximately twice that of disturbances (1.1 mm h(-1))

Thunderstorm vertical velocities and mass flux estimated from satellite data

Infrared geosynchronous satellite data with an interval of five minutes between images are used to estimate thunderstorm top ascent rates on two case study days. A mean vertical velocity of 3.5/ms for 19 clouds is calculated at a height of 8.7 km. This upward motion is representative of an area of approximately 10km on a side. Thunderstorm mass flux of approximately 2x10 to the 11th power/gs is calculated, which compares favorably with previous estimates. There is a significant difference in the mean calculated vertical velocity between elements associated with severe weather reports (w bar=4.6/ms) and those with no such reports (2.5/ms). Calculations were made using a velocity profile for an axially symmetric jet to estimate the peak updraft velocity. For the largest observed w value of 7.8/ms the calculation indicates a peak updraft of approximately 50/ms

Satellite-observed latent heat release in a tropical cyclone

Data from the Nimbus 5 electrically scanning microwave radiometer (ESMR) are used to make calculations of the latent heat release (L.H.R.) and the distribution of rainfall rate in a tropical cyclone as it grows from a tropical disturbance to a typhoon. The L.H.R. (calculated over a circular area of 4 deg latitude radius) increases during the development and intensification of the storm from a magnitude of 2.7 X 10 to the 21st power ergs/s (in the disturbance stage) to 8.8 X 10 to the 21st power ergs (typhoon stage). The latter value corresponds to a mean rainfall rate of 2.0 mm hr/s. The more intense the cyclone and the greater the L.H.R., the greater the percentage contribution of the larger rainfall rates to the L.H.R. In the disturbance stage the percentage contribution of rainfall rates less than or minus 6 mm hr/s is typically 8%; for the typhoon stage, the value is 38%. The distribution of rainfall rate as a function of radial distance from the center indicates that as the cyclone intensifies, the higher rainfall rates tend to concentrate toward the center of the circulation

No Eigenvalue in Finite Quantum Electrodynamics

We re-examine Quantum Electrodynamics (QED) with massless electron as a finite quantum field theory as advocated by Gell-Mann-Low, Baker-Johnson, Adler, Jackiw and others. We analyze the Dyson-Schwinger equation satisfied by the massless electron in finite QED and conclude that the theory admits no nontrivial eigenvalue for the fine structure constant.Comment: 13 pages, Late

Rain estimation from satellites: An examination of the Griffith-Woodley technique

The Griffith-Woodley Technique (GWT) is an approach to estimating precipitation using infrared observations of clouds from geosynchronous satellites. It is examined in three ways: an analysis of the terms in the GWT equations; a case study of infrared imagery portraying convective development over Florida; and the comparison of a simplified equation set and resultant rain map to results using the GWT. The objective is to determine the dominant factors in the calculation of GWT rain estimates. Analysis of a single day's convection over Florida produced a number of significant insights into various terms in the GWT rainfall equations. Due to the definition of clouds by a threshold isotherm the majority of clouds on this day did not go through an idealized life cycle before losing their identity through merger, splitting, etc. As a result, 85% of the clouds had a defined life of 0.5 or 1 h. For these clouds the terms in the GWT which are dependent on cloud life history become essentially constant. The empirically derived ratio of radar echo area to cloud area is given a singular value (0.02) for 43% of the sample, while the rainrate term is 20.7 mmh-1 for 61% of the sample. For 55% of the sampled clouds the temperature weighting term is identically 1.0. Cloud area itself is highly correlated (r=0.88) with GWT computed rain volume. An important, discriminating parameter in the GWT is the temperature defining the coldest 10% cloud area. The analysis further shows that the two dominant parameters in rainfall estimation are the existence of cold cloud and the duration of cloud over a point

A Shape Theorem for Riemannian First-Passage Percolation

Riemannian first-passage percolation (FPP) is a continuum model, with a distance function arising from a random Riemannian metric in $\R^d$. Our main result is a shape theorem for this model, which says that large balls under this metric converge to a deterministic shape under rescaling. As a consequence, we show that smooth random Riemannian metrics are geodesically complete with probability one

Mean meridional circulation in the Southern Hemisphere stratosphere during the polar night

Atmospheric structure derived from satellite, multichannel radiance data is used to calculate zonally averaged vertical motions in the wintertime stratosphere of both hemispheres. The Northern Hemisphere calculations confirm the two celled meridional circulation calculated by previous authors. The Southern Hemisphere results show a three celled structure with descending motion over the South Pole. The variability of the mean meridional circulation in the Southern Hemisphere in relation to the presence or absence of a minor midwinter warming is also discussed

A comparison of the structure and flow characteristics of the upper troposphere and stratosphere of the Northern and Southern Hemispheres

The general circulations of the Northern and Southern Hemispheres are compared with regard to the upper troposphere and stratosphere using atmospheric structure obtained from satellite, multi-channel radiance data. Specifically, the data are from the Satellite Infrared Spectrometer (SIRS) instrument aboard the Nimbus 3 spacecraft. The inter-hemispheric comparisons are based on two months of data (one summer month and one winter month) in each hemisphere. Topics studied include: mean meridional circulation in the Southern Hemisphere stratosphere; magnitude and distribution of tropospheric eddy heat flux; magnitudes of energy cycle components; and the relation of vortex structure to the breakdown climatology of the Antarctic stratospheric polar vortex

On Di\'osi-Penrose criterion of gravity-induced quantum collapse

It is shown that the Di\'osi-Penrose criterion of gravity-induced quantum collapse may be inconsistent with the discreteness of space-time, which is generally considered as an indispensable element in a complete theory of quantum gravity. Moreover, the analysis also suggests that the discreteness of space-time may result in rapider collapse of the superposition of energy eigenstates than required by the Di\'osi-Penrose criterion.Comment: 5 pages, no figure