Motion and wake structure of spherical particles

This paper presents results from a flow visualization study of the wake structures behind solid spheres rising or falling freely in liquids under the action of gravity. These show remarkable differences to the wake structures observed behind spheres held fixed. The two parameters controlling the rise or fall velocity (i.e., the Reynolds number) are the density ratio between sphere and liquid and the Galileo number.Comment: 9 pages, 8 figures. Higher resolution on demand. To appear in Nonlinearity January 200

A brief summary of L. van Wijngaarden's work up till his retirement

This paper attempts to provide an overview of Professor Leen van Wijngaarden's scientific work by briefly summarizing a number of his papers. The review is organized by topic and covers his work on pressure waves in bubbly liquids, bubble dynamics, two-phase flow, standing waves in resonant systems, and flow cavitation noise. A list of publications up till his retirement in March 1997 is provided in the Appendix

On the characteristics of the equations of motion for a bubbly flow and the related problem of critical flow

For the study of transients in gas-liquid flows, the equations of the so-called separated flow model are inadequate, because they possess, in the general case where gas and liquid move at different velocities, complex characteristics. This paper is concerned with the equations of motion for bubbly flow. The equations are discussed with emphasis on the aspects of relative motion and the characteristics are calculated. It is found that all characteristics are real. The results are used to establish a relation between gas velocity, liquid velocity, void fraction and sound velocity at critical flow. This relation agrees very well with experimental data for these quantities as measured by Muir and Eichhorn in the throat of a converging-diverging nozzle

Effect of Greenhouse Gases on Thermal Emissivity by Clouds

Greenhouse gases, most importantly water vapor, increase the emissivity and decrease the albedo of clouds for thermal radiation. The modifications, which can be of order 10% for optically thick clouds, depend on the attenuation coefficient $\alpha^{\{g\}}$ of the greenhouse gases, and also on the attenuation coefficient, $\alpha^{\{c\}}$, the single-scattering albedo $\tilde \omega^{\{c\}}$, and the scattering phase function $p^{\{c\}}(\mu,\mu')$ of the cloud particulates. Cold, high-altitude clouds with low partial pressures of water vapor have smaller emissivities for thermal radiation and larger albedos than otherwise identical but warmer low-altitude clouds with higher partial pressures of water vapor. In $2n$-stream scattering theory, these phenomena can be quantified with the intensity emissivities $\varepsilon_{i}$ of the streams $i=1,2,3,\ldots, 2n$, and with upward or downward flux emissivities, $\varepsilon_{\bf u}$ and $\varepsilon_{\bf d}$. The emissivities are the ratios of the outgoing thermal intensities or fluxes to those of a reference black cloud. Emission from optically-thick, isothermal clouds with scattering, as well as absorption and emission, is limb darkened. Intensity emissivities $\varepsilon_i$ for streams that are nearly normal to the cloud surface are larger than those of more nearly horizontal streams. The limb darkening increases with increasing values of the single scattering albedo $\tilde \omega$. For fixed values of $\tilde\omega$, the onset of limb darkening with increasing zenith angle is more abrupt for phase functions with more forward scattering. Black clouds, which have only absorption and emission but no scattering, have unit (Lambertian) emissivities, $\varepsilon_i = 1$, for all stream directions

Instantaneous Clear Sky Radiative Forcings of Halogenated Gases

The clear sky instantaneous radiative forcings of the 14 halogenated gases previously shown to have the largest contribution to global warming, were found. The calculation used the absorption cross sections for the halogenated gases which are assumed to be independent of temperature as well as over 1/3 million line strengths for the 5 naturally occurring greenhouse gases: H$_2$O, CO$_2$, O$_3$, CH$_4$ and N$_2$O, from the Hitran database. The total radiative forcing of the halogenated gases at their 2020 concentrations is 0.52 (0.67) W/m$^2$ at the tropopause (mesopause). Over half of this forcing is due to CFC11 and CFC12 whose concentrations are declining as a result of the Montreal Protocol. The rate of total forcing change for all 14 halogenated gases is 1.5 (2.2) mW/m$^2$/year at the tropopause (mesopause). The calculations assumed a constant altitude concentration for all halogenated gases except CFC11, CFC12 and SF$_6$. Using the observed altitude dependence for those 3 molecules reduced their radiative forcings by about 10%. The global warming potential values were comparable to those given by the Intergovernmental Panel on Climate Change. The contribution of a gas to global warming was estimated using the forcing power per molecule defined as the derivative of its radiative forcing with respect to its column density. For the present atmosphere, the per-molecule forcing powers of halogenated gases are orders of magnitude larger than those for the 5 naturally occuring greenhouse gases because the latter have much higher concentrations and are strongly saturated. But, the rates of concentration increase of the 5 main greenhouse gases are orders of magnitude greater than that of any halogenated gas. Assuming the temperature increase caused by each gas is proportional to its radiative forcing increase, the 14 halogenated gases are responsible for only 2% of the total global warming.Comment: arXiv admin note: text overlap with arXiv:2103.16465, arXiv:2006.0309

Logarithmic two-loop corrections to the Lamb shift in hydrogen

Higher order $(\alpha/\pi)^2 (Z \alpha)^6$ logarithmic corrections to the hydrogen Lamb shift are calculated. The results obtained show the two-loop contribution has a very peculiar behavior, and significantly alter the theoretical predictions for low lying S-states.Comment: 14 pages, including 2 figures, submitted to Phys. Rev. A, updated with minor change

Deuterium Lamb shift via quenching-radiation anisotropy measurements

The Lamb shift of a hydrogenic ion can be deduced from the anisotropy in the angular distribution of the 2s12-1s12 electric field quenching radiation. The accuracy of our previous anisotropy measurement for deuterium is improved to about ± 150 ppm. The derived Lamb shift is (1059.36±0.16) MHz. The sources of error are carefully analyzed and the prospects for further improvements in the accuracy are discussed. © 1978 The American Physical Society