Shallow precipitating cumuli within the easterly trades were investigated using shipboard measurements, scanning radar data, and visible satellite imagery from 2 weeks in January 2005 of the Rain in Cumulus over the Ocean (RICO) experiment. Shipboard rainfall rates of up to 2 mm h 21 were recorded almost daily, if only for 10-30 min typically, almost always from clouds within mesoscale arcs. The precipitating cumuli, capable of reaching above 4 km, cooled surface air by 1-2 K, in all cases lowered surface specific humidities by up to 1.5 g kg 21 , reduced surface equivalent potential temperatures by up to 6 K, and were often associated with shortlived increases in wind speed. Upper-level downdrafts were inferred to explain double-lobed moisture and temperature sounding profiles, as well as multiple inversions in wind profiler data. In two cases investigated further, the precipitating convection propagated faster westward than the mean surface wind by about 2-3 m s 21 , consistent with a density current of depth ;200 m. In their cold pool recovery zones, the surface air temperatures equilibrated with time to the sea surface temperatures, but the surface air specific humidities stayed relatively constant after initial quick recoveries. This suggested that entrainment of drier air from above fully compensated the moistening from surface latent heat fluxes. Recovery zone surface wind speeds and latent heat fluxes were not higher than environmental values. Nonprecipitating clouds developed after the surface buoyancy had recovered (barring encroachment of other convection). The mesoscale arcs favored atmospheres with higher water vapor paths. These observations differed from those of stratocumulus and deep tropical cumulus cold pools.

Equations that follow from the Navier-Stokes equation and incompressibility but with no other approximations are "exact.". Exact equations relating second-and third-order structure functions are studied, as is an exact incompressibility condition on the second-order velocity structure function. Opportunities for investigations using these equations are discussed. Precisely defined averaging operations are required to obtain exact averaged equations. Ensemble, temporal, and spatial averages are all considered because they produce different statistical equations and because they apply to theoretical purposes, experiment, and numerical simulation of turbulence. Particularly simple exact equations are obtained for the following cases: i) the trace of the structure functions, ii) DNS that has periodic boundary conditions, and iii) an average over a sphere in r-space. The last case (iii) introduces the average over orientations of r into the structure function equations. The energy dissipation rate ε appears in the exact trace equation without averaging, whereas in previous formulations ε appears after averaging and use of local isotropy. The trace mitigates the effect of anisotropy in the equations, thereby revealing that the trace of the third-order structure function is expected to be superior for quantifying asymptotic scaling laws. The orientation average has the same property.

Several models are developed for the high-wavenumber portion of the spectral transfer function of scalar quantities advected by high-Reynolds-number, locally isotropic turbulent flow. These models are applicable for arbitrary Prandtl or Schmidt number, v/D, and the resultant scalar spectra are compared with several experiments having different v/D. The ‘bump’ in the temperature spectrum of air observed over land is shown to be due to a tendency toward a viscous-convective range and the presence of this bump is consistent with experiments for large v/D. The wavenumbers defining the transition between the inertial-convective range and viscous-convective range for asymptotically large v/D (denoted k* and k1* for the three- and one-dimensional spectra) are determined by comparison of the models with experiments. A measurement of the transitional wavenumber k1* [denoted (k1*)s] is found to depend on v/D and on any filter cut-off. On the basis of the k* values it is shown that measurements of β1 from temperature spectra in moderate Reynolds number turbulence in air (v/D = 0·72) maybe over-estimates and that the inertial-diffusive range of temperature fluctuations in mercury (v/D ≃ 0·02) is of very limited extent.

Exact equations are given that relate velocity structure functions of arbitrary order with other statistics. "Exact" means that no approximations are used except that the Navier-Stokes equation and incompressibility condition are assumed to be accurate. The exact equations are used to determine the structure function equations of all orders for locally homogeneous but anisotropic turbulence as well as for the locally isotropic case. The uses of these equations for investigating the approach to local homogeneity as well as to local isotropy and the balance of the equations and identification of scaling ranges are discussed. The implications for scaling exponents and investigation of intermittency are briefly discussed.

The Space Telescope Imaging Spectrograph (STIS) was successfully installed into the Hubble Space Telescope (HST) in 1997 February, during the second HST servicing mission, STS-82. STIS is a versatile spectrograph, covering the 115-1000 nm wavelength range in a variety of spectroscopic and imaging modes that take advantage of the angular resolution, unobstructed wavelength coverage, and dark sky offered by the HST. In the months since launch, a number of performance tests and calibrations have been carried out and are continuing. These tests demonstrate that the instrument is performing very well. We present here a synopsis of the results to date.

The equation relating second- and third-order velocity structure functions was presented by Kolmogorov; Monin attempted to derive that equation on the basis of local isotropy. Recently, concerns have been raised to the effect that Kolmogorov's equation and an ancillary incompressibility condition governing the third-order structure function were proven only on the restrictive basis of isotropy and that the statistic involving pressure that appears in the derivation of Kolmogorov's equation might not vanish on the basis of local isotropy. These concerns are resolved. In so doing, results are obtained for the second- and third-order statistics on the basis of local homogeneity without use of local isotropy. These results are applicable to future studies of the approach toward local isotropy. Accuracy of Kolmogorov's equation is shown to be more sensitive to anisotropy of the third-order structure function than to anisotropy of the second-order structure function. Kolmogorov's 4/5 law for the inertial range of the third-order structure function is obtained without use of the incompressibility conditions on the second- and third-order structure functions. A generalization of Kolmogorov's 4/5 law, which applies to the inertial range of locally homogeneous turbulence at very large Reynolds numbers, is shown to also apply to the energy-containing range for the more restrictive case of stationary, homogeneous turbulence. The variety of derivations of Kolmogorov's and Monin's equations leads to a wide range of applicability to experimental conditions, including, in some cases, turbulence of moderate Reynolds number.

A theory is developed for ambipolar diffusion in a multiconstituent weakly ionized plasma. The implications of the presence of negative ions and of differing positive ion and negative ion diffusion coefficients are found. In particular, the presence of numerous negative ions is found to enhance the diffusion of the electrons. Furthermore, this theory of multiconstituent ambipolar diffusion is extended to include the nonneutral case in which the scale length of the inhomogeneity is smaller than or of the order of the electron Debye length.

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