Analysis of Cumulant Coefficients of Two-Component Mixtures of Shifted Non-Gaussian Distributions

The dependence of the cumulant coefficients of two-component mixtures of shifted non- Gaussian distributions on the weight coefficient is analyzed and conditions are determined under which the cumulant coefficients of any orders are equal to zero. The dependence of the cumulant coefficients of two-component mixtures on the shear parameter is investigated and the parameter values are determined at which the cumulant coefficients of any orders have extrema and zeros. The dependence of the skewness and excess kurtosis of a two-component mixture of shifted Gumbel distributions of type 1 on the weight coefficient and the shear parameter is investigated and their values are obtained at which the skewness and excess kurtosis of the mixture are equal to zero. The features of computer modeling of random variables, the probability density of which is a two-component mixture of shifted distributions, are considered.

Hairpin vortices and highly elongated flow structures in a stably stratified shear layer

Turbulent structures in stably stratified shear layers are studied with direct numerical simulation. Flow visualization confirms the existence of hairpin vortices and highly elongated structures with positive and negative velocity fluctuations, whose streamwise lengths divided by the layer thickness are $O(10^{0})$ and $O(10^{1})$, respectively. The flow at the wavelength related to these structures makes a large contribution to turbulent kinetic energy. These structures become prominent in late time, but with small buoyancy Reynolds numbers indicating suppression of turbulent mixing. Active turbulent mixing associated with the hairpin vortices, however, does occur. The structures and the vertical profile of the integral shear parameter show connections between stable stratified shear layers and wall-bounded shear flows.

Doppler images of V1358 Ori

We present Doppler images of the active dwarf star V1358 Ori using high-resolution spectra from the NARVAL spectropolarimeter mounted on the Bernard Lyot Telescope. The spectra were taken between 09-20 Dec, 2013 with a resolution of R=80000. Doppler imaging was carried out with our new generation multi-line Dopper imaging code iMap (Carroll et al. 2012). 40 individual photospheric lines were selected by line depth, temperature sensitivity and blends. Two data subsets were formed to get two consecutive Doppler images. Prominent cool spots at lower latitudes are found on both maps. At 0.5 phase there is a prominent equatorial feature on both maps. Weaker polar features can be seen on the first map, which somewhat diminishes for the second map. On the first image there is a cool surface feature at 30 degrees latitude which seems to fade greatly on the second map. Around 0.75 phase, a new spot seems to form. These changes suggest a rapid surface evolution. Spot displacements may also indicate surface differential rotation, which was derived by cross-correlating the two subsequent Doppler images (see e.g. Kővári et al. 2012). We fit the latitudinal correlation peaks with a sine-squared law. The fit suggests solar-type surface differential rotation with a shear parameter of α=0.02±0.02. The shear parameter fits the ${P_{{\rm{rot}}}} - |\alpha | $ diagram in Kővári et al. (2017) quite well.

Linear Shear Flow Past a Rotating Elliptic Cylinder

Simulations are carried out for linear shear flow past a rotating elliptic cylinder to investigate the effect of shear flow on hovering vortex. An in-house fluid solver that is based on immersed boundary method (IBM) is used to study the flow features and variation in aerodynamic forces. The simulations are carried out for various nondimensional rotation rates, axis ratio (AR) of the cylinder, and shear parameter. In shear flow past rotating elliptic cylinder, the negative vortices are sustained for longer distances in the downstream of the cylinder, and due to the velocity gradient, the sequence of the vortex street changes. It also has significant effect on the formation and composition of hovering vortex. To capture these features, each vortex is tracked as they form, detach, and move in the wake of the cylinder. Hovering vortex, formed due to coalescing of multiple vortices near the cylinder, is subdued for smaller rotation rates at moderate shear. It is also observed that lift forces increase linearly with shear, while the frequency of shedding shows no dependency on shear parameter.

Probabilistic Verification of Storm Prediction Center Convective Outlooks

Eight years’ worth of day 1 and 4.5 years’ worth of day 2–3 probabilistic convective outlooks from the Storm Prediction Center (SPC) are converted to probability grids spanning the continental United States (CONUS). These results are then evaluated using standard probabilistic forecast metrics including the Brier skill score and reliability diagrams. Forecasts are gridded in two different ways: one with a high-resolution grid and interpolation between probability contours and another on an 80-km-spaced grid without interpolation. Overall, the highest skill is found for severe wind forecasts and the lowest skill is observed for tornadoes; for significant severe criteria, the opposite discrepancy is observed, with highest forecast skill for significant tornadoes and approximately no overall forecast skill for significant severe winds. Highest climatology-relative skill is generally observed over the central and northern Great Plains and Midwest, with the lowest—and often negative—skill seen in the West, southern Texas, and the Atlantic Southeast. No discernible year-to-year trend in skill was identified; seasonally, forecasts verified the best in the spring and late autumn and worst in the summer and early autumn. Forecasts are also evaluated in CAPE-versus-shear parameter space; forecasts struggle most in very low shear but also in high-shear, low-CAPE environments. In aggregate, forecasts for all variables verified more skillfully using interpolated probability grids, suggesting utility in interpreting forecasts as a continuous field. Forecast reliability results depend substantially on the interpretation of the forecast fields, but day 1 and day 2–3 tornado outlooks consistently exhibit an underforecast bias.

Linear stability analysis of a premixed flame with transverse shear

One-dimensional planar premixed flames propagating in a uniform flow are susceptible to hydrodynamic instabilities known (generically) as Darrieus–Landau instabilities. Here, we extend that hydrodynamic linear stability analysis to include a lateral shear. This generalization is a situation of interest for laminar and turbulent flames when they travel into a region of shear (such as a jet or shear layer). It is shown that the problem can be formulated and solved analytically and a dispersion relation can be determined. The solution depends on a shear parameter in addition to the wavenumber, thermal expansion ratio, and Markstein lengths. The study of the dispersion relation shows that perturbations have two types of behaviour as wavenumber increases. First, for small shear, we recover the Darrieus–Landau results except for a region at small wavenumbers, large wavelengths, that is stable. Initially, increasing shear has a stabilizing effect. But, for sufficiently high shear, the flame becomes unstable again and its most unstable wavelength can be much smaller than the Markstein length of the zero-shear flame. Finally, the stabilizing effect of low shear can make flames with negative Markstein numbers stable within a band of wavenumbers.