Spectra of noise and amplified turbulence emanating from shock-turbulence interaction: Two scenarios

This work is a small extension of NACA studies of the early fifties that predicted amplification of turbulence on passing through a shock wave (observed for turbulent boundary layers), as well as the generation of intense noise (observed for supersonic jets). The first solved the basic gasdynamics problem of the interaction of an infinite planar shock with a single three-dimensional spectrum component of turbulence (an oblique sinusoidal shear wave). The second developed the comprehensive 3D spectrum analysis necessary to generalize the scenario to the interaction of a shock wave with convected homogeneous turbulence. Numerical calculations were carried out to yield curves (vs. Mach number) of rms sound pressure, temperature fluctuation, and two components of turbulent velocity downstream of the shock, for two cases of preshock turbulence. The present numerical study reproduces these for one case and provides in addition their one-dimensional power spectra (vs. wavenumber or frequency). Ratios of the several postshock spectra to the longitudinal preshock turbulence spectrum (1D) have been computed for a wide range of Mach numbers; curves vs. wavenumber are presented for two scenarios of preshock turbulence: isotropy and axisymmetry, both based on the von Karman 3D spectrum

Resistance and persistence: on the fortunes and reciprocal international influences of French romanticism

Resistance and Persistence: On the Fortunes and Reciprocal International Influences of French Romanticism Abstract This article addresses ambivalence toward Romanticism on the part of Romantic artists and writers active in France - a group that includes Heinrich Heine, Eugène Delacroix, Alfred de Musset and Théophile Gautier. In counterpoint, the argument sets forth the persistence of the Romantic legacy in the work of the ostensibly anti-Romantic Gustave Courbet. I contend that the unease of Romantics vis-à-vis Romanticism is inseparable from their quixotic quest to transgress convention; that, in the face of negation and ridicule, signal characteristics of the movement endured, affecting the outlook of even its most bitter enemies (e.g., the Catholic royalist writers associated with the paper L'Action française and their admirer, the London art critic and philosopher T.E. Hulme); that, in the art of Van Gogh and Rodin, new life was breathed into Romanticism through contact with its ostensible opposite, Realism; and that Romanticism continued to speak to the concerns of artists active long after the mid-nineteenth century. I conclude with a consideration of how the negative view of Romantic pathos fostered by twentieth-century Formalism has been challenged, since the 1950s, by revisionist art historians

Language counts: Early language mediates the relationship between parent education and children\u27s math ability

Children\u27s early math skills have been hailed as a powerful predictor of academic success. Disparities in socioeconomic context, however, also have dramatic consequences on children\u27s learning. It is therefore critical to investigate both of these distinct contributors in order to better understand the early foundations of children\u27s academic outcomes. This study tests an integrated model of children\u27s developing math ability so as to (1) identify the specific skills and abilities most clearly linked to early math achievement and (2) measure the influence of children\u27s socioeconomic context on each of these skills. We first evaluated the early vocabulary, number word knowledge (knower level), and Approximate Number System (ANS) acuity of a diverse group of preschoolers. Then, approximately 1 year later as they entered Kindergarten, we administered a test of early math achievement. We find that children\u27s early language (general vocabulary and number word knowledge) fully mediates the relationship between parent education and math ability. Additionally, number word knowledge mediates the relationship between ANS acuity and early math. We argue that increased focus on number word knowledge, as well as general vocabulary, may help to minimize disparities in math ability as children enter kindergarten. We also highlight the role of parent education on children\u27s learning and note that this may be an important locus for intervention

Shock-turbulence interactions in a reacting flow

A specific reactive flow configuration, the interaction of a detonation wave with convected homogeneous isotropic weak turbulence (which can be constructed by a Fourier synthesis of small amplitude shear waves) is addressed. The effect of chemical heat release on the rms fluctuations downstream of the detonation is presented as a function of Mach number. In addition, for the particular case of the von Karman spectrum, the one dimensional power spectra of these flow quantities is given

Turbulence generation by a shock wave interacting with a random density inhomogeneity field

When a planar shock wave interacts with a random pattern of pre-shock density non-uniformities, it generates an anisotropic turbulent velocity/vorticity field. This turbulence plays an important role at the early stages of the mixing process in the compressed fluid. This situation emerges naturally in shock interaction with weakly inhomogeneous deuterium-wicked foam targets in Inertial Confinement Fusion (ICF) and with density clumps/clouds in astrophysics. We present an exact small-amplitude linear theory describing such interaction. It is based on the exact theory of time and space evolution of the perturbed quantities behind a corrugated shock front for a single-mode pre-shock non-uniformity. Appropriate mode averaging in 2D results in closed analytical expressions for the turbulent kinetic energy, degree of anisotropy of velocity and vorticity fields in the shocked fluid, shock amplification of the density non-uniformity, and sonic energy flux radiated downstream. These explicit formulas are further simplified in the important asymptotic limits of weak/strong shocks and highly compressible fluids. A comparison with the related problem of a shock interacting with a pre-shock isotropic vorticity field is also presented.Comment: This article corresponds to a presentation given at the Second International Conference and Advanced School "Turbulent Mixing and Beyond," held on 27 July - 07 August 2009 at the Abdus Salam International Centre for Theoretical Physics, Trieste, Italy. That Conference Proceeding will be published as a Topical Issue of the Physica Scripta IOP scienc

A Remote Indicating Hinge-Moment Balance, Special Report

This report describes an electrical hinge-moment balance for use with wind-tunnel models of aircraft. A brief description of the principle of operation and operating experience with the balance is given in part I. Part II gives constructional details and part III gives theoretical considerations. Extensive constructional information is given to enable the reproduction of the equipment

The Post Office : A Social Studies Curriculum for Seven and Eight Year Olds

This paper presents a curriculum that I have developed and used with my class of second graders over the past three years. The curriculum is the study of the Post Office as part of a study of the neighborhood, and the subsequent planning and running of a schoolwide post office