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  • Asymptotic expansions  (1)
  • Axisymmetric jet  (1)
  • 1
    Electronic Resource
    Electronic Resource
    On the asymptotic behavior of the bestL ∞-approximation by polynomials (1987)
    Springer
    Constructive approximation 3 (1987), S. 377-388 
    Details
    ISSN: 1432-0940
    Keywords: Algebraic polynomials ; Entire functions ; Asymptotic expansions ; Chebyshev approximation ; 41A10 ; 41A25 ; 41A50
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract LetE n (f) denote the sup-norm-distance (with respect to the interval [−1, 1]) betweenf and the set of real polynomials of degree not exceedingn. For functions likee x , cosx, etc., the order ofE n (f) asn→∞ is well known. A typical result is $$2^{n - 1} n!E_{n - 1} (e^x ) = 1 + 1/4n + O(n^{ - 2} ).$$ It is shown in this paper that 2 n−1 n!E n−1(e x ) possesses a complete asymptotic expansion. This result is contained in the more general result that for a wide class of entire functions (containing, for example, exp(cx), coscx, and the Bessel functionsJ k (x)) the quantity $$2^{n - 1} n!E_{n - 1} \left( f \right)/f^{(n)} \left( 0 \right)$$ possesses a complete asymptotic expansion (providedn is always even (resp. always odd) iff is even (resp. odd)).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01890576
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  • 2
    Electronic Resource
    Electronic Resource
    On streamwise vortical structures in the near-field of axisymmetric shear layers (1994)
    Springer
    Meccanica 29 (1994), S. 403-410 
    Details
    ISSN: 1572-9648
    Keywords: Axisymmetric jet ; Streamwise vortical structures ; Braid instability ; Vortex dynamics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Description / Table of Contents: Sommario Coppie di strutture tubolari controrotanti sono state osservate usando la tecnica di visualizzazione del flusso LIF (Laser Induced Fluorescence), per mezzo di una telecamera ad alta e bassa velocità, nel campo vicino ad un getto d'acqua assialsimmetrico. Lo studio dell'evoluzione temporale di queste strutture, fissatox/d=1.0, 2.0, 4.0 e 6.0 in piani perpendicolari alla direzione del flusso ed in sezioni longitudinali perx/d=0÷6.0, per numeri di Reynolds Re=cd/v=6000, è stato il punto principale della presente indagine. Queste strutture vorticose appaiono persino quando la formazione dei vortici di Taylor-Görtler è soppressa attivamente e passivamente. Si osserva che rimangono senza risposta questioni basilari concernenti la generazione e lo sviluppo di queste strutture secondarie. Attraverso l'analisi di queste strutture è possibile far progressi nella conoscenza dell'instabilità e dei meccanismi d'interazione. Inoltre, tali strutture contribuiscono all'intrappolamento ed al mescolamento dovuti alla loro dinamica ed alla larga area interfacciale.
    Notes: Abstract Pairs of counter-rotating streamwise vortical structures have been observed using the LIF (Laser Induced Fluorescence) flow visualization technique by means of regular, video and high-speed photography in the near-field of an axisymmetric water jet. The temporal evolution of these structures at fixedx/d=1.0, 2.0, 4.0, and 6.0 in planes perpendicular to the flow direction for Reynolds numbersRe=cd/v=6000 has been the focus of attention in this investigation (d = nozzle diameter,c = mean exit velocity). These streamwise vortical structures also appear when the formation of Taylor-Görtler vortices in the nozzle is suppressed. So far basic questions pertaining to the generation and development of these secondary structures remain unanswered. Understanding of instability and interaction mechanisms can be gained by the analysis of these structures. These also contribute to entrainment and mixing due to their dynamics and large interfacial area.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00987575
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