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  • 1
    Electronic Resource
    Electronic Resource
    Atmospheric interfacial waves in the presence of two moving fluid layers (1994)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 6 (1994), S. 3306-3316 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Atmospheric waves at the interface between two flowing layers of air are studied in this paper. The lower layer is assumed to be incompressible and to flow irrotationally, and its motion might be the result of a distant thunderstorm, for example. The upper layer is modeled as a compressible isothermal atmosphere, so that if it were stationary, its density and pressure would both decrease exponentially with height. The equations of motion in the upper layer are linearized under the assumption that the lower layer of incompressible fluid is "thin'' (its weight is a small fraction of the total), but the possibility of large-amplitude disturbances at the interface is nevertheless allowed. A linearized theory of wave propagation in this system is discussed, and a numerical scheme is outlined for the solution of the nonlinear equations. The results confirm the predictions of a model of Forbes and Belward [Phys. Fluids A 4, 2222 (1992)], in which the upper atmosphere was assumed stationary, and demonstrate that this simpler model gives results that are likely to be useful over most of the range of values of the speed in the upper layer encountered in practice. Nonlinear waves near the limiting height are discussed, and a very significant qualitative difference between the predictions of the linearized theory and the nonlinear results concerning progressive waves is analyzed, and may be of importance in meteorology.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.868063
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Atmospheric interfacial waves (1992)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 4 (1992), S. 2222-2229 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Waves at the interface of a two-layer fluid are considered. The fluid in the lower layer is incompressible with constant density and is flowing irrotationally. In the upper layer, the fluid is stationary but compressible, and corresponds to an isothermal atmosphere with a density profile that decreases exponentially with height. The interface between the two fluids is assumed sharp. The formation of waves at the interface would come about typically as a result of the interaction of the moving lower layer of fluid with local topographical features, as with the classical problem of the generation of waves on the lee side of a mountain range. It is shown that the present model is capable of supporting the formation of interfacial waves that are similar in many respects to the classical gravity wave of Stokes, and that are ultimately limited in every case by the formation of a 120° angle at the wave crest. The highly nonlinear wave profiles are computed numerically and compared with the predictions of linearized theory. An extended perturbation analysis is given near the point at which the interfacial waves break down as a result of the Kelvin–Helmholtz instability.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.858463
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  • 3
    Electronic Resource
    Electronic Resource
    Supercritical flow past blunt bodies in shallow water (1981)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 32 (1981), S. 314-328 
    Details
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Description / Table of Contents: Zusammenfassung Es wird die Strömung in seichtem Wasser untersucht, welche bei der Umströmung von stumpfen Körpern einen abgelösten hydraulischen Sprung erzeugt. Dies ist eine Verallgemeinerung des gasdynamischen Problems der stumpfen Körper zur analogen Situation bei der Strömung mit freier Oberfläche. Es wird das inverse Problem gelöst, durch Reihenentwicklung der Strömungs-Variablen von der Stoß-Spitze ausgehend; damit wird der stromabwärts liegende Körper bestimmt. Das Auftreten von verschiedenen singulären Linien in der Lösung wird diskutiert.
    Notes: Abstract The flow about blunt objects in shallow water which support a detached hydraulic jump is investigated. This work is an extension of the blunt body problem of gas dynamics to an analogous situation existing in free-surface flows. The problem is solved inversely, by expressing the flow variables as series expansions about the shock apex, and then determining the position of the body downstream. The presence of various singular lines in the solution is discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00946647
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  • 4
    Electronic Resource
    Electronic Resource
    High-order series solution for unsteady thermal blooming with crosswind (1983)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 34 (1983), S. 334-346 
    Details
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Description / Table of Contents: Résumé La distorsion nonlinéaire d'un faisceau de lumière bidimensionnel est étudiée dans le cas de sa propagation dans l'atmosphère en présence d'un vent transversal uniforme. Le faisceau est admis soumis aux lois de l'optique géométrique. La technique du développement en série des coordonnées est utilisée et les coefficients des termes sont déterminés par calcul sur ordinateur. La distorsion due au vent transversal se révèle moins importante que dans le cas tridimensionnel.
    Notes: Abstract The non-linear self-distortion of a plane light beam propagating through the atmosphere is investigated. A uniform crosswind is present, acting perpendicular to the initial (unbloomed) direction of propagation of the light beam, which is assumed to be governed by the laws of geometric optics. The problem is solved by a high-order coordinate series-expansion technique, using the digital computer to obtain values for the coefficients. Distortion of the light beam due to the crosswind is found to be less severe than in the three-dimensional case.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00944854
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  • 5
    Electronic Resource
    Electronic Resource
    Series solution for transient thermal blooming of an axi-symmetric laser beam (1985)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 36 (1985), S. 275-285 
    Details
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Description / Table of Contents: Zusammenfassung Wir untersuchen die nichtlineare Verzerrung eines Laserstrahls, der ein komprimierbares Gas durchläuft. Die abhängigen Variablen drücken wir als Taylorsummen aus, deren Koeffizienten wir mittels eines Computers bestimmen. Es zeigt sich, daß der Strahl im Laufe der Zeit erheblich verzerrt wird, wobei die Schwerkraft im Falle eines senkrechten Strahls keine wesentliche Rolle spielt.
    Notes: Abstract Self-defocussing of an intense laser beam propagating through an initially quiescent compressible gas is investigated. The dependent variables are sought as Taylor series expansions involving the two space coordinates and the time, and the resulting recurrence relations are solved by digital computer. The beam is found to distort substantially as it propagates, but is not affected significantly by gravity when aimed vertically.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00945461
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  • 6
    Electronic Resource
    Electronic Resource
    A note on the quantitative structure of quasi-stationary tropical cyclone in the vicinity of the eye (1998)
    Springer
    Journal of engineering mathematics 33 (1998), S. 1-14 
    Details
    ISSN: 1573-2703
    Keywords: Atmospheric interface ; eye radius ; perturbation expansion ; vortex
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Technology
    Notes: Abstract A fully mature tropical cyclone is a complicated phenomenon, in which effects such as boundary-layer friction, latent heat release, and so on, must be accounted for, in order to give a complete description of the flow. Nevertheless, it is demonstrated here that a two-layer compressible atmosphere model, with a sharp interface separating the layers, is capable of giving a non-linear vortex-type solution at the lowest order of approximation. The ‘eye’ of the cyclone is formed when the interface is drawn down to sea level. Heat energy from the ocean into the cyclone and secondary flow within the vortex are both incorporated. The model provides an approximate description of cyclone behaviour, in terms that are easily understood. More complete descriptions are apparently only possible numerically, however, with a corresponding loss of ease of comprehension.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1004240724305
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  • 7
    Electronic Resource
    Electronic Resource
    Interfacial waves and hydraulic falls: Some applications to atmospheric flows in the lee of mountains (1995)
    Springer
    Journal of engineering mathematics 29 (1995), S. 161-179 
    Details
    ISSN: 1573-2703
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Technology
    Notes: Abstract Two dimensional flow of a layer of constant density fluid over arbitrary topography, beneath a compressible, isothermal and stationary fluid is considered. Both downstream wave and critical flow solutions are obtained using a boundary integral formulation which is solved numerically by Newton's method. The resulting solutions are compared against waves produced behind similar obstacles in which the compressible upper layer is absent (single layer flow) and against the predictions of a linearised theory. The limiting waves predicted by the full non-linear equations are contrasted with those predicted by the forced Korteweg-de Vries theory. In particular, it is shown that at some parameter values a multiplicity of solutions exists in the full nonlinear theory.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00051741
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  • 8
    Electronic Resource
    Electronic Resource
    Optimal fluid injection strategies for in situ mineral leaching in two-dimensions (1999)
    Springer
    Journal of engineering mathematics 36 (1999), S. 185-206 
    Details
    ISSN: 1573-2703
    Keywords: mineral leaching ; Darcy's law ; boundary-integral approach ; injection strategy ; withdrawal flows.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Technology
    Notes: Abstract This paper examines the ground-water flow problem associated with the injection and recovery of certain corrosive fluids into mineral bearing rock. The aim is to dissolve the minerals in situ, and then recover them in solution. In general, it is not possible to recover all the injected fluid, which is of concern economically and environmentally. However, a new strategy is proposed here, that allows all the leaching fluid to be recovered. A mathematical model of the situation is solved approximately using an asymptotic solution, and exactly using a boundary integral approach. Solutions are shown for two-dimensional flow, which is of some practical interest as it is achievable in old mine tunnels, for example.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1004406311441
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  • 9
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    Unsteady draining flows from a rectangular tank (2007)
    American Institute of Physics
    Details
    Publication Date: 2007-08-01
    Print ISSN: 1070-6631
    Electronic ISSN: 1089-7666
    Topics: Physics
    Published by American Institute of Physics
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  • 10
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    On stability and uniqueness of stationary one-dimensional patterns in the Belousov-Zhabotinsky reaction (1991)
    Elsevier
    Details
    Publication Date: 1991-05-01
    Print ISSN: 0167-2789
    Electronic ISSN: 1872-8022
    Topics: Physics
    Published by Elsevier
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