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  • 1. Bahrami, Fariba
    et al.
    Zarroug, Moundheur
    Stockholm University, Faculty of Science, Department of Meteorology .
    Lundberg, Peter
    Stockholm University, Faculty of Science, Department of Meteorology .
    Analysis of a thermosyphon using a Mandelstam condition2016In: Proceedings of the Institution of Civil Engineers: Engineering and Computational Mechanics, ISSN 1755-0777, E-ISSN 1755-0785, Vol. 169, no 1, p. 29-39, article id 1500011Article in journal (Refereed)
    Abstract [en]

    The characteristics of a thermally forced connected-vessel thermosyphon operating in an oscillatory mode have been determined using analytical techniques, the outcome of which is compared with results obtained by numerical integration of the governing equations. From a previous investigation it was known that adequate phase-plane representations of the limit cycles associated with oscillations could be obtained if the vessel-volume ratio was sufficiently small. This study aims at demonstrating how this constraint on the vessel volumes can be relaxed by prescribing a Mandelstam condition, that is, by postulating that the total heat content of the system remains conserved during the rapid phases of the oscillation. It was concluded that incorporating this Mandelstam condition in the analysis had the highly beneficial consequence that good analytical results could be obtained for much larger values of the vessel-volume ratio than those previously permitted.

  • 2.
    Falahat, Saeed
    et al.
    Stockholm University, Faculty of Science, Department of Meteorology .
    Nycander, Jonas
    Stockholm University, Faculty of Science, Department of Meteorology .
    Roquet, Fabien
    Stockholm University, Faculty of Science, Department of Meteorology .
    Zarroug, Moundheur
    Stockholm University, Faculty of Science, Department of Meteorology .
    Global Calculation of Tidal Energy Conversion into Vertical Normal Modes2014In: Journal of Physical Oceanography, ISSN 0022-3670, E-ISSN 1520-0485, Vol. 44, no 12, p. 3225-3244Article in journal (Refereed)
    Abstract [en]

    A direct calculation of the tidal generation of internal waves over the global ocean is presented. The calculation is based on a semianalytical model, assuming that the internal tide characteristic slope exceeds the bathymetric slope (subcritical slope) and the bathymetric height is small relative to the vertical scale of the wave, as well as that the horizontal tidal excursion is smaller than the horizontal topographic scale. The calculation is performed for the M-2 tidal constituent. In contrast to previous similar computations, the internal tide is projected onto vertical eigenmodes, which gives two advantages. First, the vertical density profile and the finite ocean depth are taken into account in a fully consistent way, in contrast to earlier work based on the WKB approximation. Nevertheless, the WKB-based total global conversion follows closely that obtained using the eigenmode decomposition in each of the latitudinal and vertical distributions. Second, the information about the distribution of the conversion energy over different vertical modes is valuable, since the lowest modes can propagate over long distances, while high modes are more likely to dissipate locally, near the generation site. It is found that the difference between the vertical distributions of the tidal conversion into the vertical modes is smaller for the case of very deep ocean than the shallow-ocean depth. The results of the present work pave the way for future work on the vertical and horizontal distribution of the mixing caused by internal tides.

  • 3.
    Falahat, Saeed
    et al.
    Stockholm University, Faculty of Science, Department of Meteorology .
    Nycander, Jonas
    Stockholm University, Faculty of Science, Department of Meteorology .
    Roquet, Fabien
    Stockholm University, Faculty of Science, Department of Meteorology .
    Zarroug, Moundheur
    Stockholm University, Faculty of Science, Department of Meteorology .
    Global calculation of tidal energy conversion rate into vertical normal modesManuscript (preprint) (Other academic)
  • 4.
    Karlovini, Max
    et al.
    Stockholm University, Faculty of Science, Department of Physics.
    Samuelsson, Lars
    Stockholm University, Faculty of Science, Department of Physics.
    Zarroug, Moundheur
    Stockholm University, Faculty of Science, Department of Physics.
    Elastic Stars in General Relativity: II. Radial Perturbations2004In: Classical and quantum gravity, ISSN 0264-9381, E-ISSN 1361-6382, Vol. 6, no 21, p. 1559-1581Article in journal (Refereed)
    Abstract [en]

    We study radial perturbations of general relativistic stars with elastic matter sources. We find that these perturbations are governed by a second-order differential equation which, along with the boundary conditions, defines a Sturm-Liouville-type problem that determines the eigenfrequencies. Although some complications arise compared to the perfect fluid case, leading us to consider a generalization of the standard form of the Sturm-Liouville equation, the main results of Sturm-Liouville theory remain unaltered. As an important consequence we conclude that the mass-radius curve for a one-parameter sequence of regular equilibrium models belonging to some particular equation of state can be used in the same well-known way as in the perfect fluid case, at least if the energy density and the tangential pressure of the background solutions are continuous. In particular, we find that the fundamental mode frequency has a zero for the maximum mass stars of the models with solid crusts considered in paper I of this series

  • 5.
    Lundberg, Peter
    et al.
    Stockholm University, Faculty of Science, Department of Meteorology .
    Bahrami, Fariba
    Tabriz University, Department of Applied Mathematics.
    Zarroug, Moundheur
    Stockholm University, Faculty of Science, Department of Meteorology .
    A note on the asymptotic analysis of a thermal relaxation oscillator2009In: Zeitschrift für angewandte Mathematik und Mechanik, ISSN 0044-2267, E-ISSN 1521-4001, Vol. 89, no 12, p. 995-1001Article in journal (Refereed)
    Abstract [en]

    A nonlinear oscillator, based on two connected vessels which are thermally forced around the maximum-density temperature of the working fluid, is investigated. For a suitable choice of parameters, the system executes self-sustained relaxation oscillations. This process has been examined for a large volume difference between the vessels, in which case the solution makes almost discontinuous jumps between the two branches of the slow manifold of the problem. It was found that in this limit, a lowest-order analysis does reasonable justice to the periodic behaviour of the system.

  • 6.
    Zarroug, Moundheur
    Stockholm University, Faculty of Science, Department of Meteorology .
    A heurestic higher-order analysis of a thermal relaxation oscillatorManuscript (preprint) (Other academic)
    Abstract [en]

    The oscillatory behaviour of a differentially heated system, based on two connected vessels containing a fluid with a nonlinear equation of state, has been sub jected to an asymptotically valid analysis. The quotient of the vessel volumes was used as expansion parameter, and it was found that the analytically determined corrections to the zeroth-order results served a useful purpose even for quite large values of the volume ratio.

  • 7.
    Zarroug, Moundheur
    Stockholm University, Faculty of Science, Department of Meteorology .
    Asymptotic methods applied to some oceanography-related problems2010Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    In this thesis a number of issues related to oceanographic problems have been dealt with on the basis of applying asymptotic methods. 

    The first study focused on the tidal generation of internal waves, a process which is quantifed by the conversion rates. These have traditionally been calculated by using the WKB approximation. However, the systematic imprecision of this theory for the lowest modes as well as turbulence at the seabed level affect the results. To handle these anomalies we introduced another asymptotic technique, homogenization theory, which led to signifcant improvements, especially for the lowest modes. 

    The second study dealt with the dynamical aspects of a nonlinear oscillator which can be interpreted as a variant of the classical two-box models used in oceanography. The system is constituted by two connected vessels containing a fluid characterised by a nonlinear equation of state and a large volume differences between the vessels is prescribed. It is recognised that the system, when performing relaxation oscillations, exhibits almost-discontinuous jumps between the two branches of the slow manifold of the problem. The lowest-order analysis yielded reasonable correspondence with the numerical results. 

    The third study is an extension of the lowest-order approximation of the relaxation oscillations undertaken in the previous paper. A Mandelstam condition is imposed on the system by assuming that the total heat content of the system is conserved during the discontinuous jumps. 

    In the fourth study an asymptotic analysis is carried out to examine the oscillatory behaviour of the thermal oscillator. It is found that the analytically determined corrections to the zeroth-order analysis yield overall satisfying results even for comparatively large values of the vessel-volume ratio. 

  • 8.
    Zarroug, Moundheur
    Stockholm University, Faculty of Science, Department of Meteorology .
    Improving the lowest-order analysis of a nonlinear convective oscillator by applying a Mandelstam conditionManuscript (preprint) (Other academic)
    Abstract [en]

    A lowest-order approximation of the relaxation oscillations of a nonlinear thermally forced system has been extended by prescribing a Mandelstam condition, in the present case by assuming that the total heat content of the system is conserved during rapid phase-point motion. Examples based on incorporating these improvements are shown, both of the limit-cycle representation in the phase-plane and of the calculated oscillation periods. 

  • 9.
    Zarroug, Moundheur
    et al.
    Stockholm University, Faculty of Science, Department of Meteorology .
    Lundberg, Peter
    Stockholm University, Faculty of Science, Department of Meteorology .
    Bahrami, Fariba
    An analysis of the relaxation oscillations of a nonlinear thermosyphon2016In: International Journal of Non-Linear Mechanics, ISSN 0020-7462, E-ISSN 1878-5638, Vol. 87, p. 137-152Article in journal (Refereed)
    Abstract [en]

    The oscillatory behavior of an asymmetrically forced thermosyphon constituted by two connected vessels has been subjected to an asymptotically valid analysis using the vessel-volume ratio as expansion parameter. Due to the structure of the governing equations, the problem could not be dealt with using standard techniques; instead a phase-plane analysis was conducted. The analytically determined corrections to the previously established lowest-order discontinuous results proved to be useful even for comparatively large values of the expansion parameter. The relationship between these asymptotically valid corrections and the physics underlying the relaxation oscillation as well as the behavior of the system for strong thermal forcing is discussed. The study is concluded by an overview of some specific inconsistencies associated with the discontinuous lowest-order analysis and how these were alleviated by the asymptotically valid corrections.

  • 10.
    Zarroug, Moundheur
    et al.
    Stockholm University, Faculty of Science, Department of Meteorology .
    Nycander, Jonas
    Stockholm University, Faculty of Science, Department of Meteorology .
    Döös, Kristofer
    Stockholm University, Faculty of Science, Department of Meteorology .
    Energetics of tidally generated internal waves2010In: Tellus. Series A, Dynamic meteorology and oceanography, ISSN 0280-6495, E-ISSN 1600-0870, Vol. 62, no 1, p. 71-79Article in journal (Refereed)
    Abstract [en]

    The generation of internal waves from barotropic tides can be quantified in terms of the conversion rates. These have often been obtained by applying the WKB approximation, which yields an expression for the conversion rates which is proportional to the seabed buoyancy frequency NB . For small values of NB or strong variations of the buoyancy profile N (z), this gives unreliable results. Using homogenization theory it is here shown that the conversion rate instead depends on the value of N (z) averaged over a vertical region at the bottom of the same magnitude as the vertical length-scale of the internal wave, which for the lowest modes is of the same order as the entire ocean depth. This gives a substantially larger conversion rate. 

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