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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.
    Ballarotta, Maxime
    et al.
    Stockholm University, Faculty of Science, Department of Meteorology .
    Brodeau, Laurent
    Stockholm University, Faculty of Science, Department of Meteorology .
    Brandefelt, Jenny
    Lundberg, Peter
    Stockholm University, Faculty of Science, Department of Meteorology .
    Döös, Kristofer
    Stockholm University, Faculty of Science, Department of Meteorology .
    A Last Glacial Maximum world-ocean simulation at eddy-permitting resolution – Part 1: Experimental design and basic evaluation2013In: Climate of the Past Discussions, ISSN 1814-9340, E-ISSN 1814-9359, Vol. 9, p. 297-328Article in journal (Refereed)
    Abstract [en]

    Most state-of-the-art climate models include a coarsely resolved oceanic compo- nent, which has difficulties in capturing detailed dynamics, and therefore eddy- permitting/eddy-resolving simulations have been developed to reproduce the observed World Ocean. In this study, an eddy-permitting numerical experiment is conducted to simulate the global ocean state for a period of the Last Glacial Maximum (LGM, ∼26500 to 19000yr ago) and to investigate the improvements due to taking into account these higher spatial scales. The ocean general circulation model is forced by a 49-yr sample of LGM atmospheric fields constructed from a quasi-equilibrated climate-model simulation. The initial state and the bottom boundary condition conform to the Paleoclimate Modelling Intercomparison Project (PMIP) recommendations. Be- fore evaluating the model efficiency in representing the paleo-proxy reconstruction of the surface state, the LGM experiment is in this first part of the investigation, compared with a present-day eddy-permitting hindcast simulation as well as with the available PMIP results. It is shown that the LGM eddy-permitting simulation is consistent with the quasi-equilibrated climate-model simulation, but large discrepancies are found with the PMIP model analyses, probably due to the different equilibration states. The strongest meridional gradients of the sea-surface temperature are located near 40° N and S, this due to particularly large North-Atlantic and Southern-Ocean sea-ice covers. These also modify the locations of the convection sites (where deep-water forms) and most of the LGM Conveyor Belt circulation consequently takes place in a thinner layer than today. Despite some discrepancies with other LGM simulations, a glacial state is captured and the eddy-permitting simulation undertaken here yielded a useful set of data for comparisons with paleo-proxy reconstructions. 

  • 3.
    Ballarotta, Maxime
    et al.
    Stockholm University, Faculty of Science, Department of Meteorology .
    Döös, Kristofer
    Stockholm University, Faculty of Science, Department of Meteorology .
    Lundberg, Peter
    Stockholm University, Faculty of Science, Department of Meteorology .
    Brodeau, Laurent
    Stockholm University, Faculty of Science, Department of Meteorology .
    Brandefelt, Jenny
    A Last Glacial Maximum World-Ocean simulation at eddy-permitting resolution – Part 2: Confronting the paleo-proxy data2013In: Climate of the Past Discussions, ISSN 1814-9340, E-ISSN 1814-9359, Vol. 9, p. 329-350Article in journal (Refereed)
    Abstract [en]

    Previous investigations concerning the design of an eddy-permitting LGM oceanic sim- ulation are here extended with focus on whether this type of simulation is capable of improving the numerical results with regard to the available paleo-proxy reconstructions. Consequently, an eddy-permitting and two coarse-grid simulations of the same LGM period are confronted with a dataset from the Multiproxy Approach for the Recon- struction of the Glacial Ocean Sea Surface Temperatures (MARGO SSTs) and a num- ber of sea-ice reconstructions. From a statistical analysis it was found that the eddy- permitting simulation does not significantly improve the SST representation with regard to the paleo-reconstructions. The western boundary currents are better resolved in the high-resolution experiment than in the coarse simulations, but, although these more detailed SST structures yield a locally improved consistency between modelled pre- dictions and proxies, they do not contribute significantly to the global statistical score. As in the majority of the PMIP2 simulations, the modelled sea-ice conditions are still inconsistent with the paleo-reconstructions, probably due to the choice of the model equilibrium. 

  • 4.
    Ballarotta, Maxime
    et al.
    Stockholm University, Faculty of Science, Department of Meteorology .
    Laurent, Brodeau
    Stockholm University, Faculty of Science, Department of Meteorology .
    Jenny, Brandefelt
    Lundberg, Peter
    Stockholm University, Faculty of Science, Department of Meteorology .
    Döös, Kristofer
    Stockholm University, Faculty of Science, Department of Meteorology .
    Last Glacial Maximum world ocean simulations at eddy-permitting and coarse resolutions: do eddies contribute to a better consistency between models and palaeoproxies?2013In: Climate of the Past, ISSN 1814-9324, E-ISSN 1814-9332, Vol. 9, no 6, p. 2669-2686Article in journal (Refereed)
    Abstract [en]

    Most state-of-the-art climate models include a coarsely resolved oceanic component, which hardly captures detailed dynamics, whereas eddy-permitting and eddy-resolving simulations are developed to reproduce the observed ocean. In this study, an eddy-permitting and a coarse resolution numerical experiment are conducted to simulate the global ocean state for the period of the Last Glacial Maximum (LGM, ~26 500 to 19 000 yr ago) and to investigate the improvements due to taking into account the smaller spatial scales. The ocean state from each simulation is confronted with a data set from the Multiproxy Approach for the Reconstruction of the Glacial Ocean (MARGO) sea surface temperatures (SSTs), some reconstructions of the palaeo-circulations and a number of sea-ice reconstructions. The western boundary currents and the Southern Ocean dynamics are better resolved in the high-resolution experiment than in the coarse simulation, but, although these more detailed SST structures yield a locally improved consistency between model predictions and proxies, they do not contribute sig- nificantly to the global statistical score. The SSTs in the tropical coastal upwelling zones are also not significantly improved by the eddy-permitting regime. The models perform in the mid-latitudes but as in the majority of the Paleo- climate Modelling Intercomparison Project simulations, the modelled sea-ice conditions are inconsistent with the palaeo-reconstructions. The effects of observation locations on the comparison between observed and simulated SST suggest that more sediment cores may be required to draw reliable conclusions about the improvements introduced by the high resolution model for reproducing the global SSTs. One has to be careful with the interpretation of the deep ocean state which has not reached statistical equilibrium in our simula-tions. However, the results indicate that the meridional overturning circulations are different between the two regimes, suggesting that the model parametrizations might also play a key role for simulating past climate states. 

  • 5. Borenäs, Karin
    et al.
    Hietala, Riikka
    Laanearu, Janek
    Lundberg, Peter
    Stockholm University, Faculty of Science, Department of Meteorology. Fysisk Oceanografi.
    Some estimates of the Baltic deep-water transport through the Stolpe trench2007In: Tellus: A, Vol. 59, no 2, p. 238-248Article in journal (Refereed)
    Abstract [en]

    The subsurface flow of high-saline water masses from the Bornholm Basin through the Stolpe Channel plays an important role for the renewal of the Baltic Central Basin deep waters. In order to determine whether rotating 1½-layer hydraulic theory is an appropriate tool for describing this process, maximal-transport estimates based on climatological data from the Bornholm and Gdansk Basins have been established. These were found to deviate considerably from observational realities, and hence similar hydraulic considerations were also applied to more-or-less synoptic field data from a Finnish field campaign carried through in the mid-1980s. Also in this case significant differences were found between calculated transport capacity and observations. Since it furthermore was demonstrated that the characteristics of the observed cross-channel hydrographic structure could be explained using a frictional-balance model of the deep-water flow, it has been concluded that a hydraulic framework, although providing an upper bound of the transport, is of limited use when dealing with the Stolpe-Channel overflow. Although it cannot be excluded that the inflow is inviscid, but submaximal, it is more likely that the transport is governed by the combined effects of friction and wind forcing.

  • 6. Chafik, L.
    et al.
    Nilsson, Johan
    Stockholm University, Faculty of Science, Department of Meteorology .
    Skagseth, O.
    Lundberg, Peter
    Stockholm University, Faculty of Science, Department of Meteorology .
    On the flow of Atlantic water and temperature anomalies in the Nordic Seas toward the Arctic Ocean2015In: Journal of Geophysical Research - Oceans, ISSN 2169-9275, E-ISSN 2169-9291, Vol. 120, no 12, p. 7897-7918Article in journal (Refereed)
    Abstract [en]

    The climatic conditions over the Arctic Ocean are strongly influenced by the inflow of warm Atlantic water conveyed by the Norwegian Atlantic Slope Current (NwASC). Based on sea surface height (SSH) data from altimetry, we develop a simple dynamical measure of the NwASC transport to diagnose its spatio-temporal variability. This supports a dynamical division of the NwASC into two flow regimes; the SvinOy Branch (SvB) in the southern Norwegian Sea, and the Fram Strait Branch (FSB) west of Spitsbergen. The SvB transport is well correlated with the SSH and atmospheric variability within the Nordic Seas, factors that also affect the inflow to the Barents Sea. In contrast, the FSB is influenced by regional atmospheric conditions around Svalbard and northern Barents Sea. Using a composite analysis, we further relate anomalous strong SvB flow events to temperature fluctuations along the core of Atlantic water. A warm composite anomaly is found to propagate northward, with a tendency to amplify enroute, after these events. A roughly 12 months delayed temperature signal is identified in the FSB. However, also in the Lofoten Basin interior a delayed temperature signal is found, which appears to originate from the NwASC. This study suggests that hydrographic anomalies both upstream from the North Atlantic, and locally generated in the Norwegian Sea, are important for the oceanic heat and salt transport that eventually enters into the Arctic.

  • 7.
    Chafik, Léon
    et al.
    Stockholm University, Faculty of Science, Department of Meteorology .
    Nilsson, Johan
    Stockholm University, Faculty of Science, Department of Meteorology .
    Lundberg, Peter
    Stockholm University, Faculty of Science, Department of Meteorology .
    Skagseth, Øystein
    Hannachi, Abdelwahab
    Stockholm University, Faculty of Science, Department of Meteorology .
    Atmospheric circulation patterns control the variability of the oceanic transport towards the Arctic regionManuscript (preprint) (Other academic)
  • 8.
    Chafik, Léon
    et al.
    Stockholm University, Faculty of Science, Department of Meteorology .
    Nilsson, Johan
    Stockholm University, Faculty of Science, Department of Meteorology .
    Skagseth, Øystein
    Lundberg, Peter
    Stockholm University, Faculty of Science, Department of Meteorology .
    Transport Coherency and Eddy Activity Along the Norwegian Atlantic Slope CurrentIn: Journal of Physical Oceanography, ISSN 0022-3670, E-ISSN 1520-0485Article in journal (Refereed)
  • 9. Cuthbertson, A. J. S.
    et al.
    Lundberg, Peter
    Stockholm University, Faculty of Science, Department of Meteorology .
    Davies, P. A.
    Laanearu, J.
    Gravity currents in rotating, wedge-shaped, adverse channels2014In: Environmental Fluid Mechanics, ISSN 1567-7419, E-ISSN 1573-1510, Vol. 14, no 5, p. 1251-1273Article in journal (Refereed)
    Abstract [en]

    Results are presented from a series of parametric experimental and analytical studies of the behaviour of dense gravity currents along rotating, up-sloping, wedge-shaped channels. High resolution density profile measurements at fixed cross-and along-channel locations reveal the outflowing bottom gravity currents to adjust to quasi-steady, geostrophically-balanced conditions along the channels, with the outflow layer thickness and cross-channel interface slope shown to scale with the inlet Burger number for all experimental conditions tested. A general analytical solution to the classic rotating hydraulics problem has been developed under the assumption of inviscid, zero-potential-vorticity conditions to model dense water flow through a triangular constriction and thus simulate the vee-channel configurations under consideration. Predictions from this zero-PV model are shown to provide good overall quantitative agreement with experimental measurements obtained both under hydraulically-controlled conditions at the channel exit and for subcritical conditions generated along the channel length. Quantitative discrepancies between measurements and analytical predictions are attributed primarily to assumptions and limitations associated with the zero-PV modelling approach adopted, as well as the to the rapid adjustment in outflow characteristics as the channel exit is approached, as characterised by the along-channel variation in densimetric Froude number for the outflows.

  • 10.
    Enmar, Linda
    et al.
    Stockholm University, Faculty of Science, Department of Meteorology .
    Borenäs, Karin
    Sveriges meteorologiska och hydrologiska institut, SMHI.
    Lake, Irene
    Sveriges meteorologiska och hydrologiska institut, SMHI.
    Lundberg, Peter
    Stockholm University, Faculty of Science, Department of Meteorology .
    Comments on "Is the Faroe Bank Channel owerflow hydraulically controlled"?2009In: Journal of Physical Oceanography, ISSN 0022-3670, E-ISSN 1520-0485, Vol. 39, no 6, p. 1534-1538Article in journal (Refereed)
    Abstract [en]

    In a recent paper Girton et al., due to what appears to be a misunderstanding, stated that a critical-flow analysis of the deep-water transport through the Faroe Bank Channel had been undertaken by Lake et al. on the basis of rotating hydraulic theory for a channel of parabolic cross section. In fact, this quoted investigation dealt with a rectangular passage. In the present comment it is demonstrated how the use of parabolic bathymetry leads to significant improvements of the Froude number results.

  • 11.
    Enmar, Linda
    et al.
    Stockholm University, Faculty of Science, Department of Meteorology .
    Lake, Iréne
    Lundberg, Peter
    Stockholm University, Faculty of Science, Department of Meteorology .
    Sigray, Peter
    Stockholm University, Faculty of Science, Department of Meteorology . Swedish Defence Research Agency, Sweden.
    A note on ADCP-based indirect observations of turbulence2016In: Boreal environment research, ISSN 1239-6095, E-ISSN 1797-2469, Vol. 21, no 1-2, p. 44-52Article in journal (Refereed)
    Abstract [en]

    A 70-day data set from bottom-mounted ADCPs on the two sides of the Faroe-Bank Channel was analysed using the recorded flow variance and echo intensity in the deeper reaches of the passage as proxies for turbulence. A consistent picture emerged, not least since the data losses (which were ascribed to turbulence-induced activation of the fish-elimination option in the ADCP software) could be shown to co-vary with the internal M-2 tide affecting the vertical shear, which in turn proved to be correlated with the flow variance.

  • 12. Fallah, Haniyeh
    et al.
    Lundberg, Peter
    Stockholm University, Faculty of Science, Department of Meteorology .
    Razvan, Mohammad Reza
    On the existence of canards in a nonlinear fluid system manifesting oscillatory behaviour2018In: International Journal of Non-Linear Mechanics, ISSN 0020-7462, E-ISSN 1878-5638, Vol. 98, p. 58-63Article in journal (Refereed)
    Abstract [en]

    In an earlier study dealing with a nonlinear fluid oscillator governed by two autonomous ODEs, the solutions were found to display some aberrant characteristics adjacent to the boundaries of the oscillatory regime in parameter space. It was argued that this behaviour indicated the presence of canards. In the present study it is formally proved that this indeed is the case, and some numerical examples illustrating the phenomenon as well as its effects are presented.

  • 13. Hietala, Riikka
    et al.
    Lundberg, Peter
    Stockholm University, Faculty of Science, Department of Meteorology .
    Nilsson, Jenny A.U.
    Stockholm University, Faculty of Science, Department of Meteorology .
    A note on the deep-water inflow to the Bothnian Sea2007In: Journal of marine systems, ISSN 0924-7963, Vol. 68, no 1-2, p. 255-264Article in journal (Refereed)
    Abstract [en]

    The deepest connection between the Bothnian Sea and the Baltic Proper is the narrow Understen-Märket trench with a threshold depth of around 90 m. The deep-water flow through this passage, which is of great importance for the hydrographic state of the entire Gulf of Bothnia, was surveyed by the R/V Aranda in October 2004. On the basis of these field results as well as climatological data, it has been concluded that the deep-water flow can be described using a hydraulic framework applied to a channel of parabolic cross-section. The Understen-Märket trench is sufficiently narrow to, in principle, permits neglect of the Coriolis force. Since it may prove useful for other systems, the study, however, also includes the analysis and evaluation of a scheme to determine rotational first-order corrections to controlled transports predicted using standard non-rotating hydraulic theory.

  • 14. Joensson, Bror F.
    et al.
    Doos, Kristofer
    Stockholm University, Faculty of Science, Department of Meteorology .
    Myrberg, Kai
    Lundberg, Peter A.
    Stockholm University, Faculty of Science, Department of Meteorology .
    A Lagrangian-trajectory study of a gradually mixed estuary2011In: Continental Shelf Research, ISSN 0278-4343, E-ISSN 1873-6955, Vol. 31, no 17, p. 1811-1817Article in journal (Refereed)
    Abstract [en]

    When modelling is used for investigating estuarine systems, a choice generally has to be made between applying simple mass-balance considerations or using a process-resolving three-dimensional (3-D) numerical circulation model. In the present investigation of the Gulf of Finland, a gradually mixed estuary in the Baltic Sea, it is demonstrated how Lagrangian-trajectory analysis applied to the output from a 3-D model minimizes the disadvantages associated with both of the modelling techniques referred to above. This formalism made it possible to demonstrate that the main part of the Gulf is dominated by water originating from the Baltic proper, and that the most pronounced mixing with fresh water from the river Neva takes place over a limited zone in the inner part of the Gulf. Dynamical insights were furthermore obtained by using the Lagrangian formalism to construct overturning stream-functions for the two source waters.

  • 15.
    Jönsson, Bror
    et al.
    Stockholm University, Faculty of Science, Department of Meteorology.
    Döös, Kristofer
    Stockholm University, Faculty of Science, Department of Meteorology.
    Nycander, Jonas
    Stockholm University, Faculty of Science, Department of Meteorology.
    Lundberg, Peter
    Stockholm University, Faculty of Science, Department of Meteorology.
    Standing waves in the Gulf of Finland and their relationship to the basin-wide Baltic seiches2008In: Journal of Geophysical Research: Oceans, Vol. 113, p. C03004-Article in journal (Refereed)
    Abstract [en]

    A linear shallow-water model was used to study different harmonic oscillations in the Baltic Sea. The model was initialized using a linear sea-surface slope from east to west, and was hereafter run without forcing. In our results, we could identify three different local oscillatory modes: one in the Gulf of Finland, with the two distinct periods 23 and 27 hours, one in the Danish Belt Sea, with a less distinct period in the range 23-27 hours, and one in the Gulf of Riga, with the period 17 hours. The most pronounced mode is that in the Gulf of Finland. No clear indications of basin-wide seiches in the Baltic could be found from our simulations. These results were further corroborated by a frequency analysis of sea-level observations from the Baltic. This shows an amplification of the K1 and O1 tidal modes in the Gulf of Finland, but not of the M2 and S2 modes. No such amplification was seen in the rest of the Baltic Sea. On the basis of our model simulations, we propose that sea-level oscillations of the Baltic be regarded as a ensemble of weakly coupled local oscillators. Each oscillator corresponds to a ''fjord mode" or "harbour mode" in a particular bay or sub-basin. These are not proper eigenmodes since their energy gradually leaks out to the rest of the Baltic Sea, resulting in radiation damping. Nevertheless, their resonance may in fact be sharper than that of the proper basin-wide eigenmodes.

  • 16.
    Jönsson, Bror
    et al.
    Stockholm University, Faculty of Science, Department of Meteorology.
    Lundberg, Peter
    Stockholm University, Faculty of Science, Department of Meteorology.
    Döös, Kristofer
    Stockholm University, Faculty of Science, Department of Meteorology.
    Baltic sub-basin turnover times examined using the Rossby Centre Ocean model.2004In: Ambio, ISSN 0044-7447, Vol. 33, no 4-5, p. 257-60Article in journal (Refereed)
  • 17.
    Lundberg, Peter
    Stockholm University, Faculty of Science, Department of Meteorology.
    J.W. Sandström: A biographical sketch2008In: Tellus. Series A: Dynamic Meteorology and Oceanography, Vol. 60, no 5, p. 810-818Article in journal (Refereed)
    Abstract [en]

    J. W. Sandström's (1874–1947) activities encompassed meteorological and oceanographic research in Sweden, as well as Norway. As shown in this biographical sketch, his scientific interests ranged over wide fields and were pursued well past his retirement from the Swedish Meteorological Office. In addition to Sandström's well-known results with bearing on the global thermohaline circulation on which much of his present-day reputation rests, he made other highly important theoretical contributions to both oceanography and meteorology, at the same time not neglecting field research. At a very early date, Sandström, inspired by his academic benefactor Otto Pettersson, recognized the importance of the North Atlantic inflow to the Norwegian Sea for the climate of Northwestern Europe and, furthermore, attempted to investigate this process during a number of Nordic-Sea research cruises in the 1930s.

  • 18.
    Lundberg, Peter
    Stockholm University, Faculty of Science, Department of Meteorology .
    O that awful deepdown torrent2015In: Boreal environment research, ISSN 1239-6095, E-ISSN 1797-2469, Vol. 20, no 1, p. 62-74Article in journal (Refereed)
    Abstract [en]

    An overview of the deep-water flow from the Nordic Seas through the Faroe-Bank Channel and the Denmark Strait into the North Atlantic proper is given. These fluxes are of considerable importance for the global thermohaline circulation, and it is outlined how they can be modeled on the basis of rotating hydraulic theory for zero-as well as finite-potential-vorticity flow. The hydraulic framework is also shown to be useful for analyzing various dynamic features characterizing the deep-water flow.

  • 19.
    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.

  • 20.
    Lundberg, Peter
    et al.
    Stockholm University, Faculty of Science, Department of Meteorology .
    Laanearu, Janek
    Improvements of series convergence to the rotating-channel flow problem using hydraulic solutions for a parabolic passage2018In: Journal of Hydraulic Research, ISSN 0022-1686, E-ISSN 1814-2079, Vol. 56, no 3, p. 313-323Article in journal (Refereed)
    Abstract [en]

    This study deals with the perturbative solutions of the constant-potential-vorticity hydraulic problem, where the lowest-order solution corresponds to that for a non-rotating parabolic channel. The analytical structure of the series expansions and the corresponding numerical solutions are presented for flow through a horizontally constricted passage, and it is demonstrated how the series solution can be used to bridge the gap between non-rotating and rotating hydraulic models. It was found that the perturbative expansions converged close to the branch-point that corresponds to critical flow in rotating channel. This was not the case for the sub- and supercritical solution branches, where the perturbative series proved to diverge for discrete values of the expansion parameter, and hence one focus of the study is on improving the convergence here. The location and character of the dominant singularities affecting the series convergence were determined from analysis of the expansion coefficients using Domb-Sykes plots, where after the convergence was improved using Euler transformation rather than by direct Padé summation.

  • 21. Nilsson, Jenny A. U.
    et al.
    Lundberg, Peter
    Stockholm University, Faculty of Science, Department of Meteorology .
    A comparatively general solution of the shelf-wave problem2012In: Continental Shelf Research, ISSN 0278-4343, E-ISSN 1873-6955, Vol. 34, p. 26-29Article in journal (Refereed)
    Abstract [en]

    It is demonstrated how a hyperbolic-tangential shelf bathymetry can be used to mimic classical convex and concave bottom profiles employed for previous investigations of coastally trapped waves. This bathymetry permits a transformation of the governing wave equation which makes it possible to use Frobenius series expansions for solving the associated eigenvalue problems which yield the dispersion relations.

  • 22.
    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.

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