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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Ocean dynamics 33 (1980), S. 19-37 
    ISSN: 1616-7228
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Description / Table of Contents: Zusammenfassung Eine Methode für die dynamische Kopplung zweidimensionaler und dreidimensionaler numerischer Meeresmodelle wird vorgestellt. Um die Methode zu testen, werden Strömungen berechnet in einem inneren Teilgebiet eines geschlossenen rechtwinkligen Beckens mit Hilfe eines inneren dreidimensionalen Systems (das dieses Teilgebiet bedeckt), das in Verbindung steht mit einem äußeren zweidimensionalen System (welches das übrige äußere Gebiet des Beckens bedeckt). Das so gebildete Hybrid-System wird Modell 2D/3D genannt. Die vom dreidimensionalen Teil dieses Modells abgeleiteten Strömungen werden mit den mit Hilfe eines dreidimensionalen Modells des gesamten Beckens (im folgenden Modell 3D genannt) entsprechenden berechneten Strömungen verglichen. Die Vergleiche veranschaulichen die Bedeutung des Ansatzes der Bodenreibung im 2D-Bereich des Modells 2D/3D bei der Bestimmung der Größe des Transports im 3D-Bereich dieses Modells. Bei einem Ansatz für die Bodenreibung, der auch den Windschub an der Oberfläche mit einschließt, ergibt sich eine Übereinstimmung bis auf 4 cm/s für die mit dem Modell 2D/3D berechnete Änderung der horizontalen Strömung mit der mit Hilfe des gesamten Modells berechneten.
    Abstract: Résumé On présente une méthode pour raccorder dynamiquement des modèles numériques de la mer à deux et trois dimensions. Pour tester la méthode, on calcule les courants dans une zone intérieure à un bassin fermé rectangulaire, à l'aide d'un modèle tridimensionnel (couvrant cette zone), raccordé à un modèle bidimensionnel (couvrant le reste du bassin). Le système hybride ainsi réalisé est appelé un modèle 2D/3D. Les courants obtenus à l'aide de la partie à 3 dimensions sont comparés avec les courants correspondants calculés à l'aide d'un modèle à 3 dimensions du bassin entier (appelé ci-après le modèle 3D). Cette comparaison met en lumière l'importance de la loi de frottement sur le fond dans la région 2D du modèle 2D/3D pour une bonne détermination de la valeur du flux dans la région 3D de ce modèle. En utilisant une loi de frottement sur le fond qui tient compte de la force d'entraînement du vent en surface, la vitesse du courant horizontal en fonction de la profondeur, calculée sur le modèle 2D/3D, est en accord à 4 cm/s près avec celle calculée sur le modèle 3D complet.
    Notes: Summary A method is presented for dynamically connecting two-dimensional and three-dimensional numerical sea models. To test the method, currents are computed in an interior sub-area of a closed rectangular basin, using an inner three-dimensional system (covering that sub-area) connected to an outer two-dimensional system (covering the remaining outer area of the basin). The hybrid scheme thus formed is called a 2D/3D model. The currents derived from the three-dimensional part of it are compared with the corresponding currents calculated using a three-dimensional model of the whole basin (henceforth known as the 3D model). The comparisons illustrate the importance of the formulation of bottom friction in the 2D region of the 2D/3D model in determining the magnitude of the transport in the 3D region of this model. By using a formulation of bottom friction which includes the surface wind stress, the variation of horizontal current with depth computed with the 2D/3D model agrees to within 4 cm/s with that computed with the full 3D model.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 5 (1985), S. 405-425 
    ISSN: 0271-2091
    Keywords: DuFort-Frankel ; Saul'ev ; Instability ; Sea Model ; Hydrodynamic ; Three-dimensional Time-splitting ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A three dimensional hydrodynamic sea model of an arbitrary sea area is formulated using sigma co-ordinates in the vertical. The solution of the equations using finite difference grids in the horizontal and the vertical is described.Discretization of the vertical viscosity term in the hydrodynamic equations using the DuFort-Frankel and Saul'ev methods is developed. Some numerical instabilities occur with the DuFort-Frankel method which can be overcome by splitting the hydrodynamic equations into equations describing the mean flow and equations describing the deviations from it. The computational advantages of solving these equations with different time steps are discussed.The accuracy and stability of the various methods is demonstrated for wind induced flow in a simple rectangular basin having dimensions representing the North Sea.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 16 (1993), S. 105-131 
    ISSN: 0271-2091
    Keywords: Tidal-currents ; Stratification ; Galerkin ; Spectral ; Log-layer ; Resolution ; B-spline ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The paper deals with the accurate determination of tidal current profiles in both homogeneous and stratified regions when a no-slip condition is used at the seabed with a flow-dependent eddy viscosity related to the depth-mean current or the bed frictional velocity.Calculations show that it is essential to accurately resolve the high-shear region which occurs at the bed and across the pycnocline/thermocline in the case of stratified flow. A computationally accurate and economic method of resolving these regions is demonstrated using the Galerkin method with a set of basis functions designed to accurately reproduce the high-shear layers which occur in these regions.With a flow-independent eddy viscosity a stability analysis can be readily performed and an unconditionally stable algorithm developed. However, with a flow-dependent viscosity, in particular a viscosity computed from the frictional velocity, a non-linear numerical instability can occur. A method of maintaining numerical stability in this case is also described.The importance of near-bed resolution to the computed value of the frictional velocity is demonstrated and its influence on the total tidal velocity profile is illustrated by a number of idealized calculations using various eddy viscosity formulations.The influence of stratification on the computed tidal profiles is shown in the latter part of the paper.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 13 (1991), S. 235-250 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A method is presented for solving the 3D hydrodynamic equations in homogeneous sea regions using the Galerkin approach in the vertical with a mixed basis set. The basis set is composed of eigenfunctions of the eddy viscosity profile and a fixed function through the vertical, the amplitude of which is related to the externally applied surface wind stress. By this means the high-shear near-surface layer, which has previously been difficult to resolve using eigenfunction expansions, is accurately represented in the solution.The computational advantages of this approach compared with other basis functions, in terms of computer time and memory, and the ease of implementation on parallel processors with vector facilities are briefly discussed.The accuracy of the method and the choice of the additional function is demonstrated for the problem of wind-induced currents in a rectangular sea region.Calculations clearly show that for wind-induced currents this new approach is significantly more accurate than the ‘classical’ eigenfunction method. Also, the new method retains the advantages of the eigenfunction approach, namely insight into the mechanisms involved and ease of implementation on vector-parallel computers, together with minimization of computer time and memory.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 26 (1998), S. 1055-1084 
    ISSN: 0271-2091
    Keywords: internal tides ; shelf edge ; stratification ; turbulence energy ; baroclinic ; eddy viscosity ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A non-linear, three dimensional, baroclinic model with a range of turbulence energy submodels and algebraic models for the vertical mixing of momentum and density, is used in a cross shelf form to examine the spatial variation of vertical mixing due to the internal tide at the shelf edge off the west coast of Scotland. Particular emphasis is placed on the sensitivity of the mixing to the form of the parameterization of the subgrid scale processes. Calculations using a fine finite difference grid in the horizontal of the order of 0.6 km with 50 sigma levels in the vertical and a typical winter time stratification, show that the model can reproduce the major features of the internal tide with the range of parameterizations considered here, although there are some differences in the magnitude of both the velocity and mixing intensity of the internal tide, depending upon the parameterization of the mixing. In particular, the turbulence energy models show regions of intense mixing at the sea bed where the internal tide is generated and at the sea surface above the shelf break associated with the shear production of turbulence. These differences suggest that detailed measurements of current, internal displacement of density fields and turbulence dissipation rate may be able to assess the accuracy of the various mixing models. Calculations, however, show that the internal tide is particularly sensitive to small perturbations in the initial density field, suggesting that besides detailed measurements to validate the model, a detailed synoptic data set is required for model initialization. © 1998 John Wiley & Sons, Ltd.
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
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