A modified sigma equations' approach to the numerical modeling of Great Lakes hydrodynamics

Freeman, N. G.; Hale, A. M.; Danard, Maurice B.

doi:10.1029/jc077i006p01050

Cited by 49 publications

(13 citation statements)

References 7 publications

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“…Figure la shows the irregularity that occurs in the solution domain due to the variation of the surface elevation over the hill. In order to simplify the application of boundary conditions along the lower boundary, the irregular domain was transformed into the regular domain in Figure lb using the sigma transformation proposed by Phillips (1957) and extended by Freeman et al (1972) cr = x3/m% x2),…”

Section: The Equations Of Motionmentioning

confidence: 99%

The Askervein hill project: A finite control volume prediction of three-dimensional flows over the hill

Raithby

Stubley

Taylor

1987

Boundary-Layer Meteorol

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A three-dimensional nonlinear numerical model, that has been extensively used previously to predict environmental water flows, was applied to predict the flow over an isolated hill, Askervein. Predictions are reported for winds approaching the hill from 210" and 180" clockwise from north, both under almost neutral atmospheric conditions.The model predictions were compared with data collected during a major field study in 1983. From the comparisons it was concluded that the model predicts the mean flow variables with good accuracy. Larger discrepancies were found for quantities related to the turbulence, pointing to deficiencies in the turbulence model, and perhaps in some of the measurements.

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Section: The Equations Of Motionmentioning

confidence: 99%

The Askervein hill project: A finite control volume prediction of three-dimensional flows over the hill

Raithby

Stubley

Taylor

1987

Boundary-Layer Meteorol

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“…Later, other discretisations were developed, mainly inspired by the progress in atmospheric modelling, for which coordinates based on the pressure field were used (Sutcliffe, 1947;Eliassen, 1949;Phillips, 1957). In oceanography, such developments led to ρ or σ coordinates (Freeman et al, 1972;Owen, 1980;Bleck and Boudra, 1986;Nihoul et al, 1986;Blumberg and Mellor, 1987). For the ρ coordinates, the vertical coordinate is based on the density field.…”

Section: Introductionmentioning

confidence: 99%

A fully consistent and conservative vertically adaptive coordinate system for SLIM 3D v0.4 with an application to the thermocline oscillations of Lake Tanganyika

et al. 2018

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Abstract. The discontinuous Galerkin (DG) finite element method is well suited for the modelling, with a relatively small number of elements, of three-dimensional flows exhibiting strong velocity or density gradients. Its performance can be highly enhanced by having recourse to r-adaptivity. Here, a vertical adaptive mesh method is developed for DG finite elements. This method, originally designed for finite difference schemes, is based on the vertical diffusion of the mesh nodes, with the diffusivity controlled by the density jumps at the mesh element interfaces.The mesh vertical movement is determined by means of a conservative arbitrary Lagrangian-Eulerian (ALE) formulation. Though conservativity is naturally achieved, tracer consistency is obtained by a suitable construction of the mesh vertical velocity field, which is defined in such a way that it is fully compatible with the tracer and continuity equations at a discrete level.The vertically adaptive mesh approach is implemented in the three-dimensional version of the geophysical and environmental flow Second-generation Louvain-la-Neuve Iceocean Model (SLIM 3D; www.climate.be/slim). Idealised benchmarks, aimed at simulating the oscillations of a sharp thermocline, are dealt with. Then, the relevance of the vertical adaptivity technique is assessed by simulating thermocline oscillations of Lake Tanganyika. The results are compared to measured vertical profiles of temperature, showing similar stratification and outcropping events.

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“…Major disadvantages of this approach are the poor reproduction of along-bed advection and turbulence production due to the step-like representation of sloping beds. The prototype of terrain and surface following coordinates (r coordinates with vertical cell heights being a fixed fraction of the actual water depth) has been introduced into numerical models for natural waters by Freeman et al (1972). The concept of general vertical coordinates (see Kasahara 1974 andRuddick 1992) in which layers are arbitrarily distributed in the vertical has been applied to ocean modelling by various authors, see e.g.…”

Section: Spatial Discretisationmentioning

confidence: 99%

Three-dimensional modelling of estuarine turbidity maxima in a tidal estuary

Bolding²,

2004

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A new numerical model for simulating estuarine dynamics is introduced here. This model, called General Estuarine Transport Model (GETM), has been specifically designed for reproducing baroclinic, bathymetry-guided flows where the tidal range may exceed the mean water depth in large parts of the domain such that drying and flooding processes are relevant. Several physical and numerical features of the model support exact and stable results for such domains. For the physics, high-order turbulence closure schemes guarantee proper reproduction of vertical exchange processes. Among the specific numerical features, generalised vertical coordinates, orthogonal curvilinear horizontal coordinates, high-order TVD advection schemes and stable drying and flooding algorithms have been implemented into GETM. The model is applied here to simulate the dynamics of estuarine turbidity maxima (ETMs), a complex feature present in most tidal estuaries. First, idealised simulations for a two-dimensional domain in the xz space will be shown to reproduce the basic generation mechanisms for ETMs. Then, a realistic three-dimensional simulation of the Elbe estuary in Northern Germany will be carried out. It is demonstrated that for a given forcing situation the model reproduces a stable ETM at the correct location.

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A modified sigma equations' approach to the numerical modeling of Great Lakes hydrodynamics

Cited by 49 publications

References 7 publications

The Askervein hill project: A finite control volume prediction of three-dimensional flows over the hill

The Askervein hill project: A finite control volume prediction of three-dimensional flows over the hill

A fully consistent and conservative vertically adaptive coordinate system for SLIM 3D v0.4 with an application to the thermocline oscillations of Lake Tanganyika

Three-dimensional modelling of estuarine turbidity maxima in a tidal estuary

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