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Numerical modeling of lake dynamics

Wang, Yongqi and Hutter, Kolumban
Pandalai, S. G. (ed.) :

Numerical modeling of lake dynamics.
In: Recent Research Developments in Physical Oceanography. Transworld Resaerch Network, Kerala , pp. 97-122. ISBN 81-7895-092-8
[Book Section] , (2003)

Abstract

Three-dimensional numerical modeling for the shallow water equations is presented, suitable for determining the wind-driven currents in lakes or the coastal ocean. Different numerical treatments of the advection terms emerging in the governing equations are compared and discussed. It is demonstrated that the traditional numerical treatments of advection terms, e.g. central and upstream difference schemes, are rather questionable, although they are most frequently employed in ocean/lake circulation models, whereas a so-called high-resolution total variation diminishing (TVD) technique yields the most reasonable results. Because of the relatively small water depths of lakes in comparison to the ocean, an explicit integration technique on the vertical diffusion terms requires excessively small time steps for numerical modeling of lake circulations which leads to very long integration times. A semi-implicit temporal integration scheme is recommended. With regard to the vertical spatial discretisation, two numerical techniques -- a finite difference scheme and a spectral technique -- are compared. Although it is well known that the spectral methods generally enjoy faster convergence and smaller numerical diffusion than the finite difference methods, the use of the spectral method is very restricted in the modeling of lakes with a strong summer stratification. As turbulence closure conditions, two subgrid-scale modeling techniques -- Smagorinsky's postulation for the horizontal eddy viscosity and the Mellor-Yamada level-2 model for the vertical eddy viscosity -- are applied. Finally, the recommendable three-dimensional semi-implicit finite difference model with the TVD scheme applied on the numerical treatment of the advection terms and subgrid-scale modeling techniques is tested as to whether it is capable to predict or reproduce physically relevant processes that are commonly observed by physical limnologists.

Item Type: Book Section
Erschienen: 2003
Editors: Pandalai, S. G.
Creators: Wang, Yongqi and Hutter, Kolumban
Title: Numerical modeling of lake dynamics
Language: English
Abstract:

Three-dimensional numerical modeling for the shallow water equations is presented, suitable for determining the wind-driven currents in lakes or the coastal ocean. Different numerical treatments of the advection terms emerging in the governing equations are compared and discussed. It is demonstrated that the traditional numerical treatments of advection terms, e.g. central and upstream difference schemes, are rather questionable, although they are most frequently employed in ocean/lake circulation models, whereas a so-called high-resolution total variation diminishing (TVD) technique yields the most reasonable results. Because of the relatively small water depths of lakes in comparison to the ocean, an explicit integration technique on the vertical diffusion terms requires excessively small time steps for numerical modeling of lake circulations which leads to very long integration times. A semi-implicit temporal integration scheme is recommended. With regard to the vertical spatial discretisation, two numerical techniques -- a finite difference scheme and a spectral technique -- are compared. Although it is well known that the spectral methods generally enjoy faster convergence and smaller numerical diffusion than the finite difference methods, the use of the spectral method is very restricted in the modeling of lakes with a strong summer stratification. As turbulence closure conditions, two subgrid-scale modeling techniques -- Smagorinsky's postulation for the horizontal eddy viscosity and the Mellor-Yamada level-2 model for the vertical eddy viscosity -- are applied. Finally, the recommendable three-dimensional semi-implicit finite difference model with the TVD scheme applied on the numerical treatment of the advection terms and subgrid-scale modeling techniques is tested as to whether it is capable to predict or reproduce physically relevant processes that are commonly observed by physical limnologists.

Title of Book: Recent Research Developments in Physical Oceanography
Volume: 2
Place of Publication: Kerala
Publisher: Transworld Resaerch Network
Divisions: Study Areas
16 Department of Mechanical Engineering
16 Department of Mechanical Engineering > Fluid Dynamics (fdy)
Study Areas > Study Area Mechanic
Date Deposited: 24 Aug 2011 18:22
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