Subgrid-Scale Parameterization in Numerical Simulations of Lake Circulation

  • Kolumban HutterEmail author
  • Yongqi Wang
  • Irina P. Chubarenko
Part of the Advances in Geophysical and Environmental Mechanics and Mathematics book series (AGEM)


Turbulence is ubiquitous in geophysical flows. There are hardly any situations in the dynamics of natural waters and the atmosphere that do not involve turbulent effects at some point, and only little insight can be gained in the dominant processes, if turbulence is not taken into account. Thus, the modelling of this phenomenon has attracted a great many researchers and more and more advanced models, suitable for the description of a large variety of geophysical flows, evolved over the last decades. A general model embracing all aspects of turbulence is still out of reach. Nevertheless, there has been an enormous progress in the understanding of turbulence in the past. More recently, Direct Numerical Simulations (DNS) and Large Eddy Simulations (LES) provided data that were previously only available by high-precision laboratory setups (or not at all) and had a large impact on the development of new turbulence models. It seems likely that, especially in oceanography and meteorology, LES will take a position equitable to the ensemble averaged methods in the near future. At present, however, in spite of the development of larger and faster computers, LES is still too expensive for standard simulations of geophysical interest. In this chapter, we will mainly investigate a simple parameterization of the subgrid-scale turbulent closure which is based on the Reynolds Averaged Navier-Stokes Equations (RANS) and the subgrid-scale eddy viscosity parameterizations. We employ the three-dimensional, hydrodynamic, semi-implicit, finite difference model, developed by Song and Haidvogel and extended for the TVD treatment of the advection terms by Y. Wang. Subgrid-Scale Parameterization in Numerical Simulations of Lake Circulation are used and Smagorinsky’s formulation and MellorYamada ’s level-2.5 model are used to parameterize the horizontal and vertical eddy viscosities. Numerical results in an assumed rectangular basin with constant depth and in Lake Constance are displayed and discussed. A comparison is made with prescribed constant eddy viscosities; it clearly shows the importance of subgrid-scale parameterizations in numerical simulations of lake circulation. We do not claim that such subgrid-scale parameterizations are the best choice of possible closure conditions, but only show that suitable parameterizations of the small-scale (subgrid-scale) turbulent motions are needed.


Turbulent Kinetic Energy Direct Numerical Simulation Eddy Viscosity Vertical Eddy Viscosity Turbulent Eddy Viscosity 
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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Kolumban Hutter
    • 1
    Email author
  • Yongqi Wang
    • 2
  • Irina P. Chubarenko
    • 3
  1. 1.c/o Laboratory of Hydraulics, Hydrology and Glaciology at ETHZürichSwitzerland
  2. 2.Chair of Fluid Dynamics, Department of Mechanical EngineeringTU DarmstadtDarmstadtGermany
  3. 3.P.P. Shirshov Institute of OceanologyRussian Academy of SciencesKaliningradRussia

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