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Formulae for Pressure Gradients in One-Dimensional Lake Models
Computer-Aided Fluid Engineering, Norrköping, Sweden.
Swedish Meteorological and Hydrological Institute, Norrköping.
1989 (English)In: Journal of Geophysical Research, ISSN 0148-0227, E-ISSN 2156-2202, Vol. 94, no C4, 4939-4946 p.Article in journal (Refereed) Published
Abstract [en]

Formulae for barotropic and baroclinic pressure gradients, suitable for one-dimensional lake models, are derived and explored. The derivation is based on the equation for free standing oscillations and a continuity relation. The formulae, which are easy to derive and use, give the correct external and internal seiche frequencies for nonrotating, rectangular one- or two-layered basins of constant depth. When applied to situations with continuous stratification, further assumptions need to be introduced. These are discussed in the paper. Applications to a laboratory experiment, dealing with wind-induced entrainment, show that pressure gradients for the entrainment process are significant and that the pressure formulae derived capture this effect. The formulae are also used in combination with a one-dimensional lake model. Comparisons with field measurements of the seasonal stratification show that the inclusion of pressure gradients improves the predictive capabilities of the lake model.

Place, publisher, year, edition, pages
1989. Vol. 94, no C4, 4939-4946 p.
National Category
Social Sciences Interdisciplinary
Identifiers
URN: urn:nbn:se:liu:diva-78949DOI: 10.1029/JC094iC04p04939OAI: oai:DiVA.org:liu-78949DiVA: diva2:537186
Available from: 2012-06-26 Created: 2012-06-26 Last updated: 2017-12-07Bibliographically approved
In thesis
1. Physical control of primary production in a sub-arctic reservoir
Open this publication in new window or tab >>Physical control of primary production in a sub-arctic reservoir
2004 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

The first paper (Paper I) in this thesis treats autumn cooling in the Swedish lake Väsman. The water temperature is simulated using a one-dimensional lake model where the vertical mixing is calculated by a k - ɛ turbulence model. The heat exchange between the atmosphere and the lake is formulated in terms of heat fluxes. A great advantage with the actual heat flux formulation is that it requires only standard meteorological variables, which makes it possible to apply the model to arbitrary lakes. After the autumn cooling comes the winter season, which is described in Paper II. A simple ice model describing ice formation, growth and decay is incorporated into the lake model. Equations are derived for the insolation through snow and ice cover. Both ice and temperature during winter are simulated in a small lake with good results.

One-dimensional lake models may include the effect of horizontal pressure gradients, which changes the vertical velocity profile and thus the rate of vertical mixing. Equations describing the horizontal pressure gradients due to wind set-up in both homogeneous and two-layered lakes (Paper ill) are derived and verified against wind-induced entrainment in laboratory experiments and the water temperature development in lake Velen. Further studies of deeper lakes show that the deep water mixing, based only on the k - ɛ turbulence model, is too small. This is especially true during summer when thermal stratification inhibits the wind induced mixing to penetrate down into deeper layers. An empirical eddy viscosity, based on the buoyancy frequency N, is therefore incorporated into the model.

In Paper IV the model is applied to the Akkajaure reservoir, which has a maximum depth of 92m and a maximum surface area of 266 km2. The model is capable of simulating the seasonal water temperature cycle using standard meteorological data. Continuous simulations have been performed during the years 1998-2002 where the water temperature and ice data are verified against measurements. In the upper 40-50m the discrepancy is only 0.5-1.0 °C between measured and calculated water temperature. However in the bottom water it is not possible to verify the empirical eddy viscosity term because the temperature measurementsdid not cover this layer. From measurements and simulations Akkajaure is found to be more or less vertically homogeneous throughout the whole year, only a weak stratification exists during one to two summer weeks.

A Lagrangian particle dispersion model, coupled to the lake model, is used to explore the effects of vertical mixing on the primary production in the Akkajaure reservoir (Paper V). The particle model is used to describe the vertical movements of phytoplankton in the entire water column. The primary production of each phytoplankton cell is assumed to be a function of the ambient light (no nutrient limitations). A light model is describing the photosynthesis of each individual phytoplankton. The simulation of net production in Akkajaure is performed under realistic conditions during four different growth seasons. The main result is that the turbulence intensity controls the primary production in this sub-arctic reservoir and that the production during summertime increases as the turbulence intensity increases. This means that the primary production is larger in a relatively cold summer with a weak stratification (strong, deep reaching turbulence) compared to a warm, more stratified, summer with weak turbulence.

Place, publisher, year, edition, pages
Linköping: Linköpings universitet, 2004. 72 p.
Series
Linköping Studies in Arts and Science, ISSN 0282-9800 ; 292
National Category
Social Sciences Interdisciplinary
Identifiers
urn:nbn:se:liu:diva-29537 (URN)14904 (Local ID)91-7373-949-9 (ISBN)14904 (Archive number)14904 (OAI)
Public defence
2004-06-04, Sal Elysion, Hus-T, Universitetsområdet Valla, Linköping, 10:00 (Swedish)
Supervisors
Available from: 2009-10-09 Created: 2009-10-09 Last updated: 2014-09-03Bibliographically approved

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