A diffusion model for the development of a boundary layer in lakes

The development of a boundary layer characterised by very low gradients in temperature and salinity near the bottom boundary of a lake does not necessarily imply an increase in diapycnal mixing within the boundary layer. The results of a quasi three-dimensional diffusion model for a basin with sloping boundaries demonstrate that in lakes a boundary layer also develops when the diapycnal diffusivity is chosen to be constant. In the model mixing is assumed to be anisotropic and is described as an isopycnal and diapycnal turbulent diffusion process. Advective transport is not considered. Therefore, the model is restricted to the description of the purely diffusive response of a lake. It should be regarded as a contribution to the discussion of boundary mixing and not as a complete mixing model for a specific lake. The isopycnal and diapycnal turbulent diffusion coefficients are presumed to be constant in space and time. The direction of isopycnal and diapycnal density flux changes with time since mixing of the density distribution influences the orientations of the isopycnals. This interaction between mixing process and density distribution is accounted for by the model. According to the model the density distribution, and therefore the development of a boundary layer, only depends on diapycnal mixing while the distribution of a passive tracer depends on both, isopycnal and diapycnal mixing. The application of the model to the subalpine Lake Alpnach demonstrates that a simple diffusion model is sufficient to predict the development of a boundary layer. Considering that the model does not include advective processes and that diffusivities have been assumed to be constant in space and time, the structure of the boundary layer predicted agrees surprisingly well with experimental data

Horizontal mixing in lakes

Horizontal mixing in the upper hypolimnion of lakes far from the boundaries was studied in lake basins with surface areas between 5 and 220 km2 by observing the growth of the concentration distribution of the fluorescent dye sodium fluorescein(uranin). In each of the eight experiments, between 0.2 and 2 kg of uranin was instantaneously released into the lake in the appropriate depth (between 15 and 25 m) in such a way to keep the initial cloud size as small as possible. The horizontal extension of the cloud was repeatedly determined by integration of numerous vertical profiles. These surveys served to test theoretical models for horizontal mixing. The temporal development of the size and of the variances along the principal axes of the tracer concentration distribution was the main property considered here. The experiments cover a range of cloud sizes between 3 X 102 and 3 X 105 m2. None of them support the hypothesis that cloud size grows with elapsed time raised to the power of 3 as predicted by the inertial subrange turbulence model first applied to dispersion by Batchelor [1950]. The shear-diffusion model of Carter and Okubo [1965] was found to provide a good description of the development of cloud size with time. This model also accounts for the fact that the tracer distributions were not radially symmetric. Effective horizontal diffusivities lie between 0.02 and 0.3 m2 S-l. Reevaluation of published data from experiments in Lake Ontario [e.g., Murthy, 1976] and in the ocean [e.g., Okubo, 1971] supports both the applicability of the shear-diffusion model and the doubts raised against the appropriateness of the inertial subrange model for scales up to 1000 m

Description of stability and neutrally buoyant transport in freshwater lakes

The concept of potential density, introduced by oceanographers to describe the vertical stability of a water column, may be inadequate if the water temperature is close to the temperature of maximum density, Tmd, where the thermal expansion coefficient changes its sign. Because Tmd decreases with increasing pressure, potential density especially fails to provide a reliable means for the analysis of the local stability of a water column in deep, cold freshwater lakes. A new quantity called quasi-density is introduced. Its vertical gradient correctly describes the local stability of a water column for every water body (warm, cold, fresh, or salty). Application of this concept to field data from Lake Baikal shows that quasi-density-in contrast to potential density - is an ideal tool to assess vertical stability. In a two- or three-dimensional field of potential temperature and salinity, the neutral surface is defined by the direction along which an infinitesimal isentropic displacement of a water parcel is buoyancy-free. The neutral surfaces do not define a potential; that is, there is no scalar property that is constant along the neutral surface. Isentropic transport over finite distances is not buoyancy-free along neutral surfaces or along surfaces of constant potential density (isopycnals. We define the neutral track as the path along which isentropic transport of a water parcel is buoyancy-free. In general, each water parcel defines a different neutral track. Neutral track and neutral surface are complementary concepts used to assess the potential movement of a water parcel over some distance. The latter describes the path of a water parcel that after each infinitesimal displacement completely exchanges its identity with the characteristics of its new environment, whereas the former describes a parcel that totally keeps its identity specified by potential temperature and salinity

Processes of deep-water renewal in Lake Baikal

Deep-water renewal in Lake Baikal (Siberia), the world s deepest lake and largest lake by volume, is relatively fast. Water age calculated from tritium and helium as well as from chlorofluorocarbons does not exceed 19 yr. Relative saturation of dissolved oxygen typically exceeds 80%. The equation of state of Baikal water was determined including the effect-of dissolved ions and silicic acid. Based on nearly 600 CTD profiles taken between 1993 and 1995, two mechanisms of deep-water mixing were identified. (1) In spring, cold and relatively saline water from the Selenga, the major inflow to the lake, forms a density plume that reaches the bottom of the central basin during April and early May. Due to entrainment of lake water the plume transports about 125 km3 of water per year to the deepest part of the basin. Later in spring, the river water forms the thermal bar observed along the eastern shore. There are indications that parts of the Selenga are also plunging to the deep part of the southern basin. (2) At Academician Ridge, separating the cold and saline water of the central basin from the warmer and slightly less saline water of the northern basin, horizontal mixing results in a water mass that can sink on either side of the sill. Whereas in the central basin the water mass stays at intermediate depth, in the northern basin it sinks to the deepest part. More detailed data are needed to quantify this density flux. No indication of a wind-induced thermobaric instability was found