Thermally driven interaction of the littoral and limnetic zones by autumnal cooling processes

In autumn, during the transition period, shores influence the interior dynamics of large temperate lakes by the formation of horizontal water-temperature gradients between the shallow and deep areas, whilst vertical temperature gradients are smoothed by convection due to surface cooling. A simple heat budget model, based on the heat balance of the water column without horizontal advection and turbulent mixing, allows deduction of the time-dependent difference between the mean temperature within the littoral area and the temperature in the upper mixed layer. The model corroborates that littoral areas cool faster than regions distant from shores, and provides a basis for an estimation of structure of flows from the beginning of cooling process till the formation of the thermal bar. It predicts the moment in the cooling process, when the corresponding density difference between the littoral and limnetic parts reaches a maximum. For a linear initial vertical temperature profile, the time-dependent "target depth" is explicitly calculated; this is the depth in the pelagic area with a temperature, characteristic of the littoral zone. This depth is estimated as 4/3 of the (concurrent) thickness of the upper mixed layer. It is shown that, for a linear initial vertical temperature profile, the horizontal temperature profile between the shore and the lake has a self-similar behavior, and the temperature difference between the littoral waters and the upper mixed off-shore layer, divided by the depth of the upper mixed layer, is an invariant of the studied process. The results are in conformity with field data.