Length‐scale dependence of horizontal dispersion in the surface water of lakes

<jats:title>Abstract</jats:title><jats:p>Horizontal dispersion in the surface waters of a medium‐sized lake was investigated based on four experiments with ensembles of 14 to 17 drifters deployed in Lake Constance during the winter season. The experiments cover length scales between ∼30 and ∼3000 m which are typical for the grid length scales employed in 3‐D models. Horizontal dispersion coefficients <jats:italic>K</jats:italic><jats:sub>disp</jats:sub> were estimated to range from ∼0.01 to ∼0.03 m<jats:sup>2</jats:sup> s<jats:sup>−1</jats:sup> at 100 m and from ∼0.1 to ∼0.7 m<jats:sup>2</jats:sup> s<jats:sup>−1</jats:sup> at 1000 m length scale <jats:italic>L</jats:italic> of the drifter distributions. In all experiments <jats:italic>K</jats:italic><jats:sub>disp</jats:sub> increased with <jats:italic>L</jats:italic> and in three of the four experiments this increase was about linear in <jats:italic>L</jats:italic>. However, although a linear increase of <jats:italic>K</jats:italic><jats:sub>disp</jats:sub> with <jats:italic>L</jats:italic> is consistent with dispersion by shear diffusion in flow fields with constant current shear, numerical modelling of the paths of the drifters, and the resulting spreading of the drifter ensembles indicates that horizontal shear diffusion is not sufficient to explain the increase of <jats:italic>K</jats:italic><jats:sub>disp</jats:sub> with <jats:italic>L</jats:italic>. The model results suggest that not shear diffusion due to large‐scale shear across the entire drifter distribution, but scale‐dependent turbulent diffusion is dominating the scale‐dependence of <jats:italic>K</jats:italic><jats:sub>disp</jats:sub> at length scales between 100 and 1000 m. According to the model results, effects due to horizontal shear contribute less than 40% to the overall dispersion coefficient at length scales between 100 and 1000 m. However, horizontal shear is required to explain shape and orientation of the drifter distributions.</jats:p>