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Field calibration of a formula for entrance mixing of river inflows to lakes: Lake Taupo, North Island, New Zealand

Abstract Field measurements were used to validate predictions for the initial dilution of negatively buoyant, cold‐water inflows to Lake Taupo, as part of a study to quantify mixing processes associated with the two largest inflows to the lake. The predictions were made using a formulation originally derived for positively buoyant, warm‐water inflows to cooling ponds. The formulation predicts the total dilution of an inflow during its inertia‐dominated phase between its entrance to the lake and the point where buoyancy forces are great enough to cause the inflow to plunge and form a submerged density current. In one of the measured inflows, the inflowing jet was free to entrain from both sides; in the other, entrainment was restricted on one side by attachment of the inflowing jet to the shoreline of a bay just upstream of the plunge point. In the former example, the unmodified coefficients from the cooling pond formulation provided an excellent prediction of initial dilution. In the latter example, entrainment was reduced and different coefficients were derived. In both examples the inflows remained attached to the lake bed throughout their course until their liftoff at depths of 45–55 m to form interflows. The difference between coefficients for the two inflows indicates that the coefficient values should be considered site‐specific. The formulation is not valid for inflows that separate from the bottom of the inflow channel before plunging. The entrance mixing formulation was incorporated in a more general model of lake stratification, DYRESM, which already includes a well‐documented routine for routing underflows down submerged channels on the bed of a lake. Application of the model to the inflows measured in Lake Taupo gave good results for two model outputs that were not involved in the calibration of the entrance mixing formulation, but that are affected by the result of the initial dilution calculation—the temperatures in the river plume after it has plunged, and the insertion depth.