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.

Mixing of an interflow into the ambient water of Lake Iseo

“…Inflow mixing-In their previous study, Spigel et al (2005) observed a value of c p of 1.9 in the plunge region of both rivers, which is much larger than the value of 0.06 predicted by the laboratory experiments of Britter and Simpson (1978). The larger c p was caused by the inflows being in the entraining jet regime for larger Fr 0 .…”

“…The dominance of mixing in the underflow observed in Lake Iseo does not necessarily occur at inlets with other parameter values. When Fr & 1 or when the bathymetry at the inlet is stepped, the plunge region mixing ratio will be greater (Spigel et al 2005). When the neutral buoyancy depth in the ambient is reduced, the entrainment into the underflow will reduce because the underflow will not travel as far before lifting away from the lake bed.…”

“…Spigel et al (2005) measured c p for two inflows into Lake Taupo (New Zealand) using a tracer injection method and found that c p was 1.87 and 1.94 in the two inflows, respectively. To find a linear relationship between c p and Fr 0 , different site-specific coefficients were required for each inflow.…”

Transition zones in small lakes: the importance of dilution and biological uptake on lake-wide heterogeneity

“…Spigel et al, 2005;Rueda et al, 2007). However, biological uptake of point source nutrients such as sewage effluent in rivers has been clearly established (McColl, 1974;Marti et al, 2004), and enhanced growth of algae in lakes has also been shown to occur near river inflows and attributed to nutrient-enriched waters (Auer & Bub, 2004;MacIntyre et al, 2006).…”

“…Carmack et al, 1979;Fischer et al, 1979;Pickrill & Irwin, 1982;Fischer & Smith, 1983;Stevens et al, 1995;Vidal, 2006). Entrance mixing prior to this flow separation and initial dilution due to channel expansion at the river-lake interface is also associated with entrainment of water in the transition zone (Spigel et al, 2005) but has received little attention in the literature, where most studies have focused on mixing at the plunge point, the area where denser influent water sinks to form an under-or interflow (Rueda et al, 2007). However, this initial dilution and entrainment was found to be a particularly important mixing process in the shallow water of some artificial cooling ponds, where flow separation is not observed and water columns remain partially or fully mixed (Jirka & Watanabe, 1980).…”