The dimensionless numbers and equations that decide whether a reservoir stays stratified or overturns — the documented framework, from Schmidt’s 1928 stability to the Lake number of Imberger & Patterson, that sets every destratification design.
Every assessment begins with a bathymetric survey — the depth–area–volume curve, morphometry and per-position bed depths that the stratification, oxygen-budget and bubble-plume models depend on. Without the basin geometry, none of the downstream numbers are defensible.
Bathymetric SurveyStability is not academic — once the hypolimnion is sealed off, water quality degrades from the bottom up.
When a reservoir stratifies, the dense bottom layer (hypolimnion) is cut off from the atmosphere and from surface mixing. Its dissolved oxygen is consumed by sediment and biological demand and is never replenished, so over a few weeks it goes anoxic. Anoxia at the sediment–water interface flips the chemistry of the whole basin and triggers a cascade of problems that raise treatment cost and risk consent — which is exactly what a destratification or hypolimnetic-oxygenation system exists to prevent.
No oxygen reaches the bottom water; fish habitat is lost and reducing conditions take over — the root cause of everything below.
Under anoxia, insoluble Fe and Mn reduce to soluble forms and diffuse into the water, causing discolouration and heavy coagulant/oxidant demand at the works.
Anoxic sediment releases bound phosphorus back into the water, fuelling algal and cyanobacterial growth even when external inputs are controlled.
Sulphate reduces to hydrogen sulphide and organic nitrogen to ammonia — corrosive, odorous and a direct taste-and-odour and disinfection-demand problem.
A warm, stable, nutrient-rich epilimnion is the ideal habitat for buoyant cyanobacteria and their toxins.
Each of the above adds chemical dose, oxidant demand, sludge and monitoring — and pushes raw-water quality toward consent limits.
The Brunt–Väisälä (buoyancy) frequency N² = −(g/ρ)(dρ/dz) measures the strength of density stratification and the restoring force on a displaced parcel; it sets the thermocline sharpness.
The epilimnion, metalimnion (thermocline) and hypolimnion structure follows from the temperature–density relationship of water, which peaks near 4°C.
Seasonal surface heating and wind mixing set the stratification cycle, the Birgean heat budget describing the stored thermal energy.
The Schmidt stability S is the documented measure of a lake’s resistance to complete mixing — the work per unit area needed to mix the whole water column to a uniform density without adding or removing heat. In Idso’s (1973) per-area form, S = (g/A₀) ∫ (z − zᵒ)(ρ(z) − ρᵒ) A(z) dz, where zᵒ is the depth of the centre of volume and ρᵒ the mean density. A high S means a strongly stratified, hard-to-mix reservoir; destratification systems are sized to deliver more mixing energy than S over the operating season.
Thompson & Imberger (1980) defined W = g′h² / (u*² L) — the balance of baroclinic restoring force to wind stress; W < 1 indicates upwelling of the thermocline and strong mixing.
Imberger & Patterson (1990) generalised this to the Lake number, the ratio of the stabilising moment of the stratification about the centre of volume to the destabilising moment of the wind — the single best predictor of whole-lake mixing and deep-water entrainment.
The gradient Richardson number Ri = N²/(du/dz)² governs shear-driven turbulence; Ri below ~0.25 permits Kelvin–Helmholtz mixing across the thermocline.
Reynolds & Bauhm sizes destratification and oxygenation systems using these documented models, validated by CFD against your bathymetry and water-quality targets.
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