In the > 590-m deep, tropical Lake Matano (Indonesia), stratification is characterized by weak thermal gradients (< 2°C per 500 m) and weak salinity gradients (< 0.14‰ per 500 m). These gradients persist over seasons, decades, and possibly centuries. Under these nearly steady-state conditions, vertical eddy diffusion coefficients (K z ) cannot be estimated by conventional methods that rely on time derivatives of temperature distributions. We use and compare several alternative methods: one-dimensional k-ε modeling, three-dimensional hydrodynamic modeling, correlation with the size of Thorpe instabilities, and correlation with the stability frequency. In the thermocline region, at 100-m depth, the K z is ~ 5 × 10⁻⁶ m⁻²s⁻¹, but, below 300 m, the small density gradient results in large (20 m) vertical eddies and high mixing rates (K z ~ 10⁻² m² s⁻¹). The estimated timescale of water renewal in the monimolimnion is several hundred years. Intense evaporation depletes the surface mixed layer of ¹⁶O and ¹H isotopes, making it isotopically heavier. The lake waters become progressively isotopically lighter with depth, and the isotopic composition in the deep waters is close to those of the ground and tributary waters. The vertical distribution of K z is used in a biogeochemical reaction-transport model. We show that, outside of a narrow thermocline region, the vertical distributions of dissolved oxygen, iron, methane, and phosphorus are shaped by vertical variations in transport rates, rather than by sources or sinks.