A One-Equation Turbulence Model for Geophysical Applications: Comparison with Data and the k−ε Model

A one-equation turbulence model is presented, in which the turbulent kinetic energy k is calculated with a transport equation whereas the turbulent length scale l is calculated with an algebraic expression. The value of l depends on the local stratification and reduces to the classical κ|z| scaling for unstratified flows near a wall, where |z| is the distance to the wall. The length scale decreases during stable stratification, and increases for unstable stratification compared to the neutral case. In the limit of strong stable stratification, the so-called buoyancy length scale proportional to k1/2N−1 is obtained, where N is the buoyancy frequency. The length scale formulation introduces a single model parameter which is calibrated against experimental data. The model is verified extensively against laboratory measurements and oceanic data, and comparisons are made with the two-equation k-ε model. It is shown that the performance of the proposed k model is almost identical to that of the k-ε model. In addition, the stability functions of Launder are revisited and adjusted to obtain better agreement with recent data.