ar X iv : m at h - ph / 0 70 10 59 v 8 1 6 Ju l 2 00 7 A comparison of three turbulence models with an application to the West Pacific Warm Pool

In this work, we compare three turbulence models used to parameterize the oceanic boundary layer. These three models depend on the bulk Richardson number, which is coherent with the studied region, the West Pacific Warm Pool, because of the large mean shear associated with the equatorial undercurrent. One of these models, called R224, is new and the others are Pacanowski and Philander's model (R213 model) and Gent's model (R23 model). The numerical implementation is based on a non-conservative numerical scheme. The following (three criteria) are used to compare the models: the surface current intensity, the pycnocline's form and the mixed layer depth. We initialize the code with realistic velocity and density profiles thanks the TOGA-TAO array (McPhaden, 1995, [21]). In case of static instability zone on the initial density profile, only the R224 model gives realistic results. Af-terwards, we study a mixed layer induced by the wind stress. In this case, the R224 results and the Pacanowski and Philander's results are similar. Furthermore, we simulate a long time case. We obtain a linear solution for all models that is in agreement with Bennis and al [1]. Summary 0.1 Keywords: vertical mixing, Richardson number, mixed layer.