On the performance of a generic length scale turbulence model within an adaptive finite element ocean model

Research into the use of unstructured mesh methods for ocean modelling has been growing steadily in the last few years. One advantage of using unstructured meshes is that one can concentrate resolution where it is needed. In addition, dynamic adaptive mesh optimisation (DAMO) strategies allow resolution to be concentrated when this is required. Despite the advantage that DAMO gives in terms of improving the spatial resolution where and when required, small-scale turbulence in the oceans still requires parameterisation. A two-equation, generic length scale (GLS) turbulence model (one equation for turbulent kinetic energy and another for a generic turbulence length-scale quantity) adds this parameterisation and can be used in conjunction with adaptive mesh techniques. In this paper, an implementation of the GLS turbulence parameterisation is detailed in a non-hydrostatic, finite-element, unstructured mesh ocean model, Fluidity-ICOM. The implementation is validated by comparing to both a laboratory-scale experiment and real-world observations, on both fixed and adaptive meshes. The model performs well, matching laboratory and observed data, with resolution being adjusted as necessary by DAMO. Flexibility in the prognostic fields used to construct the error metric used in DAMO is required to ensure best performance. Moreover, the adaptive mesh models perform as well as fixed mesh models in terms of root mean square error to observation or theoretical mixed layer depths, but uses fewer elements and hence has a reduced computational cost.