Modelling rotating stratified flows at laboratory-scale using spectrally-based DNS

We describe the use of spectrally-based numerical methods in process studies of rotating stratified fluid dynamics relevant to oceans, lakes and the atmosphere. The objective is to take advantage of the well-known numerical properties of methods based on expansions in terms of trigonometric functions in applications for which inhomogeneous boundary conditions and/or irregular domains are desired. The underlying mathematical idea is the exchange of inhomogeneity from boundary conditions to forcing terms. The fundamental techniques for handling inhomogeneity in boundary conditions, symmetry mismatches between body forces and dependent variables at boundaries and the imposition of boundary conditions on internal or immersed boundaries are described and illustrated using simple idealized examples. These techniques are then combined to illustrate how these methods can be applied to several examples of flows from laboratory experiments.