Evidence and reduction of spurious numerical mixing in a numerical model including internal tides : a case study on the South-East Asian seas

Because they attempt to represent the complexity of continuous processes on discrete grids, computer simulations used to study the ocean have a fundamental tendency to generate numerical inaccuracies that must be controlled in order for the output to be realistic. Among these, spurious numerical mixing between layers of different densities is particularly troublesome. Indeed, physical mixing in this direction, though of major importance, is quite subtle, still poorly understood, and can easily be overwhelmed by numerical errors. In numerical models that use fixed levels to represent the vertical physics of the ocean, transport across these levels – and errors associated with their discretization – is the main source of such spurious cross-isopycnal mixing.

    This work focuses first on showing that since these errors scale with velocities, explicitly resolving the strong vertical displacements generated by internal tides propagating in the interior of the ocean can lead to intense levels of such spurious mixing if care is not taken in how vertical advection is implemented. Using the Symphonie ocean model, and taking the simulation of the South-East Asian Seas as a realistic case study, we show that while internal tides are essential for a correct representation of the water masses in the region, numerical errors generated by using an overly diffusive vertical advection scheme can severely bias the output.
Investigating the choice of a better scheme for handling vertical transport, we then recognize that the reduction of numerical mixing cannot be properly achieved without taking into account the properties of the time-stepping algorithm. We thus propose a new way to design advection schemes aiming at counteracting its spurious effect. Overall, this work offers a deep look into the way vertical advection is handled in the fixed coordinate model and suggests ways to improve it.

• Guillaume ROULLET, rapporteur, UBO
• Knut KLINGBEIL, rapporteur, IOW
• Florian LEMARIÉ, examinateur, INRIA
• Julien LE SOMMER, examinateur, IGE
• Aurore VOLDOIRE, examinatrice, CNRM
• Marine HERRMANN,  directrice de thèse, IRD
• Patrick MARSALEIX, co-directeur de thèse, CNRS