The Role of Noise in Ocean Circulation Variability: Applications of the Dynamical Orthogonal Field Method

Abstract

Short-time fluctuations in oceanic systems which cannot be resolved in models but might have influence on larger-scale phenomena, can be incorporated as stochastic (white or red) noise. However, this requires solving stochastic partial differential equations. The Dynamically Orthogonal (DO) field method (Sapsis, Lermusiaux, 2009) has been developed to deal with such systems in an efficient way, following only the ensemble mean and the most dominant (orthogonal) modes rather than performing calculations for a while ensemble.

In this master project, the DO method is applied to two oceanic systems, the Kuroshio-current (wind-driven circulation) and El Niño.

The Kuroshio current is studied in a Double Gyre system, for which a DO computer code was already and parts of the parameter space (low Reynolds number) were already investigated. Here the focus lies on the region between the pitchfork bifurcation which leads to the bimodal behaviour of the Kuroshio current, and the first Hopf bifurcation which destabilises the pitchfork branches. It turned out that modes associated with the Hopf bifurcation can be excited as transient response by noise; in particular one finds a gyre mode and a Rossby basin mode.

For El Niño I derived the DO equations and implemented them into an existing (DO-free) code for the Zebiak-Cane model of El Niño. In particular, an inner product for the orthogonality projection had to be defined. It turned out that in case of a non-trivial inner product, the procedure for obtaining the initial conditions as described in (Sapsis, Lermusiaux, 2009) has to be generalised. Also the question arose whether it is consistent to take the co-called long-wave limit (neglecting the time derivative in the meridional momentum equation) before or after applying the DO method; these two procedures are indeed equivalent. Due to lack of time the DO code for El Niño was not completed but preliminary studies with the original code suggest that El Niño can be described as a system before a Hopf bifurcation with Hopf-like modes being excited by noise.