STUOD (Stochastic Transport in Upper Ocean Dynamics) project looks at changing regimes of uncertainty in ocean fluid transport.
Our approach accounts for transport on scales that are currently unresolvable in computer simulations, yet are observable by satellites, drifters and floats. Our research is: driven by data and new methods for its analysis, informed by mathematical modelling, quantified in concert with computer simulation.
Novel methodologies, and/or inter-disciplinary developments over the past two years include: (i) A comprehensive approach to stochastic climate modelling has developed for the example of an idealised Atmosphere-Ocean model that rests upon Hasselmann's paradigm for stochastic climate models; (ii) A new mathematical approach to stochastic wave-current interaction has been developed based on assuming that the wave motion is evolving in the frame of the current motion; (iii) Similar to our Stochastic Advection by Lie Transport approach based on stochastic transport which preserves circulation of the fluid, the new Stochastic Forcing by Lie Transport approach based on stochastic forcing preserves fluid energy; and (iv) We prove the existence of martingale solutions for the stochastic Navier-Stokes equations in Location Uncertainty approach, which preserves the energy of transported quantities.
The following studies recently investigated go beyond the state of the art: (i) composition of maps (CoM) approach for wave-current interactions using Stochastic Advection by Lie Transport extends the ongoing series of applications of stochastic geometric mechanics in multiscale, multiphysics continuum dynamics to the case of the interaction of fluid waves and currents; (ii) The Stochastic Forcing by Lie Transport approach is a stochastic geometric mechanics and is complementary to the Stochastic Advection by Lie Transport approach in that Stochastic Forcing by Lie Transport forgoes conservation of circulation properties in order to exactly preserve total integrated energy, while Stochastic Advection by Lie Transport preserves circulation properties but forgoes exact conservation of total integrated energy; (iii) The Holm-Mémin paradigm provides stochastic parameterisations that model uncertainty generated by the reduction of high-resolution solutions to coarser scale. (iv) For the Location Uncertainty setting we proved that if the noise intensity goes to zero, these solutions converge, up to a subsequence in dimension 3, to a solution of the deterministic Navier-Stokes equation (in 2D it converges toward the unique solution). By the end of the project, we will provide solutions for collecting, coordinating and interpreting data, which will be made widely available for oceanographic community research and benefit society by providing forecast capabilities for ocean science.
