Stochastic Transport in Upper Ocean Dynamics

This open access proceedings volume brings selected, peer-reviewed contributions presented at the Stochastic Transport in Upper Ocean Dynamics (STUOD) 2021 Workshop, held virtually and in person at the Imperial College London, UK, September 20–23, 2021. The STUOD project is supported by an ERC Synergy Grant, and led by Imperial College London, the National Institute for Research in Computer Science and Automatic Control (INRIA) and the French Research Institute for Exploitation of the Sea (IFREMER). The project aims to deliver new capabilities for assessing variability and uncertainty in upper ocean dynamics. It will provide decision makers a means of quantifying the effects of local patterns of sea level rise, heat uptake, carbon storage and change of oxygen content and pH in the ocean. Its multimodal monitoring will enhance the scientific understanding of marine debris transport, tracking of oil spills and accumulation of plastic in the sea. All topics of these proceedings are essential to the scientific foundations of oceanography which has a vital role in climate science. Studies convened in this volume focus on a range of fundamental areas, including: Observations at a high resolution of upper ocean properties such as temperature, salinity, topography, wind, waves and velocity; Large scale numerical simulations; Data-based stochastic equations for upper ocean dynamics that quantify simulation error; Stochastic data assimilation to reduce uncertainty. These fundamental subjects in modern science and technology are urgently required in order to meet the challenges of climate change faced today by human society. This proceedings volume represents a lasting legacy of crucial scientific expertise to help meet this ongoing challenge, for the benefit of academics and professionals in pure and applied mathematics, computational science, data analysis, data assimilation and oceanography

Quasi-geostrophic flow under location uncertainty

International audienc

On coupling resolved and unresolved physical processes in finite element discretisations of geophysical fluids

At the heart of modern numerical weather forecasting and climate modelling lie simulations of two geophysical fluids: the atmosphere and the ocean. These endeavours rely on numerically solving the equations that describe these fluids. A key challenge is that the fluids contain motions spanning a range of scales. As the small-scale processes (unresolved by the numerical model) affect the resolved motions, they need to be described in the model, which is known as parametrisation. One major class of methods for numerically solving such partial differential equations is the finite element method. This thesis focuses on the coupling of such parametrised processes to the resolved flow within finite element discretisations. Four sets of research are presented, falling under two main categories. The first is the development of a compatible finite element discretisation for use in numerical weather prediction models, so as to avoid the bottleneck in computational scalability associated with the convergence at the poles of latitude-longitude grids. We present a transport scheme for use with the lowest-order function spaces in such a compatible finite element method, which is motivated by the coupling of the resolved and unresolved processes within the model. This then facilitates the use of the lower-order spaces within Gusto, a toolkit for studying such compatible finite element discretisations. Then, we present a compatible finite element discretisation of the moist compressible Euler equations, parametrising the unresolved moist processes. This is a major step in the development of Gusto, extending it to describe its first unresolved processes. The second category with which this thesis is concerned is the stochastic variational framework presented by Holm [Variational principles for stochastic fluid dynamics, P. Roy. Soc. A-Math. Phy. 471 (2176), (2015)]. In this framework, the effect of the unresolved processes and their uncertainty is expressed through a stochastic component to the advecting velocity. This framework ensures the circulation theorem is preserved by the stochastic equations. We consider the application of this formulation to two simple geophysical fluid models. First, we discuss the statistical properties of an enstrophy-preserving finite element discretisation of the stochastic quasi-geostrophic equation. We find that the choice of discretisation and the properties that it preserves affects the statistics of the solution. The final research presented is a finite element discretisation of the stochastic Camassa-Holm equation, which is used to numerically investigate the formation of ‘peakons’ within this set-up, finding that they do still always form despite the noise’s presence.Open Acces

Deciphering the role of small-scale inhomogeneity on geophysical flow structuration: a stochastic approach

International audienceAn important open question in fluid dynamics concerns the effect of small-scales in structuring a fluid flow. In oceanic or atmospheric flows, this is aptly captured in wave-current interactions through the study of the well-known Langmuir secondary circulation. Such wave-current interactions are described by the Craik-Leibovich system, in which the action of a wave induced velocity, the Stokes drift, produces a so called "vortex force" that causes streaking in the flow. In this work, we show that these results can be generalized as a generic effect of the spatial inhomogeneity of the statistical properties of the small-scale flow components. As demonstrated, this is well captured through a stochastic representation of the flow