### Erwin Luesink

**Based at:**Imperial College London

MPE CDT Aligned student

Research Interests: (Stochastic) Partial Differential Equations, Numerical Analysis, Geometric Mechanics, Hamiltonian Dynamics, Chaos Theory, Integrability, Fluid Dynamics, Measure Theory and Probability, Differential Geometry, Functional Analysis.

Research Project: Ocean and weather prediction is done with dynamical cores that require a huge amount of computational power. One of the reasons behind this computational cost is that the models describe many small scale effects (e.g. turbulence) that determine the spatial and temporal scales on which the model is allowed to be resolved. Additionally, fluid models have been shown to be chaotic in nature, meaning that they are sensitive to initial conditions. Hence small errors can lead to completely different outcomes. By replacing the small scale effects with a clever type of noise (see Holm 2015), the fluid model is made stochastic in a way that preserves most conservation laws, leading to a model that is easier to resolve than its deterministic counterpart with a higher accuracy. A particular well-studied example is the Lorenz 1963 (L63) model, which is a Fourier-mode projection of a Rayleigh-Bénard convection problem. By introducing the noise as dictated by the method of Holm 2015, the stochastic version of the L63 model is derived. It is discovered that this type of noise behaves differently to the most common noise found in literature both on a theoretical level as well as on a numerical level. This gives insight into how the models for ocean and weather prediction can be made stochastic with as much resemblance as possible to the physics of the deterministic version.

Research Interests: (Stochastic) Partial Differential Equations, Numerical Analysis, Geometric Mechanics, Hamiltonian Dynamics, Chaos Theory, Integrability, Fluid Dynamics, Measure Theory and Probability, Differential Geometry, Functional Analysis.

Research Project: Ocean and weather prediction is done with dynamical cores that require a huge amount of computational power. One of the reasons behind this computational cost is that the models describe many small scale effects (e.g. turbulence) that determine the spatial and temporal scales on which the model is allowed to be resolved. Additionally, fluid models have been shown to be chaotic in nature, meaning that they are sensitive to initial conditions. Hence small errors can lead to completely different outcomes. By replacing the small scale effects with a clever type of noise (see Holm 2015), the fluid model is made stochastic in a way that preserves most conservation laws, leading to a model that is easier to resolve than its deterministic counterpart with a higher accuracy. A particular well-studied example is the Lorenz 1963 (L63) model, which is a Fourier-mode projection of a Rayleigh-Bénard convection problem. By introducing the noise as dictated by the method of Holm 2015, the stochastic version of the L63 model is derived. It is discovered that this type of noise behaves differently to the most common noise found in literature both on a theoretical level as well as on a numerical level. This gives insight into how the models for ocean and weather prediction can be made stochastic with as much resemblance as possible to the physics of the deterministic version.