Jun-Ichi Yano | Searcharxiv

arXiv2023

Formation of Thermal Vortex Rings

An evolution of a spherical region, subjected to uniform buoyancy force, is investigated. Incompressibility and axial symmetry are assumed, together with a buoyancy discontinuity at the boundary. The boundary turns into a vortex sheet and the system evolves into a ring. Contrary to the case of mechanically generated rings, buoyancy-driven rings are unstable. This is due to the generation of negative vorticity at the bottom. Furthermore, a sequence of Kelvin-Helmholtz instabilities arises along the buoyancy anomaly boundary. This sequence transfers the energy toward large scales with $κ^{-3}$ distribution. The vortex blob method has been used to simulate the system numerically. An optimization algorithm, used previously in two dimensions, has been extended to the axisymmetric case. It reduces computational complexity from $N^2$ to $N \log N$, where N is the number of nodes. Additionally, a new algorithm has been developed as a remedy for the exponential growth of the number of nodes required. It exploits a tendency of the vortex sheet to form many parallel stripes, by merging them together.

physics.flu-dyn↗

arXiv2017

Stochastic Parameterization: Towards a new view of Weather and Climate Models

The last decade has seen the success of stochastic parameterizations in short-term, medium-range and seasonal forecasts: operational weather centers now routinely use stochastic parameterization schemes to better represent model inadequacy and improve the quantification of forecast uncertainty. Developed initially for numerical weather prediction, the inclusion of stochastic parameterizations not only provides better estimates of uncertainty, but it is also extremely promising for reducing longstanding climate biases and relevant for determining the climate response to external forcing. This article highlights recent developments from different research groups which show that the stochastic representation of unresolved processes in the atmosphere, oceans, land surface and cryosphere of comprehensive weather and climate models (a) gives rise to more reliable probabilistic forecasts of weather and climate and (b) reduces systematic model bias. We make a case that the use of mathematically stringent methods for the derivation of stochastic dynamic equations will lead to substantial improvements in our ability to accurately simulate weather and climate at all scales. Recent work in mathematics, statistical mechanics and turbulence is reviewed, its relevance for the climate problem demonstrated, and future research directions outlined.

physics.ao-ph↗