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This paper introduces a two-phase interfacial fluid model based on the impulse variable to capture complex vorticity-interface interactions. Our key idea is to leverage bidirectional flow map theory to enhance the transport accuracy of both vorticity and interfaces simultaneously and address their coupling within a unified Eulerian framework. At the heart of our framework is an impulse ghost fluid method to solve the two-phase incompressible fluid characterized by its interfacial dynamics. To deal with the history-dependent jump of gauge variables across a dynamic interface, we develop a novel path integral formula empowered by spatiotemporal buffers to convert the history-dependent jump condition into a geometry-dependent jump condition when projecting impulse to velocity. We demonstrate the efficacy of our approach in simulating and visualizing several interface-vorticity interaction problems with cross-phase vortical evolution, including interfacial whirlpool, vortex ring reflection, and leapfrogging bubble rings. 

We propose a novel solid-fluid interaction method for coupling elastic solids with impulse flow maps. Our key idea is to unify the representation of fluid and solid components as particle flow maps with different lengths and dynamics. The solid-fluid coupling is enabled by implementing two novel mechanisms: first, we developed an impulse-to-velocity transfer mechanism to unify the exchanged physical quantities; second, we devised a particle path integral mechanism to accumulate coupling forces along each flow-map trajectory. Our framework integrates these two mechanisms into an Eulerian-Lagrangian impulse fluid simulator to accommodate traditional coupling models, exemplified by the Material Point Method (MPM) and Immersed Boundary Method (IBM), within a particle flow map framework. We demonstrate our method's efficacy by simulating solid-fluid interactions exhibiting strong vortical dynamics, including various vortex shedding and interaction examples across swimming, falling, breezing, and combustion. 

Abstract The boreal summer climate is of significant societal importance and is trending toward increased risks of extreme climate events such as heatwaves. The summer North Atlantic Oscillation, as the primary mode of atmospheric variability in the northern hemisphere, has been long considered lacking predictability on seasonal time scales. Here we show that the summer North Atlantic Oscillation is predictable with a 2‐month lead for the recent decades. The primary predictor is the March North Atlantic jet strength, which is correlated with the summer North Atlantic Oscillation index at a correlation coefficient of 0.66 over 1979–2018. Spring stratosphere‐troposphere coupling plays a critical role in this extended predictability from spring to summer, in contrast to the common knowledge that this dynamical coupling is relatively inactive outside the winter season. These results may bring sound prospects for summer seasonal prediction of boreal climate that benefits the energy and public health sectors.