It has long been known that the excitation of fast motion in certain two-scale dynamical systems is linked to the singularity structure in complex time of the slow variables. We demonstrate, in the context of a fast harmonic oscillator forced by one component of the Lorenz 1963 model, that this principle can be used to construct time-discrete surrogate models by numerically extracting...
Physical imbalances introduced by local sequential Bayesian data assimilation pose a significant challenge for numerical weather prediction. Fast-mode acoustic imbalances, for instance, can severely degrade solution quality. We present a novel dynamics-driven method to dynamically suppress these imbalances. Our approach employs a blended numerical model that seamlessly integrates compressible,...
We present a phase-averaging framework for the rotating shallow-water equations and a time-integration methodology for it. Phase averaging consists of averaging the nonlinearity over phase shifts in the exponential of the linear wave operator. Phase averaging aims to capture the slow dynamics in a solution that is smoother in time (in transformed variables), so that larger timesteps may be...
In the atmosphere, fast oscillations such as gravity waves coexist with slow features such as geostrophic vortices. Numerical modelling of the fast and slow dynamics requires a small time step and long simulation time, which is computationally costly. Phase averaging filters out the fast oscillations whilst capturing their effect on the slow features, allowing for larger time steps.
We...
