Applied Math Seminar | Han Wang, Disentangling balanced and unbalanced flows under weak nonlinearity via a Helmholtz decomposition-based approach

MS Teams 

Speaker

Han Wang | University of Toronto

Title

Disentangling balanced and unbalanced flows under weak nonlinearity via a Helmholtz decomposition-based approach

Abstract

Flows in the atmosphere or ocean span over a wide range of temporal and spatial scales, a proper decomposition of which into different dynamical components is a fundamental topic relevant to classical puzzles as well as numerous practical applications. Recently in 2014, a decomposition method is proposed by Bühler et al., which manages to decompose power spectra observed in either one or two spatial dimensions into two consituents: a balanced component consisting of geostrophic flows, and an unbalanced component of linear inertia-gravity waves. This dynamical decomposition is based on a Helmholtz decomposition and utilizes differences in the fingerprints of balanced and unbalanced flows onto rotational and divergent components.

While the 2014 method is relatively easy to implement and proves useful in a wide range of data sets, it is restricted by several assumptions, among which the linearity of dynamics has been often criticized. In this talk, I will elaborate on a modification of the method that incorporates nonlinearities induced by quasi-geostrophic(QG) dynamics in the balanced flow. A new statistical relation that links the power spectra of rotational and divergent components in the QG flow is derived. Combined with ideas from the 2014 method, this leads to a decomposition of three-dimensional flows into a weakly nonlinear QG component and a linear wave component. A robust numerical method is then designed for implementations on one-dimensional data, based on additional assumptions on vertical structures. Compared to the 2014 method, this revision does not require additional observed fields. An application onto aircraft observations is conducted, revealing that outcomes from the 2014 method are robust in the stratosphere but questionable in the troposphere. Further possible improvements, as well as an evaluation of the other assumptions made in the 2014 method will be discussed at the end of the talk.