English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Dynamic Mode Decomposition (DMD) describes complex dynamic processes througha hierarchy of simpler coherent features. DMD is regularly used to understandthe fundamental characteristics of turbulence and is closely related to Koopmanoperators. However, verifying the decomposition, equivalently the computedspectral features of Koopman operators, remains a major challenge due to theinfinite-dimensional nature of Koopman operators. Challenges include spurious(unphysical) modes, and dealing with continuous spectra, both of which occurregularly in turbulent flows. Residual Dynamic Mode Decomposition (ResDMD),introduced by (Colbrook & Townsend 2021), overcomes some of these challengesthrough the data-driven computation of residuals associated with the fullinfinite-dimensional Koopman operator. ResDMD computes spectra andpseudospectra of general Koopman operators with error control, and computessmoothed approximations of spectral measures (including continuous spectra)with explicit high-order convergence theorems. ResDMD thus provides robust andverified Koopmanism. We implement ResDMD and demonstrate its application in avariety of fluid dynamic situations, at varying Reynolds numbers, arising fromboth numerical and experimental data. Examples include: vortex shedding behinda cylinder; hot-wire data acquired in a turbulent boundary layer; particleimage velocimetry data focusing on a wall-jet flow; and acoustic pressuresignals of laser-induced plasma. We present some advantages of ResDMD, namely,the ability to verifiably resolve non-linear, transient modes, and spectralcalculation with reduced broadening effects. We also discuss how a new modalordering based on residuals enables greater accuracy with a smaller dictionarythan the traditional modulus ordering. This paves the way for greater dynamiccompression of large datasets without sacrificing accuracy.

Residual Dynamic Mode Decomposition: Robust and verified Koopmanism