Imperial College London


Faculty of Natural SciencesDepartment of Mathematics

Chair in Applied Mathematics







753Huxley BuildingSouth Kensington Campus






BibTex format

author = {Noack, BR and Stankiewicz, W and Morzyski, M and Schmid, PJ},
doi = {10.1017/jfm.2016.678},
journal = {Journal of Fluid Mechanics},
pages = {843--872},
title = {Recursive dynamic mode decomposition of transient and post-transient wake flows},
url = {},
volume = {809},
year = {2016}

RIS format (EndNote, RefMan)

AB - A novel data-driven modal decomposition of fluid flow is proposed, comprising key features of proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD). The first mode is the normalized real or imaginary part of the DMD mode that minimizes the time-averaged residual. The NNth mode is defined recursively in an analogous manner based on the residual of an expansion using the first N−1N−1 modes. The resulting recursive DMD (RDMD) modes are orthogonal by construction, retain pure frequency content and aim at low residual. Recursive DMD is applied to transient cylinder wake data and is benchmarked against POD and optimized DMD (Chen et al., J. Nonlinear Sci., vol. 22, 2012, pp. 887–915) for the same snapshot sequence. Unlike POD modes, RDMD structures are shown to have purer frequency content while retaining a residual of comparable order to POD. In contrast to DMD, with exponentially growing or decaying oscillatory amplitudes, RDMD clearly identifies initial, maximum and final fluctuation levels. Intriguingly, RDMD outperforms both POD and DMD in the limit-cycle resolution from the same snapshots. Robustness of these observations is demonstrated for other parameters of the cylinder wake and for a more complex wake behind three rotating cylinders. Recursive DMD is proposed as an attractive alternative to POD and DMD for empirical Galerkin models, in particular for nonlinear transient dynamics.
AU - Noack,BR
AU - Stankiewicz,W
AU - Morzyski,M
AU - Schmid,PJ
DO - 10.1017/jfm.2016.678
EP - 872
PY - 2016///
SN - 1469-7645
SP - 843
TI - Recursive dynamic mode decomposition of transient and post-transient wake flows
T2 - Journal of Fluid Mechanics
UR -
UR -
VL - 809
ER -