  A novel data-driven modal decomposition of fluid flow is proposed comprising
key features of POD and DMD. The first mode is the normalized real or imaginary
part of the DMD mode which minimizes the time-averaged residual. The N-th mode
is defined recursively in an analogous manner based on the residual of an
expansion using the first N-1 modes. The resulting recursive DMD (RDMD) modes
are orthogonal by construction, retain pure frequency content and aim at low
residual. RDMD is applied to transient cylinder wake data and is benchmarked
against POD and optimized DMD (Chen et al. 2012) for the same snapshot
sequence. Unlike POD modes, RDMD structures are shown to have pure frequency
content while retaining a residual of comparable order as 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
snaphots. RDMD is proposed as an attractive alternative to POD and DMD for
empirical Galerkin models, with nonlinear transient dynamics as a niche
application.
