  We present experiments on oscillating hydrofoils undergoing combined heaving
and pitching motions, paying particular attention to connections between
propulsive efficiency and coherent wake features extracted using modal
analysis. Time-averaged forces and particle image velocimetry (PIV)
measurements of the flow field downstream of the foil are presented for a
Reynolds number of Re=11$\times$10$^3$ and Strouhal numbers in the range
St=0.16-0.35. These conditions produce 2S and 2P wake patterns, as well as a
near-momentumless wake structure. A triple decomposition using the optimized
dynamic mode decomposition (opt-DMD) method is employed to identify dominant
modal components (or coherent structures) in the wake. These structures can be
connected to wake instabilities predicted using spatial stability analyses.
Examining the modal components of the wake provides insightful explanations
into the transition from drag to thrust production, and conditions that lead to
peak propulsive efficiency. In particular, we find modes that correspond to the
primary vortex development in the wakes. Other modal components capture
elements of bluff body shedding at Strouhal numbers below the optimum for peak
propulsive efficiency and characteristics of separation for Strouhal numbers
higher than the optimum.
