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We use 
$123$ three-dimensional direct numerical simulations to study fingering convection in non-rotating spherical shells. We investigate the scaling behaviour of the flow length scale, the non-dimensional heat and compositional fluxes 
$Nu$ and 
$Sh$ and the mean convective velocity over the fingering convection instability domain defined by 
$1 \leq R_\rho < Le$, 
$R_\rho$ being the ratio of density perturbations of thermal and compositional origins and 
$Le$ the Lewis number. We show that the chemical boundary layers are marginally unstable and adhere to the laminar Prandtl–Blasius model, hence explaining the asymmetry between the inner and outer spherical shell boundary layers. We develop scaling laws for two asymptotic regimes close to the two edges of the instability domain, namely 
$R_\rho \lesssim Le$ and 
$R_\rho \gtrsim 1$. For the former, we develop novel power laws of a small parameter 
$\epsilon$ measuring the distance to onset, which differ from theoretical laws published to date in Cartesian geometry. For the latter, we find that the Sherwood number 
$Sh$ gradually approaches a scaling 
$Sh\sim Ra_\xi ^{1/3}$ when 
$Ra_\xi \gg 1$; and that the Péclet number accordingly follows 
$Pe \sim Ra_\xi ^{2/3} |Ra_T|^{-1/4}$, 
$Ra_T$ and 
$Ra_{\xi}$ being the thermal and chemical Rayleigh numbers. When the Reynolds number exceeds a few tens, we report on a secondary instability which takes the form of large-scale toroidal jets which span the entire spherical domain. Jets distort the fingers, resulting in Reynolds stress correlations, which in turn feed the jet growth until saturation. This nonlinear phenomenon can yield relaxation oscillation cycles.
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 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 
$St=0.16\unicode{x2013}0.35$. 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 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.
