Scaling laws for the propulsive performance of rigid foils undergoing oscillatory heaving and pitching motions are presented. Water tunnel experiments on a nominally two-dimensional flow validate the scaling laws, with the scaled data for thrust, power, and efficiency all showing excellent collapse. The analysis indicates that the behaviour of the foils depends on both Strouhal number and reduced frequency, but for motions where the viscous drag is small the thrust closely follows a linear dependence on reduced frequency. The scaling laws are also shown to be consistent with biological data on swimming aquatic animals.Comment: 11 page

We consider the propulsive performance of an unsteady heaving and pitching foil, experimentally studying an extensive parameter space of motion amplitudes, frequencies, and phase offsets between the heave and pitch motions. The phase offset φ between the heaving and pitching motions proves to be a critical parameter in determining the dynamics of the foil and its propulsive performance. To maximize thrust, the heave and pitch motions need to be nearly in phase (φ = 330 • ), but to maximize efficiency, the pitch motion needs to lag the heave motion (φ = 270 • ), corresponding to slicing motions with a minimal angle of attack. We also present scaling relations, developed from lift-based and added mass forces, which collapse our experimental data. Using the scaling relations as a guide, we find increases in performance when foil amplitudes (specifically pitch) increase while maintaining a modest angle of attack.

Results on turbulent skin friction reduction over air- and liquid-impregnated surfaces are presented for aqueous Taylor-Couette flow. The surfaces are fabricated by mechanically texturing the inner cylinder and chemically modifying the features to make them either non-wetting with respect to water (air-infused, or superhydrophobic case), or wetting with respect to an oil that is immiscible with water (liquid-infused case). The drag reduction, which remains fairly constant over the Reynolds number range tested (100 ≤ Reτ ≤ 140), is approximately 10% for the superhydrophobic surface and 14% for the best liquid-infused surface. Our results suggest that liquid-infused surfaces may enable robust drag reduction in high Reynolds number turbulent flows without the shortcomings associated with conventional superhydrophobic surfaces, namely, failure under conditions of high hydrodynamic pressure and turbulent flow fluctuations.

Many swimming and flying animals are observed to cruise in a narrow range of Strouhal numbers, where the Strouhal number [Formula: see text] is a dimensionless parameter that relates stroke frequency f, amplitude A, and forward speed U. Dolphins, sharks, bony fish, birds, bats, and insects typically cruise in the range [Formula: see text], which coincides with the Strouhal number range for maximum efficiency as found by experiments on heaving and pitching airfoils. It has therefore been postulated that natural selection has tuned animals to use this range of Strouhal numbers because it confers high efficiency, but the reason why this is so is still unclear. Here, by using simple scaling arguments, we argue that the Strouhal number for peak efficiency is largely determined by fluid drag on the fins and wings.

The effects of stable thermal stratification on turbulent boundary layers are experimentally investigated for smooth and rough walls. For weak to moderate stability, the turbulent stresses are seen to scale with the wall shear stress, compensating for changes in fluid density in the same manner as done for compressible flows. This suggests little change in turbulent structure within this regime. At higher levels of stratification turbulence no longer scales with the wall shear stress and turbulent production by mean shear collapses, but without the preferential damping of near-wall motions observed in previous studies. We suggest that the weakly stable and strongly stable (collapsed) regimes are delineated by the point where the turbulence no longer scales with the local wall shear stress, a significant departure from previous definitions. The critical stratification separating these two regimes closely follows the linear stability analysis of Schlichting (Z. Angew. Math. Mech., vol. 15 (6), 1935, pp. 313–338) for both smooth and rough surfaces, indicating that a good predictor of critical stratification is the gradient Richardson number evaluated at the wall. Wall-normal and shear stresses follow atmospheric trends in the local gradient Richardson number scaling of Sorbjan (Q. J. R. Meteorol. Soc., vol. 136, 2010, pp. 1243–1254), suggesting that much can be learned about stratified atmospheric flows from the study of laboratory scale boundary layers at relatively low Reynolds numbers.