Propulsive force calculations in swimming frogs II. Application of a vortex ring model to DPIV data

Frogs propel themselves by kicking water backwards using a synchronised extension of their hind limbs and webbed feet. To understand this propulsion process, we quantified the water movements and displacements resulting from swimming in the green frog Rana esculenta, applying digital particle image velocimetry (DPIV) to the frog's wake. The wake showed two vortex rings left behind by the two feet. The rings appeared to be elliptic in planform, urging for correction of the observed ring radii. The rings' long and short axes (average ratio 1.75:1) were about the same size as the length and width of the propelling frog foot and the ellipsoid mass of water accelerated with it. Average thrust forces were derived from the vortex rings, 1445 assuming all propulsive energy to be compiled in the rings. The calculated average forces (F-av=0.10 +/- 0.04 N) were in close agreement with our parallel study applying a momentum-impulse approach to water displacements during the leg extension phase. We did not find any support for previously assumed propulsion enhancement mechanisms. The feet do not clap together at the end of the power stroke and no 'wedge-action' jetting is observed. Each foot accelerates its own water mantle, ending up in a separate vortex ring without interference by the other leg

Hydrodynamics of unsteady fish swimming and the effects of body size:Comparing the flow fields of fish larvae and adults

Zebra danios (Brachydanio rerio) swim in a burst-and-coast mode. Most swimming bouts consist of a single tail flick and a coasting phase, during which the fish keeps its body straight. When visualising the flow in a horizontal section through the wake, the effects of the flow regime become apparent in the structure of the wake. In a two-dimensional, medio-frontal view of the flow, larvae and adults shed two vortices at the tail during the burst phase. These vortices resemble a cross section through a large-core vortex ring: two vortex cores packed close together with the central flow directed away from the fish. This flow pattern can be observed in larvae (body length approximately 4mm) at Reynolds numbers below 100 as well as in adult fish (body length approximately 35mm) at Reynolds numbers above 1000. Larval vortices differ from those of adult zebra danios mainly in their relatively wider vortex cores (higher ratio of core radius to ring radius) and their lower vortex circulation, Both effects result from the increased importance of viscosity on larval flows. During the coasting phase, larval and adult flows again differ because of the changing importance of viscosity. The high viscosity of the water causes large vortical flows adjacent to the larva's body. These regions of high vorticity represent the huge body of water dragged along by the larva, and they cause the larva to stop almost immediately after thrust generation ceases. No such areas of high vorticity are visible adjacent to adult zebra danios performing a comparable swimming manoeuvre. The rapid decrease in vortex circulation and the severe reduction in the coasting distance due to viscous drag contribute to the high cost that larvae - unlike adult fish face when using a burst-and-coast swimming style

On the Effect of a Secondary Structure upon the Interference of X-rays

Laue's dynamic theory of x-ray interference is shown to be applicable, with only a few minor changes, to crystals having a very general type of secondary structure. It is thus applied for the purpose of obtaining a quantitative estimate of the effect of such a structure upon the nature of the x-ray interference maxima. The estimate is relative insofar as it compares the intensities of respectively the "secondarily" and the "primarily" reflected interference beams and applies only in the region where the latter have been, or can be observed. In this region the "two-dimensional lattice" type of secondary structure is found to give rise to a fine structure which, with the present insufficient resolving power, would be manifested experimentally as a weak, diffuse background. The secondary structure of this type produces no broadening of the primary lines. The existence of this type of structure, therefore, is not inconsistent with the sharpness of the interference maxima obtained from such crystals as calcite, and a possible objection to the existence of the secondary structure in such crystals is removed. The extinction effect is briefly considered, but absorption is not taken into account, except with a few qualitative remarks

Copepod feeding currents:flow patterns, filtration rates and energetics

Particle image velocimetry was used to construct a quasi 3-dimensional image of the flow generated by the feeding appendages of the calanoid copepod Temora longicornis. By scanning layers of flow, detailed information was obtained on flow velocity and velocity gradients. The flow around feeding T. longicornis was laminar, and was symmetrical viewed dorsally, but highly asymmetrical viewed laterally, with high levels of vorticity on the ventral side. The flow rate through the feeding appendages varied between 77 and 220 ml day(-1) per individual. The morphology of the flow field ensured that water was entrained over the full length of the first antennae. These were kept out of areas with high velocity gradients that could interfere with distant mechano- or chemoreception. The volume of influence, i.e. the volume of water around the foraging copepod, where shear rates were significantly higher than background levels, was calculated. Implications for encounter probability and mechanoreception are discussed. The average rate of energy dissipation within the copepod's volume of influence is several times higher than the levels of turbulent energy dissipation these animals are likely to encounter in their environment. Even in highly turbulent environments, adult T. longicornis will not experience very significant effects of turbulence. Within the volume of influence of the copepods the energy dissipation due to viscous friction varied between 6.6x10(-11) and 2.3x10(-10) W. Taking mechanical efficiency and muscle efficiency into account, this results in a total energetic cost of the feeding current of 1.6x10(-9) W per copepod. This value represents only a small percentage of the total energy budget of small calanoid copepods