Figure 1
The sailfish vortex (a), the interaction model (b) and the sailfish coefficient of moment in the swim plane (symbol, c). In (a), the flying fish school (not shown) is situated opposite to the sailfish. The oppositely placed concave and vertically tilted sailfish and the flying fish school in the swim plane constitute the cloak. (a) Boundary-layer classification of the vortex into nozzle and diffuser flows. The sailfish is vertically tilted at angle \(\theta _s\). (b) Topological instability of the flying fish school; first a singularity is formed when the flying fish motion comes to a halt at \(\theta _b = 0\), \(z = 0\), then two branches are formed; in the upper branch, individual flying fish escape up along spiraling streamlines in the nozzle; in the lower branch, the school reforms, swimming below, in parallel, in the diffuser. In the swimplane (\(z=0\), \(h=h_0\) for both predator and prey), the rapidly declining velocity U and separation \(\theta _b\) of sailfish dominate the interaction pre-bifurcation from \(-\theta _b\) to 0. The close-range zig-zag motion of interaction is intense in the immediate post-bifurcation near \(\theta _b = 0\). The sailfish does not interact later post-bifurcation where \(\theta _b > 0\) and for flying fish \(z > 0\) or \(z < 0\); the sailfish remains in the swimplane thereby increasing the separation. The flying fish cruising returns where \(z > 0\) or \(z < 0\). The interaction then is about reduction of swim velocity and separation−a frictional process. The concave sail fish and flying fish bodies cloak (wrap around) the space of vorticity and acoustics. (c): shaded area is laboratory disk measurements, left line is laminar, right line is turbulent and the curved line is transitional.
