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Rapporti scientifici volume 13, numero articolo: 13820 (2023) Citare questo articolo

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Quando un pesce vela gira in circolo per radunare un banco di pesci volanti in un vortice vicino alla superficie dell'oceano, una minuscola porzione di onde superficiali arcuate confinate in settori di 70° posizionati opposti sembra disperdersi in modo coerente, ma perché? È stato modellato che, quando i movimenti dei pesci si fermano improvvisamente, il banco recintato si compatta, i vortici di propulsione della coda si toccano, si rompono e irradiano la pressione rilasciata dalla rotazione del vortice centrifugo creando un monopolo acustico. La zona delle onde superficiali è una sezione della sfera di radiazione. I corpi curvi posizionati in modo opposto del pesce vela e del pesce volante agiscono come specchi acustici concavi attorno al monopolo creando un mantello riverberante a forma di campana tra il quale vibrano le ossa dell'orecchio e le vesciche dei pesci volanti disorientandoli. Una tazza d'acqua battuta con decisione su un tavolo induce una vibrazione simile di modo puramente radiale. Il pesce vela gira intorno al banco a una profondità dove il movimento toroidale subacqueo indotto dal vento sul piano verticale diventa trascurabile in modo tale che il pesce volante non è in grado di percepire la direzione del vento in coda sopra, limitando la capacità di nuotare ed emergere nella giusta direzione per planare. . Gli esperimenti confermano che la rigidità della coda del pesce volante è troppo bassa per un'uscita balistica rapida, che non è nemmeno richiesta.

A causa della fotosintesi, gli strati superficiali dell'oceano tropicale abbondano di forme di vita e di interazioni predatore-preda (definite nella sezione "Metodi"). Nell'interazione predatore-preda tra pesci vela e pesci volanti catturata nelle vivide videografie di Attenborough1 (e https://drive.google.com/file/d/1gn-uobapyDTq7DYlEkmlRuEBC7ExYxA2/view?usp=drive_link), al timestamp m :s durante 0:45−0:51 (sezione "Metodi"), un piccolo pacchetto di onde superficiali altamente organizzato e facile da perdere appare sulla superficie libera, disperdendosi radialmente mantenendo la coerenza. Da dove proviene il pacchetto d'onde e perché si forma? Inoltre, in prossimità della superficie libera, l'oceano è semi infinito. Quindi, come fa un pesce vela a radunare un centinaio di pesci volanti che da solo ostacola la loro fuga verso l'alto per planare o giù nelle profondità dell'oceano? (Un secondo pesce vela a volte si unisce, ma più tardi). Mentre il pesce vela ha un notevole successo nel catturare, perché non riesce altrettanto straordinariamente a catturare quasi nessun pesce volante nonostante l’inseguimento attivo? Quest’ultimo è più sorprendente perché il pesce vela è un consumatore terziario, un predatore all’apice, mentre il pesce volante è un consumatore secondario. Viene fornito un modello teorico di interazione che spiega come si forma l'onda e perché il raggruppamento ha inizialmente così successo, ma in seguito un'insolita instabilità topologica della biforcazione consente ai pesci preda di scappare.

Un contesto critico dell'interazione è che il pesce vela inizialmente stabilisce 1 m come scala di lunghezza mentre la scala di lunghezza del pesce volante è 0,1 m, la lunghezza del loro corpo a cui sono correlate le velocità di crociera. L'aspetto più notevole dell'interazione risiede nella topologia del banco e un istante di tempo appare all'improvviso quando il banco si compatta e collassa asintoticamente fino a un "punto" in cui il banco di pesci volanti, invece di nuotare parallelamente l'uno all'altro, nuota collettivamente verso un virtuale origine come in un flusso di lavandino, con le bocche spalancate in apparente panico. Fisicamente, la scala di interazione diminuisce da 1 m $\rightarrow$ a 0,1 m. Poiché la scuola, che è legata alla paura, è profonda quanto l’evoluzione, cosa potrebbe aver prevalso su un istinto così basilare? L'instabilità topologica e l'innesco della conseguente paura sono modellati come se provenissero da un impulso acustico che alla fine agisce sul cervello del pesce volante provocando un dolore insopportabile. L'energia cinetica della rotazione del vortice viene bruscamente interrotta dal pesce vela per creare un impulso di pressione che riverbera tra il pesce vela posizionato in modo opposto e il banco di pesci volanti che agiscono come specchi acustici concavi. Le equazioni delle onde di Eulero e del rumore di Lighthill vengono utilizzate per confrontare la teoria con l'impronta delle onde di superficie libera dell'evento acustico. Viene fornito un modello di rottura del vortice per stimare la pressione e le scale temporali dell'impulso.

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./p>> I_x\) in the sailfish, but $I_x \approx I_y$ in the flying fish allowing the former to camber easily in the horizontal plane while the latter can apply torsion. One-to-one pursuit shows torsional escape by a corralled flying fish below the swim-plane1. The sailfish then is a planar swimmer while the flying fish is a three-dimensional swimmer. Because the smaller flying fish swim in schools, it is easier to corral them in the horizontal plane. Assume $\pi d = 2L$, where d is the minimum packing diameter of the school and L is the length of the sailfish. For L = 1 m, $d =$ 0.64 m. If $d=20 b$, $b =$ 3 cm, which is reasonable, that is 10 flying fish are stacked side by side. We get $10^2$ fish in the school which is approximately as observed1. Alternatively, for a 50 kg sailfish, the equivalent flying fish mass is 0.50 kg which is reasonable. Approximately, the packed flying fish school equates to a sailfish./p>>1\) in the winglets. The wide winglet portfolio means that the sailfish reduces $C_{di}$ at all speeds. Methods gives the properties of the axial locations of the two primary winglets $W_1$ and $W_2$, where the streamlines and circulation gradients change sign in order to improve stability. In Fig. 2d–f, the winglets are deployed then merged back as the camber $\rightarrow$ 0, and $U \rightarrow 0$. The sequence is similar to bald eagle landing./p>> | \Gamma _f |\) resulting in $\Delta r_f (t) \rightarrow 0$ -an irreversible, topological and unstable singularity forms whence at least five fish turn simultaneously inward toward a point ("Methods" section)1. To disturb the equilibrium to induce a topological instability, the sailfish suddenly starts swimming in the counter direction nullifying the induced oscillations in order to still the water. There is evidence that the sailfish motion then is opposite to the school1. The instability is modeled as a one dimensional pitchfork instability given by $Dz = \theta _b z - z^3$33. The steady state solutions for $\theta _b < 0$ and $\theta _b > 0$ are shown in Fig. 1b where the corralling singularity is located at $\theta _b, z = 0$. Post-bifurcation, two stable branches are possible. In the lower branch, most of the fish restore the school to swim below the swimplane in the diffuser (Fig. 1). In the upper branch, a few individual fish swim up to the nozzle, breaching the interface in order to glide (Fig. 1)./p>> \rho _a\)) interface of $\nabla \rho$ under the gravitational acceleration g (Fig. 4). Receiving little resistance, water penetrates the air. As circulations $+\Gamma , -\Gamma$ deposit sequentially at the inflection points along the interface length, a single mode interface of wave number $k=2\pi /\lambda$ is formed. The single mode amplitude first grows linearly with time through symmetric crests and troughs. This mode is followed by the growth of multiple modes and nonlinearities when asymmetric crowns and spikes form. The tip of the spike rolls up into a crown. Small scale disturbances appear on the interface, developing into a chaotic regime19,39. In Fig. 4, there are nonuniformities in the spacing and the heights of the spikes meaning that extraneous perturbations contributing to nonlinearities are also growing. Hence, while the stabilizing forces remain the same, the destabilizing inertia forces are higher compared to when the most organized crowns and spikes first form at $We=$ 20019. The destabilizing force drops during taxiing after emergence, that is when the sailfish threat recedes ("Methods" section)1./p> We > 800\)19 and is similar to in the ocean ("Methods" section). That the emergence is at a shallow angle of 19$^{\circ }$ and a ballistic 90$^{\circ }$ exit is not undertaken for a faster escape means the thrust is 0.03 N and not 0.981 N for a 100 g flying fish (60A hardness and not 95A or 75D−Fig. 4A). Moreover, a taxiing (Fig. 4C) is not avoided for quicker gliding. The flying fish is not in a tearing hurry to escape−a surprise. But, then the sailfish does not chase the prey after the topology is fully bifurcated (Fig. 1b). The flying fish motion becomes even more friction limited swimming up breaching the interface at a shallow angle./p> We > 800\) in Fig. 4B vs. $200< We < 600$ in Fig. 4C) is definitely different (video time stamps in "Methods" section), which indicates the presence of multistability in the hydrodynamics, tail rigidiy EI and the olivo-cerebellar control of the flying fish tail oscillation18. The inertia force and disorganization are reduced while taxiing on the ocean surface than when emerging because the distance from the sailfish threat has increased. The multistability is not random, but chaotically controlled, depending on the threat perception./p>110\) Hz. The bones between the bladder and ears, the mechanical links, vibrate. The wave interference may cause a sudden bending of the polarized cilia in the fish ear, which are used for direction sensing, disorienting the flying fish36. Theoretically, the resonant frequency of a fish increases with depth. Models of reflection of resonant frequencies from fish show that for a given frequency, the target strength is greater for the side aspect than for the dorsal aspect. Further, the target strength increases with the size of the fish. That is, the ability of the sailfish in reflecting sound is higher than in an individual flying fish, but equals to the school. In shallow waters, the propagation loss due to fish populations is complex. The sailfish-flying fish interaction under consideration occurred in the early morning. It is unknown if the propagation loss increased or decreased when the acoustic predation occurred. However, in some populations there can be a drop during the early morning. The sailfish acoustic predation utilizes body concave mirroring, echo wave interference and precise spatial localization at the prey fish ear drums. The energy expense is lower than man-made noise. The dB level along the black lines in Fig. 3 may only be $>85$ dB as in humans threshold, but applied suddenly to startle (the bladder does not burst out of the mouth)1. The pile driving guideline of 150 dB re 1 $\upmu$Pa (rms) amplitude is irrelevant41. Underwater ambient SPL is as follows. In air, the corn popping mean SPL is 85 dBA18,51. In a controlled 200–300 Hz impulse of amplitude 2 psims for 1 ms in a 9.1 m deep tank the peak SPL is 185.5 dB (re 20 $\upmu$Pa) in-water, equivalent to 5.44 psi, causes no human hearing loss at 1006 m away52. The ambient SPL is $\le$ 70 dB, the quietest sea conditions at dawn. The ocean ambient SPL level near the free surface is $\approx$80 dB (Fig. 1)18 . In the UK, the ambient ocean noise is higher, $\ge$ the survey vessel. It is painful to humans when the intensity is $\ge$ 85 dB. The noise is unbearable at 120 dB (= disco noise; $\ge$ trawler noise)15,51,53,54,55. Because the noise is not prolonged, the high dB levels along the bold black lines in Fig. 3a is only what will intensify the SPL in the ears of the flying fish. For the same reason, the energy input in the present example of predation should be lower than more commonly studied man-made noise13,15,36,55. Masking is the hearing threshold above the near free surface oceanic noise which is 70 dB at dawn. Median ocean noise levels ranged in UK measurements from 81.5 to 95.5 dB re 1 $\upmu$Pa for 0.33 octave bands from 63 to 500 Hz53, but deeper in the ocean away from the UK shores, the noise level is closer to $\le$ 70 dB, also $\approx$ 70 dB re 1 $\upmu$Pa due to baleen whales, toothed whales, bottlenose dolphins and killer whales55./p> 0\), the boundary layer has thinning effect; $\partial \Gamma /\partial x > 0$; the streamlines near winglet-body junction are converging, that is, this is a line sink flow, if $s, \delta$ are the surface distance and the boundary layer thickness, $\partial \delta /\partial s < 0$. The rear half of the body and the sail has these opposed properties. The axial pressure gradient is $\partial p/\partial x > 0$, that is adverse and decelerating; the boundary-layer is laminar, thick and prone to separation; the body axial curvature is concave on the pressure side and destabilizing and convex on the suction side and stabilizing; the axial gradient of the elliptic body cross sectional area A is $\partial A/\partial x < 0$, the boat tail boundary-layer has thickening effect; $\partial \Gamma /\partial x < 0$; the streamlines near the winglet-body junction are diverging, that is, this is a line source flow and $\partial \delta /\partial s > 0$. Inflection in streamline is minimized. The streamlines follow the axial direction closely and not the spanwise direction. Circulation $\Gamma$ is load whose moment about the center of pressure determines the roll, pitch and yaw control force and moment laws. The circulation is front-loaded (Fig. 2c). The sail is multiply split in the ’boat tail’ where $\Gamma$ is declining./p> We > 600\), which reproduces the lower We of the flying fish tail strike on ocean surface during taxiing after emergence indicating multistability of We. The unstable We drops as the sailfish threat recedes./p>

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