Scientific Reports volume 13, Artigo número: 13820 (2023) Citar este artigo
151 acessos
1 Altmétrico
Detalhes das métricas
Quando um veleiro circula para encurralar um cardume de peixes voadores num vórtice perto da superfície do oceano, uma pequena mancha de ondas superficiais arqueadas confinadas a sectores de 70° colocados em posições opostas parece dispersar-se de forma coerente, mas porquê? É modelado que, quando os movimentos dos peixes param repentinamente, o cardume encurralado se compacta, os vórtices de propulsão da cauda tocam, quebram e irradiam a pressão liberada pela rotação do vórtice centrífugo, criando um monopolo acústico. A mancha de onda superficial é uma seção da esfera de radiação. Os corpos curvos do veleiro e do peixe voador, posicionados de forma oposta, atuam como espelhos acústicos côncavos em torno do monopolo, criando um manto reverberante em forma de sino, entre os quais vibram os ossos dos ouvidos e as bexigas dos peixes voadores, desorientando-os. Um copo de água firmemente batido sobre uma mesa induz uma vibração semelhante de modo puramente radial. O veleiro circula ao redor do cardume a uma profundidade onde o movimento toroidal subaquático induzido pelo vento no plano vertical se torna insignificante, de modo que o peixe voador é incapaz de sentir a direção do vento de cauda acima, limitando a capacidade de nadar para cima e emergir na direção certa para planar. . Experimentos confirmam que a rigidez da cauda do peixe voador é muito baixa para uma saída balística rápida, o que também não é necessário.
Devido à fotossíntese, as camadas superiores do oceano tropical são abundantes em formas de vida e interações predador-presa (definidas na seção "Métodos"). Na interação predador-presa de peixes voadores veleiro capturados nas videografias vívidas de Attenborough1 (e https://drive.google.com/file/d/1gn-uobapyDTq7DYlEkmlRuEBC7ExYxA2/view?usp=drive_link), no carimbo de data / hora m :s durante 0:45-0:51 (seção "Métodos"), um pequeno pacote de ondas de superfície altamente organizado e fácil de perder aparece na superfície livre, dispersando-se radialmente enquanto mantém a coerência. De onde vem o pacote de ondas e por que ele é formado? Além disso, perto da superfície livre, o oceano é semi-infinito. Portanto, como é que um veleiro encurrala cerca de uma centena de peixes voadores, impedindo sozinho a sua fuga para planar ou para as profundezas do oceano? (Um segundo veleiro às vezes se junta a nós, mas mais tarde). Embora o veleiro seja notavelmente bem-sucedido no encurralamento, por que ele também não consegue capturar quase nenhum peixe voador, apesar da perseguição ativa? Este último é mais surpreendente porque o veleiro é um consumidor terciário – um predador de ponta, enquanto o peixe voador é um consumidor secundário. É fornecido um modelo teórico de interação que explica como a mancha de onda é formada e por que o encurralamento é inicialmente tão bem-sucedido, mas depois uma instabilidade de bifurcação topológica incomum permite que os peixes-presa escapem.
Um contexto crítico da interação é que o veleiro estabelece inicialmente 1 m como escala de comprimento, enquanto a escala de comprimento do peixe voador é 0,1 m, comprimento de seu corpo ao qual as velocidades de cruzeiro estão relacionadas. O aspecto mais notável da interação reside na topologia do cardume e um instante de tempo aparece repentinamente quando o cardume se compacta e colapsa assintoticamente até um “ponto” em que o cardume de peixes voadores, em vez de nadar paralelos uns aos outros, nada coletivamente até um ponto virtual. origem como em um fluxo de pia, com bocas abertas em aparente pânico. Fisicamente, a escala de interação diminui de 1 m \(\rightarrow\) 0,1 m. Dado que a escolaridade, que está relacionada com o medo, é tão profunda como a evolução, o que poderia ter sobrepujado um instinto tão básico? A instabilidade topológica e o desencadeamento do medo concomitante são modelados como se fossem originados por um impulso acústico que, em última análise, atua no cérebro do peixe voador, causando uma dor insuportável. A energia cinética da rotação do vórtice é interrompida abruptamente pelo veleiro para criar um impulso de pressão que reverbera entre o veleiro colocado em posição oposta e o cardume de peixes voadores que atuam como espelhos acústicos côncavos. As equações de onda de Euler e ruído de Lighthill são usadas para comparar a teoria com a pegada de onda de superfície livre do evento acústico. Um modelo de quebra de vórtice é fornecido para estimar as escalas de pressão e tempo do 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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