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When we study the movement of birds by air and fish by water, we must first determine what kind of physics to deal with. In particular if it is a displacement in a medium that shows laminar or turbulent behavior.

An estimate of the Reynold Re number shows that this is clearly higher than 2000 so it must be assumed that in most cases it was turbulent behavior.

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One way to visualize turbulent flow is by injecting ink into a flow using a thin needle that doesn't disturb the flow.

The resulting behavior shows abrupt deviation and a degree of diffusion caused by the turbulence in the flow.

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In the laboratory, blue ink is injected, which significantly deviates from a linear flow, revealing the presence of vortices and a degree of diffusion due to smaller amplitude disturbances.

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An example of this can be seen when a cigarette heats the air around its match, generating convection. As the heated air rises, it reaches critical conditions and forms vortices.

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The flow behavior around a sphere exhibits dramatic changes based on the Reynolds number calculated with respect to the sphere's radius. The following diagram provides a concise summary of the different behaviors:

Flow type scheme according to Reynold number (book Introduction to Transport Phenomena Modeling, Gianpaolo Ruocco - https://link.springer.com/chapter/10.1007/978-3-319-66822-2_3)

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When Reynold's number is between 5 and 40 the flow shows two whirlwinds behind the sphere:

Flow around a sphere for Reynold number between 5 and 40 (https://aerospaceengineeringblog.com/how-quickly-do-gas-bubbles-rise-in-a-pint-of-beer/)

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When the Reynolds number is between 40 and 150, the flow exhibits the formation of alternating vortices, creating what is known as a Karman vortex street:

Flow around a sphere for Reynold number between 40 and 150 (https://www.researchgate.net/publication/303369967_Experimental_investigation_of_low_mode_number_cylinders_subjected_to_vortex-induced_vibrations)

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When the Reynolds number is between 150 and 3E+5, the flow exhibits a significant level of turbulence within a macroscopic structure:

Flow around a sphere for Reynold number between 150 and 3E + 5 ()

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When the Reynolds number exceeds 3E+5, a chaotic zone begins to form behind the sphere, where vortices are no longer recognizable (or they have very small dimensions).

Flow around a sphere for Reynold number greater than 3E+5 (https://www.pinterest.cl/pin/514888169895997311/)

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