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What comes first? Pressure or flow? Without potential, a pressure differential, there is no flow. It's pressure that needs to be there first. So rather than ask what pressure drop you get, it's better to ask what flow you get from applied pressure. We can never measure pressure drop across an infinite pipe because we can never reach the infinite point. ...

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A simple way to understand this is as follows. Every system can be linearized and decomposed into linear eigenmodes. If the system was truly linear, the amplitude and phase of each eigenmode would remain constant, and each eigenmode would evolve dynamically by its corresponding eigenfrequency. In the weak turbulence limit, we allow non-linearities, but ...

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Turbulence is well defined in the bulk of the flow, hence in 3D in the examples you quote, while surface tension acts, well, at the surface! I believe a good reformulation of your question would be "will a flow be less chaotic with larger surface tension?" Surface tension is highly dependent on geometry. It stabilizes some flows (e.g. a not-too-shallow ...

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First, give an illustration of a linear system. You know you have to eat healthy, so you are prepared to pay 50 cents for an apple. But the next day, if apple prices double, you will forget the health benefits. Now a non linear system, because it's based on people's reaction to supply and demand. An everyday example based on the Uber taxis system. Uber ...

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