I Reynolds Number in Organism-Fluid Interactions

[vetenar]

Recently I read an article that relates fish larval survival to Reynolds number. It is a new and very interesting concept to me.
After some researching, the definition "ratio of inertial forces to viscous forces" still confuses me. As I understand it, both are resistant while the former to change in flow velocity, and the later to shape of the fluid. But in the case of an object immersed in a fluid (such as fish in water), are we still describing the forces in terms of the fluids?

For example, it is suggested that fish larvae have limited swimming activities and mainly drift with currents, therefore experiencing environments at low Reynolds number (viscous forces dominate).
As they grow, they swim much faster and independently of current (high Reynolds number; inertial forces dominate).

This is how I understand it: low Reynolds number means larvae will experience more viscous forces from the water, so as they move with the water current, a coat of water will cover their surface skin (feeling like a drag).
What I do not understand is when at high Reynolds number as for adult fish; swimming velocity is proportional to Reynolds number, and so to inertial forces. Do these inertial forces refer to that of water? But how can the inertial forces of water increase? Is it a result of the faster swimming of the fish - that it swims through a greater volume of water and so must experience more inertia?

 

[hutchphd]

Here is a nice explanation of "Life at Low Reynolds Number" by a very good physicist. Worth a look. https://science.curie.fr/wp-content/uploads/2016/04/Purcell_life_at_low_reynolds_number_1977.pdf

 

[Chestermiller]

By inertial forces, we mean momentum per unit volume, $\rho v^2$ where $\rho$ is the water density. Viscous forces per unit volume are proportional to $\mu v/D$, where $\mu$ is the water viscosity and D is a nominal "diameter" of the object. The Reynolds number is the ratio of these quantities. So both quantities increase with velocity, but inertial increases with the square of object velocity (relative to the surrounding water), while viscous forces increase with velocity to the first power. And, the ratio is proportional to the diameter of the object, so the bigger the object, the higher the ratio. So Reynolds number increases both in proportion to the velocity of the object (relative to the surrounding water) and to its diameter.

 

[hilbert2]

The preview chapter of this book describes how biofluid mechanics can be either about fluid flow around the organism (air flow around a bird or water flow around a fish, etc.) or about fluid flowing inside it (like the blood circulation in veins and arteries).

https://link.springer.com/chapter/10.1007/0-387-21803-3_13

 

[vetenar]

Here is a nice explanation of "Life at Low Reynolds Number" by a very good physicist. Worth a look.

Thanks so much for the link. It was very fun to read and leads to many interesting references. Now I see when we talk about low Reynolds number, viscosity plays a big part.
I have the fortune to have organisms of size ranging from 10 $\mu m$ to 1 cm. This makes me really think about how and why they swim the way they do in the water.

By inertial forces, we mean momentum per unit volume, $\rho v^2$ where $\rho$ is the water density. Viscous forces per unit volume are proportional to $\mu v/D$, where $\mu$ is the water viscosity and D is a nominal "diameter" of the object. The Reynolds number is the ratio of these quantities.

Thank you for the clear explanation. Their relationships make more sense to me now.

Another question comes into mind. Reynolds number is about the object velocity relative to water. But fish larvae behave differently when the water is at rest or in motion; they swim to avoid sinking to the bottom. When water is at rest, the larvae have to spend more time and energy on swimming. When water is in circular motion at a certain velocity in the tank, they are generally carried by water passively and occasionally make some feeding movements on their way. In this sense, do the larvae in static water have higher Reynolds numbers than those in dynamic water?

The preview chapter of this book describes how biofluid mechanics can be either about fluid flow around the organism (air flow around a bird or water flow around a fish, etc.) or about fluid flowing inside it (like the blood circulation in veins and arteries).

Thank you for the source. It is exactly these two situations - flows past objects and internal flows (in pipe or in circulation) - which I find confusing. It is unclear to me how both of them can be described by the same formula. I may be missing something fundamental.