Can a fish swim in incredibly viscous-dominated liquids?

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Discussion Overview

The discussion revolves around the feasibility of fish swimming in highly viscous liquids, exploring the implications of fluid dynamics, particularly through the lens of the Navier-Stokes equations and the scallop theorem. Participants consider the mechanics of swimming in low Reynolds number environments, drawing comparisons to single-celled organisms and proposing alternative swimming motions.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant suggests that a fish cannot swim in viscous-dominated liquids, referencing the Navier-Stokes equations and the small inertial terms that imply no acceleration.
  • Another participant proposes that a different swimming motion, specifically one that is not time-symmetric, would be necessary for swimming in such conditions.
  • The scallop theorem is introduced, stating that time-symmetric motion in Newtonian fluids at low Reynolds numbers does not result in net movement.
  • A request for proof or intuitive explanation of the scallop theorem is made, along with a consideration of an asymmetric fin motion as a potential solution.
  • Discussion includes the need for asymmetric motion to achieve net movement, as time-symmetric motions do not lead to position changes in low Reynolds number fluids.
  • One participant mentions that the arm stroke could work in viscous liquids due to its asymmetry, while the legs may present more challenges.
  • There is a clarification regarding the viscosity of syrup compared to honey, with a participant arguing that the syrup used in a referenced video is less viscous than typical honey.

Areas of Agreement / Disagreement

Participants express differing views on the mechanics of swimming in viscous liquids, particularly regarding the necessity of asymmetric motion and the implications of the scallop theorem. No consensus is reached on the viability of fish swimming in such environments.

Contextual Notes

Participants reference the scallop theorem and its implications without providing detailed proofs or sources. The discussion also touches on the definitions of viscosity in relation to different liquids, which may affect the conclusions drawn.

member 428835
I was wondering, can a fish swim in incredibly viscous-dominated liquids? I'm thinking it cannot. My first thought is to consider the Navier-Stokes equations and see that the inertial and transient terms are small, so flow is not accelerating, and thus the fish couldn't accelerate either.

Any thoughts?
 
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You need a different swimming motion - one that is not time-symmetric. For single-celled organisms, water is a very viscous liquid, and they can swim (some of them). Something similar to the way snakes moved on the ground is an interesting option.
 
mfb said:
You need a different swimming motion - one that is not time-symmetric.
Could you elaborate why you need something different?
 
Scallop theorem
For low Reynolds numbers, time-symmetric motion in Newtonian fluids won't lead to position changes.
 
mfb said:
Scallop theorem
For low Reynolds numbers, time-symmetric motion in Newtonian fluids won't lead to position changes.
Could you prove this, or intuitively explain it, or direct me to a source where this is explained? I believe you but would like to understand why.

Alongside what you've said, what if the fish fins press back very fast and then reset forward very slow (not time-symmetric, right?)
 
The article has references, and you can search the literature for "scallop theorem".
If the motion is time-symmetric, and all equations describing the water are time-symmetric as well (low Reynolds number!), how could be there net motion? If you reverse the time direction, the motion looks the same, the reaction of the water is the same, but the swimming direction suddenly has to reverse? Moving faster or slower doesn't break the time symmetry enough. You need asymmetric motion.
 
Thanks for this! I didn't see the link before, but I'll check it out now.
 
 
That was still with large Reynolds numbers. You would need something honey-like to get low Reynolds numbers with humans.

The arm stroke would still work there, it is asymmetric in time. The legs are more problematic.
 
  • #10
Syrup is very honey like it's sort of a defining characteristic of syrup
Honey is in fact a syrup
So I don't understand what you mean by that
 
  • #11
The syrup they used in the video is certainly not as viscous as every honey I ever saw (at reasonable swimming temperatures).
Look how much it splashes around.
 

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