Simulating shape of spinning water surface

The velocity is the same as the ball's velocity, so the ball will not experience any buoyancy force. The shape of the surface can be calculated by assuming zero viscosity and using a specified velocity profile. Bernoulli's principle does not have a role in this scenario since the cross section of the flow does not vary. In summary, in this simplified version of the phenomenon, the shape of the surface can be calculated by assuming zero viscosity and using a specified velocity profile. Bernoulli's principle does not play a role in this scenario and the buoyancy force on a ball held at a specific position along the central axis will be zero due to the matching velocities.
  • #1
Swamp Thing
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I would like to simulate a simplified version of this phenomenon:



where I will assume that the viscosity is zero and the liquid can therefore swirl around "laminarly" forever according to some velocity profile that I specify.

How can I calculate the shape of the surface, at least in this simplified case, and hopefully estimate the buoyancy force on a ball that is held at some position along the central axis?

Another question: there were some comments referring to Bernoulli pressure differences due to differences in velocity. But is it not the case that Bernoulli has no role in this scenario, since the cross section does not vary along the direction of flow?

What is happening below the ball at 05:22 ?
 
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  • #2
To address your final question first; Bernoulli’s principle is not directly caused by surfaces having different shapes, but by differences in the lateral motion of fluids. The change in shape only comes into play because it causes the fluid to flow at different rates.

In this case, the difference is between water that is stationary and water that is moving (in a circle).
 

1. How does the shape of a spinning water surface affect its movement?

The shape of a spinning water surface, also known as a vortex, can greatly impact its movement. The faster the water is spinning, the more pronounced the vortex shape will be, creating a strong downward force due to centrifugal force. This can result in faster and more turbulent water movement.

2. What factors influence the shape of a spinning water surface?

The shape of a spinning water surface is influenced by a variety of factors, including the speed of the water, the depth of the water, the viscosity of the water, and any surrounding obstacles or boundaries. These factors can all impact the size, shape, and intensity of the vortex.

3. How can the shape of a spinning water surface be simulated?

The shape of a spinning water surface can be simulated using computational fluid dynamics (CFD) software. This involves creating a mathematical model of the water flow and using numerical methods to solve for the shape and movement of the water surface. Other methods, such as physical models or experimental setups, can also be used to simulate the shape of a spinning water surface.

4. Can the shape of a spinning water surface be controlled?

In some cases, the shape of a spinning water surface can be controlled, such as in a laboratory setting. This can be achieved by manipulating the speed, direction, and other variables of the water flow. However, in natural settings, the shape of a spinning water surface is often influenced by external factors and can be difficult to control.

5. What applications does simulating the shape of a spinning water surface have?

The simulation of spinning water surfaces has many practical applications, including in the design of hydraulic structures, such as dams and spillways. It can also be used to study the behavior of ocean currents and weather patterns, as well as in industries such as aerospace and marine engineering where understanding fluid dynamics is crucial.

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