# Stokes drag of oscillation sphere

• chaosma
In summary, In Laudau's book, the velocity of a fluid is defined as v=e^{iwt}*F, where F is a vector with only spatial variable involved. When considering a sphere oscillating in a viscous fluid with frequency w, the sphere has a velocity of u=u_0*e^{-iwt}. This boundary condition becomes u=v at |x|=R, where R is the radius of the sphere and the origin is the center of the sphere. The question arises about this being a non-inertial frame without any extra periodic force being introduced. However, by using a non-inertial frame and writing down the NS equation with velocity w, it can be shown that u=w+u_0, where
chaosma
If we consider a sphere oscillates in viscous fluid with frequency w,
then sphere has velocity u=$u_0*e^{-iwt}$

In Laudau's book, he defined the velocity of fluid is:
v=$e^{iwt}*F$
where F is a vector with only spatial variable involved.
The boundary condition then becomes $u=v$ at $|x|=R$,
where R is radius of sphere and origin is center of sphere.

My question is that this is a non-inertial frame, but Landau didn't introduce any
extra periodic force. Why is this true? Thank you!

I figured it out.
First, use non-inertial frame, write down the NS equation with velocity w.
Then let $u=w+u_0$
where $u_0$ is velocity of sphere.

## 1. What is Stokes drag of oscillation sphere?

The Stokes drag of oscillation sphere is a phenomenon in fluid mechanics where a spherical object oscillating in a viscous fluid experiences a drag force that is proportional to its velocity and the viscosity of the fluid. This drag force is known as the Stokes drag force.

## 2. How is the Stokes drag force calculated?

The Stokes drag force is calculated using the formula F = 6πμrv, where F is the drag force, μ is the viscosity of the fluid, r is the radius of the spherical object, and v is the velocity of the object relative to the fluid.

## 3. What factors affect the Stokes drag force?

The Stokes drag force is affected by the size and shape of the spherical object, the viscosity of the fluid, and the velocity of the object. The drag force also increases with increasing velocity and viscosity, and decreases with increasing size of the object.

## 4. What is the significance of Stokes drag of oscillation sphere?

The Stokes drag of oscillation sphere is an important concept in fluid mechanics, as it helps explain the behavior of objects moving through a viscous fluid. It is also used in various engineering applications, such as in the design of vehicles and equipment that operate in fluids.

## 5. How can the Stokes drag force be reduced?

The Stokes drag force can be reduced by decreasing the velocity of the object, increasing the size of the object, or by using a less viscous fluid. Other methods such as streamlining the shape of the object or using surface treatments can also help reduce the drag force.

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