Understanding the Divergence Operator for Time-Varying Vectors

[tomwilliam2]

Homework Statement

I'm trying to find the divergence of a vector field (a fluid flow vector), but the vector takes the form u = u(x,y,z,t)

The Attempt at a Solution

I only really know how to take the divergence of a time-independent vector, so I'm guessing I just take the partial derivatives with respect to x,y,z and hold t= constant...is that right?
I am interested in knowing whether the divergence operator is even defined for time-varying vectors, or whether divergence is only defined for a given point in time.

Thanks

 

[DeIdeal]

Del operates on spatial dimensions*. So yes, you just take the partial derivatives with respect to x, y and z.

*Unless otherwise specified.

 

[tomwilliam2]

Thanks very much.

 

[HallsofIvy]

I agree with DeIdeal. The divergence operator involves partial derivatives with respect to x, y, z and so t is treated as a constant.