Physical meaning of material derivative

[utab]

Dear all,

For my Ph.D research. I have to use the material derivative concept. I reviewed some of my previous continuum mechanics course notes but this topic was superficial in our course. I am reading the book "A first course in continuum mechanics" by Fung. I also noted from some books in the library that the material derivative is the "time rate change measured by an observer moving with the specific particles under study". I can understand the mathematical concept from Fung's book but I have difficulty in visualizing it in my mind.

Can someone kindly explain the physical meaning of the material derivative with some physical examples?

Regards,

Umut

 

[momentum_waves]

It is the Total Derivative that mathematicians use, with variables t,x,y,z.

Sometimes called the Substantial Derivative - in fluid mechanics - as used in the derivation of the Navier-Stokes equations.