Dr. K. R. Rajagopal, Dept. of Mechanical and Biomedical Engineering, Texas A&M
What do we mean by a fluid and how do we model them?
3PM Friday, Nov. 5, MEC 4-3
While we have some sort of intuitive feel for what we mean by a
fluid, when asked to give a precise definition of the same,
we are hard pressed to do so. After a brief discussion of
the difficulty of providing a precise definition I outline
the quintessential characteristics of a fluid-like body. I
then discuss the numerous assumptions that underlie the
Navier-Stokes model which is incapable of describing
the behavior of many real fluids and contrary to popular belief
incapable of describing turbulence. I then discuss
different classes of fluid models that include fluids models
of the differential, rate and integral type. I conclude the
talk with a discussion of some important open problems both
from the perspective of mathematics and mechanics. I end the
talk by discussing the modelling of turbulence and try to
provide a rationale for the need for a different perspective
for developing models for turbulence, models that are totally
different from the ones that are in vogue.