368 17 Tensor Dynamics
flow responsible for the friction occurs in a layer which is approximately constant, a
constantvelocitycorrespondstoaconstantvelocitygradient.Thenonlineardynamics
observed here is linked with aShilnikov bifurcation[195].
So far, a plane Couette flow with an imposed the shear rate was considered here.
In general, however, the stress tensor has to be inserted into the momentum balance
equation and the velocity field has to be solved, in accord with boundary conditions.
Calculations for a 3D flow problem show that the generalized nonlinear Maxwell
model yields turbulent flow behavior at low Reynolds numbers [202]. Such a behavior
is typical for ‘elastic turbulence’, [204, 205].
The special case of an ‘isotropic’ potential function which just depends onI 2 ,but
not onI 3 , viz. the caseB=D=F=0 withA=A 0 ( 1 −T 0 /T)andA 0 ,E>0,
C<0, was also treated in [206].