The discussion revolves around the physical interpretation of deviatoric strain rate in the context of fluid dynamics, particularly within the Earth's mantle. Participants explore the relationship between deviatoric strain rate, total strain rate, and isotropic volumetric strain rate, as well as the implications for understanding convection cells and velocity fields.
Participants express uncertainty and seek clarification on several points, particularly regarding the definitions and implications of deviatoric strain rate and its invariants. There is no consensus on the interpretation of certain terms or the physical implications of the calculations presented.
Some limitations are noted, such as the need for clearer definitions of terms and the dependence on specific assumptions regarding the flow and boundary conditions. The mathematical steps involved in calculating the second invariant and its relation to shear rates remain unresolved.
The deviatoric strain rate is equal to the total strain rate minus the isotopic volumetric strain rate. So it "factors out" the rate of volumetric deformation. The second invariant of the strain rate tensor is usually regarded as a scalar measure of the rate of shear.Atr cheema said:How these properties are related to velocity fluid. The https://postimg.org/image/674a6sw4t/ https://postimg.org/image/674a6sw4t/ figure shows an area of Earth's mantle where upwelling of hot semi-liquid mantle is occurring in middle and then two downwelling currents on two sides (forming convection cells). The figure shows deviatoric strain rate (left) and its second invariant (right)
Can you please elaborate what will remain if we subtract isotropic strain rate from total strain rate tensor? I am having difficulty in perceiving it in a physical sense.Chestermiller said:So it "factors out" the rate of volumetric deformation. .
Is there a difference between invariant of deviatoric strain rate tensor and 'strain rate tensor'? I am worrying as you used just 'invariant of strain rate tensor' while I read it like 'second invariant of deviatoric strain rate'.Chestermiller said:The second invariant of the strain rate tensor is usually regarded as a scalar measure of the rate of shear.
If the strain rate were purely volumertic (isotropic) with no shear, the deviatoric part of the rate of stain tensor would be zero.Atr cheema said:Can you please elaborate what will remain if we subtract isotropic strain rate from total strain rate tensor? I am having difficulty in perceiving it in a physical sense.
Is there a difference between invariant of deviatoric strain rate tensor and 'strain rate tensor'? I am worrying as you used just 'invariant of strain rate tensor' while I read it like 'second invariant of deviatoric strain rate'.
The x and y components of velocity field in the modeled area are as; ## v_x = v_x0 sin \left (2 \Pi \frac x W \ right) cos \ left ( \Pi \frac y H \ right )##Chestermiller said:Regarding the link you provided, what are the thermal boundary conditions? What is the nature of the flow?
Thank you very much for your interest. Here is the velocity field diagram.Chestermiller said:Have you drawn the diagram showing the velocity vector as a function of position within the box? If so, please show us. To understand why the strain rates have the values shown, you need to understand the velocity field.
It is because I used the equation for deviatoric strain rate to draw this diagram. I used following code of MATLAB to draw this.Chestermiller said:Why do you think that this is the deviatoric strain rate? Also, let's see the equation you used for calculating the 2nd invariant.
for i=1:1:31
for j=1:1:31
dvxdy(i,j)=vx0*pi/ysize*sin(pi*x(j)/xsize*2)*sin(pi*y(i)/ysize);
dvydx(i,j)=-vy0*pi/xsize*2*sin(pi*y(i)/ysize)*sin(pi*x(j)/xsize*2);
eps1xy(i,j)=1/2*(dvxdy(i,j)+dvydx(i,j));
end
end