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Old Aug 31st 2017, 06:38 AM   #1
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What causes rotation in the Navier-Stokes Equation?

It is known that rotation in the flow results from the viscous terms in the Navier-Stokes (N-S) equation. However, when deriving the N-S equation from the general principle of linear momentum in Continuum Mechanics, we use the constitutive relation for isotropic Newtonian fluids which states that the deviatoric part of the stress tensor is proportional to the deviatoric part of the rate of deformation tensor. Since the rate of deformation tensor is the symmetric part of the velocity gradient tensor and the vorticity tensor is the skew-symmetric part, how is the vorticity generated when we assume that there is no vorticity produced by the stress?
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Old Aug 31st 2017, 03:16 PM   #2
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Originally Posted by gbclimber View Post
It is known that rotation in the flow results from the viscous terms in the Navier-Stokes (N-S) equation. However, when deriving the N-S equation from the general principle of linear momentum in Continuum Mechanics, we use the constitutive relation for isotropic Newtonian fluids which states that the deviatoric part of the stress tensor is proportional to the deviatoric part of the rate of deformation tensor. Since the rate of deformation tensor is the symmetric part of the velocity gradient tensor and the vorticity tensor is the skew-symmetric part, how is the vorticity generated when we assume that there is no vorticity produced by the stress?
Yes indeed but the NS equations themselves don't contain the circulation, the boundary conditions do.
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