You can take the curl of Navier Stokes and have an equation expressed in vorticity, which looks like our angular momentum world. Does it mean that the equation with velocity somehow embed the both kind of momentum, and they are totally correlated for fluids ?

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Tiberlaue · Accepted Answer

Momentum conservation is the equation      ∂          ∂      t            π    i    +      ∇    j        τ          i      j        =  0where       π    i    =  ρ      v    i   is the momentum density. Using      τ          i      j        =  P      δ          i      j        +  ρ      v    i        v    j  this equation is equivalent to the Euler equation, and including dissipative stresses gives the Navier-Stokes equation.The density of angular momentum (about the origin) is       l    i    =      ϵ          i      j      k            x    j        π    k   and       l    i   is conserved if       ϵ          i      j      k            τ          j      k        =  0. We get      ∂          ∂      t            l    i    +      ∇    j        m          i      j        =  0where       m          i      j        =      ϵ          i      k      l            x    k        τ          l      j       is the angular momentum flux.Of course, the angular momentum of the fluid can change because of external torques, and the angular momentum of a fluid cell can change because of surface stresses.

Navier Stokes: what about angular momentum?

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