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- Taylor–Proudman_theorem abstract "In fluid mechanics, the Taylor–Proudman theorem (after G. I. Taylor and Joseph Proudman) states that when a solid body is moved slowly within a fluid that is steadily rotated with a high angular velocity , the fluid velocity will be uniform along any line parallel to the axis of rotation. must be large compared to the movement of the solid body in order to make the coriolis force large compared to the acceleration terms.That this is so may be seen by considering the Navier–Stokes equations for steady flow, with zero viscosity and a body force corresponding to the Coriolis force, which are:where is the fluid velocity, is the fluid density, and the pressure. If we now make the assumption that is scalar potential and the advective term may be neglected (reasonable if the Rossby number is much less than unity) and that the flow is incompressible (density is constant) then the equations become:where is the angular velocity vector. If the curl of this equation is taken, the result is the Taylor–Proudman theorem:To derive this, one needs the vector identities and and (because the curl of the gradient is always equal to zero).Note that is also needed (angular velocity is divergence-free).The vector form of the Taylor–Proudman theorem is perhaps better understood by expanding the dot product:Now choose coordinates in which and then the equations reduce toif . Note that the implication is that all three components of the velocity vector are uniform along any line parallel to the z-axis.".
- Taylor–Proudman_theorem wikiPageID "1024614".
- Taylor–Proudman_theorem wikiPageRevisionID "597833621".
- Taylor–Proudman_theorem subject Category:Fluid_dynamics.
- Taylor–Proudman_theorem subject Category:Physics_theorems.
- Taylor–Proudman_theorem comment "In fluid mechanics, the Taylor–Proudman theorem (after G. I. Taylor and Joseph Proudman) states that when a solid body is moved slowly within a fluid that is steadily rotated with a high angular velocity , the fluid velocity will be uniform along any line parallel to the axis of rotation.".
- Taylor–Proudman_theorem label "Taylor–Proudman theorem".
- Taylor–Proudman_theorem label "Teorema de Taylor-Proudman".
- Taylor–Proudman_theorem label "Teorema de Taylor-Proudman".
- Taylor–Proudman_theorem label "Teorema di Taylor-Proudman".
- Taylor–Proudman_theorem label "Théorème de Taylor-Proudman".
- Taylor–Proudman_theorem label "Twierdzenie Taylora–Proudmana".
- Taylor–Proudman_theorem sameAs Taylor%E2%80%93Proudman_theorem.
- Taylor–Proudman_theorem sameAs Teorema_de_Taylor-Proudman.
- Taylor–Proudman_theorem sameAs Théorème_de_Taylor-Proudman.
- Taylor–Proudman_theorem sameAs Teorema_di_Taylor-Proudman.
- Taylor–Proudman_theorem sameAs Twierdzenie_Taylora–Proudmana.
- Taylor–Proudman_theorem sameAs Teorema_de_Taylor-Proudman.
- Taylor–Proudman_theorem sameAs Q2600653.
- Taylor–Proudman_theorem sameAs Q2600653.
- Taylor–Proudman_theorem wasDerivedFrom Taylor–Proudman_theorem?oldid=597833621.