A note on decomposition of solenoidal fields

Padmavati, B. Sri; Amaranath, T.

doi:10.1016/s0893-9659(02)00045-9

Cited by 8 publications

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“…This fact has been observed in the steady case also [5,6]. In fact, this solution is also valid in an infinite domain which follows by employing the proof given in [4]. Lastly, a necessary and sufficient condition has been derived for a divergence-free vector field to be a solution of a possible unsteady Stokes flow in the absence of body forces.…”

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confidence: 55%

Unsteady stokes equations: Some complete general solutions

2004

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Abstract.The completeness of solutions of homogeneous as well as nonhomogeneous unsteady Stokes equations are examined. A necessary and sufficient condition for a divergence-free vector to represent the velocity field of a possible unsteady Stokes flow in the absence of body forces is derived. Keywords.Complete general solution; unsteady Stokes flow. Unsteady Stokes flows: Homogeneous caseThe equations governing the motion of an arbitrary unsteady Stokes flow of an incompressible, viscous fluid in the absence of any body forces arewhere V is the velocity, p is the pressure, ρ is the density and µ is the coefficient of dynamic viscosity of the fluid. Equation (1) can also be written aswhere ν = (µ/ρ) is the kinematic coefficient of viscosity. Taking divergence of eq. (3) and making use of eq. (2), it is easy to see that the pressure is harmonic. Hence, on operating the Laplace operator on eq. (3), we find that the velocity vector satisfies the equation A complete general solution of unsteady Stokes equationsLet (V, p) be any solution of (2) 203

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