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Convection is often categorised or described by the main effect causing the convective flow; for example, thermal convection. Convection cannot take place in most solids because neither bulk current flows nor significant diffusion of matter can take place. Granular convection is a similar phenomenon in granular material instead of fluids.
Convective acceleration is present in most flows (exceptions include one-dimensional incompressible flow), but its dynamic effect is disregarded in creeping flow (also called Stokes flow). Convective acceleration is represented by the nonlinear quantity u ⋅ ∇ u , which may be interpreted either as ( u ⋅ ∇) u or as u ⋅ (∇ u ) , with ...
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The left side of the equation describes acceleration, and may be composed of time-dependent and convective components (also the effects of non-inertial coordinates if present). The right side of the equation is in effect a summation of hydrostatic effects, the divergence of deviatoric stress and body forces (such as gravity).
Oseen flow is an improved description of these flows, as compared to Stokes flow, with the (partial) inclusion of convective acceleration. [ 1 ] Oseen's work is based on the experiments of G.G. Stokes , who had studied the falling of a sphere through a viscous fluid.
The local acceleration (a) can also be thought of as the "unsteady term" as this describes some change in velocity over time. The convective acceleration (b) is an acceleration caused by some change in velocity over position, for example the speeding up or slowing down of a fluid entering a constriction or an opening, respectively.
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In fluid dynamics, Lamb vector is the cross product of vorticity vector and velocity vector of the flow field, named after the physicist Horace Lamb. [1] [2] The Lamb vector is defined as