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Three examples of vector fields. From left to right: a field with a source, a field with a sink, a field without either. In the physical sciences, engineering and mathematics, sources and sinks is an analogy used to describe properties of vector fields.
The propensity of a fluid to swirl is used to promote good fuel/air mixing in internal combustion engines.. In fluid mechanics and transport phenomena, an eddy is not a property of the fluid, but a violent swirling motion caused by the position and direction of turbulent flow.
Swirl is the tangential flow component of the velocity vector. The velocity profile should be referred to as the axial velocity profile. As the velocity vector can be resolved into three mutually orthogonal components, the velocity profile only represents the axial component of velocity. fig.(2) showing the Swirl Angle which explains the ...
Interchanging the vector field v and ∇ operator, we arrive at the cross product of a vector field with curl of a vector field: = () , where ∇ F is the Feynman subscript notation, which considers only the variation due to the vector field F (i.e., in this case, v is treated as being constant in space).
The vorticity would be twice the mean angular velocity vector of those particles relative to their center of mass, oriented according to the right-hand rule. By its own definition, the vorticity vector is a solenoidal field since ∇ ⋅ ω = 0. {\displaystyle \nabla \cdot {\boldsymbol {\omega }}=0.}
Setting the three dimensions of to zero, we obtain 3 independent linear constraints, so the solution space has 1 dimension, and it is spanned by the vector (,,,). Thus, any dimensionless quantity constructed out of ρ , u , L , μ {\displaystyle \rho ,u,L,\mu } is a function of ρ u L μ − 1 {\displaystyle \rho uL\mu ^{-1}} , the Reynolds number.
A common problem in computer graphics is to generate a non-zero vector in ℝ 3 that is orthogonal to a given non-zero vector. There is no single continuous function that can do this for all non-zero vector inputs. This is a corollary of the hairy ball theorem. To see this, consider the given vector as the radius of a sphere and note that ...
Sega Swirl, a 1999 puzzle game for the Sega Dreamcast Swirl (fluid dynamics) , a quantity in fluid dynamics Sources and sinks , vectors fields with zero divergence but non-zero curl.