solenoidal's Usage Examples:

In vector calculus a solenoidal vector field (also known as an incompressible vector field, a divergence-free vector field, or a transverse vector field).

An incompressible flow is described by a solenoidal flow velocity field.

But a solenoidal field, besides having a zero divergence, also has the.

v must be a solenoidal vector field.

Let v : R 3 → R 3 {\displaystyle \mathbf {v} :\mathbb {R} ^{3}\to \mathbb {R} ^{3}} be a solenoidal vector field.

It is often used in the spherical coordinates analysis of solenoidal vector fields, for example, magnetic fields and incompressible fluids.

resolved into the sum of an irrotational (curl-free) vector field and a solenoidal (divergence-free) vector field; this is known as the Helmholtz decomposition.

In this case, u {\displaystyle \mathbf {u} } is said to be solenoidal.

are obtained for the effective resistances of single- and multi-layer solenoidal coils of either solid or stranded wire.

magnetic field B has divergence equal to zero, in other words, that it is a solenoidal vector field.

If F {\displaystyle \mathbf {F} } is solenoidal - that is, if ∇ ⋅ F = 0 {\displaystyle \nabla \cdot \mathbf {F} =0} such.

form of the vorticity equation for an inviscid, divergence-free flow (solenoidal velocity field), the barotropic vorticity equation can simply be stated.

are zeros on the wave function, around which this velocity field has a solenoidal shape, similar to that of irrotational vortex on potential flows of traditional.

include frictional forces, magnetic forces, and in fluid mechanics a solenoidal field velocity field.

In other words, the stream function accounts for the solenoidal part of a two-dimensional Helmholtz decomposition, while the velocity.

For the electromagnetic wave with axial (solenoidal) magnetic field: E = E ϕ = ω ρ 0 c B 0 cos ⁡ ω ξ 1 , {\displaystyle E=E_{\phi.

that the volume form is preserved under the flow of a solenoidal vector field.

Thus solenoidal vector fields are precisely those that have volume-preserving.