In low-dimensional topology, a boundary-incompressible surface is a two-dimensional surface within a three-dimensional manifold whose topology cannot be...

A surface other than a sphere is incompressible if any disk with its boundary on the surface spans a disk in the surface. Incompressible surfaces are...

u = 0 {\textstyle \nabla \cdot \mathbf {u} =0} for an incompressible fluid. Incompressibility rules out density and pressure waves like sound or shock...

mechanics, a boundary layer is the thin layer of fluid in the immediate vicinity of a bounding surface formed by the fluid flowing along the surface. The fluid's...

mechanics, incompressible flow is a flow in which the material density does not vary over time. Equivalently, the divergence of an incompressible flow velocity...

sufficiently large, meaning that it contains a properly embedded two-sided incompressible surface. Sometimes one considers only orientable Haken manifolds, in which...

Therefore, the fluid can be considered to be incompressible, and these flows are called incompressible flows. Bernoulli performed his experiments on...

As the fluid flows along the wall, the fluid at the wall surface satisfies a no-slip boundary condition and has zero velocity, but as you move away from...

thickness and shape of boundary layers formed by fluid flowing along a solid surface. The defining characteristic of boundary layer flow is that at the...

u-U=h-h_{\infty }=0\ {\text{for}}\ y=\infty \ {\text{or}}\ x=0.} Unlike the incompressible boundary layer, similarity solution exists only if the transformation x...

the phase change at the free surface, the following boundary conditions apply. The free surface should be a sharp boundary separating the two fluids. There...

{u}\right)=-\nabla p+\mu \,\Delta u(x,t)+f(x,t)} and if the flow is incompressible, we have the further condition that ∇ ⋅ u = 0. {\displaystyle \nabla...

describe the force balance at a given point within a fluid. For an incompressible fluid with vector velocity field u {\displaystyle \mathbf {u} } , the...

region where these forces change behavior is known as a boundary layer, such as the bounding surface in the interior of a pipe. A similar effect is created...

the energy per unit volume in an ideal, incompressible liquid is constant throughout its vessel. At the surface, gravitational potential energy is large...

conductivity. The Euler equations can be applied to incompressible and compressible flows. The incompressible Euler equations consist of Cauchy equations for...

analyzed by cutting the surface along the preserved union of simple closed curves Γ. Each of the resulting compact surfaces with boundary is acted upon by some...

of infinite depth, so the boundary condition is at z = − ∞ . {\displaystyle \scriptstyle z=-\infty .} The undisturbed surface is at z = 0 {\displaystyle...

to be spatially-constant. Boundary layer equations (BL): Start with the C-NS (I-NS) for compressible (incompressible) boundary layers. Assume that there...

modelled as an incompressible flow. Otherwise the more general compressible flow equations must be used. Mathematically, incompressibility is expressed...

\mathbf {u} } the fluid velocity. To obtain the equations of motion for incompressible flow, it is assumed that the density, ρ {\displaystyle \rho } , is a...

Laplacian vector field is a vector field which is both irrotational and incompressible. If the field is denoted as v, then it is described by the following...

The incompressible and compressible flow regimes produce many associated phenomena, such as boundary layers and turbulence. The concept of a boundary layer...

(1883) On the dynamical theory of incompressible viscous fluids and the determination of the criterion (1895) A boundary layer can transition to turbulence...

gradient of a scalar always being equal to zero. In the case of an incompressible flow the velocity potential satisfies Laplace's equation, and potential...

vector normal to the cylinder surface. The upstream flow is uniform and has no vorticity. The flow is inviscid, incompressible and has constant mass density...

as those with an incompressible surface) are homeomorphic if there is an isomorphism of fundamental groups which respects the boundary. Waldhausen conjectured...

because the surface pressure as well as the external pressure in the mixing zone is everywhere equal to the atmospheric pressure and the boundary layer does...

certain compressible flow problems by incompressible-flow calculation methods. It also allows applying incompressible-flow data to compressible-flow cases...

effect to include the tendency of any fluid boundary layer to adhere to a curved surface, not just the boundary layer accompanying a fluid jet. It is in...