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...

on S. Culler, Marc, and Peter B. Shalen. "Bounded, separating, incompressible surfaces in knot manifolds." Inventiones mathematicae 75 (1984): 537–545...

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

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...

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...

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...

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...

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...

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

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

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...

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

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...

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...

{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...

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...

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

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...

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

mathematician Jean le Rond d'Alembert. D'Alembert proved that – for incompressible and inviscid potential flow – the drag force is zero on a body moving...

(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...

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

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

Predictive-Corrective SPH (PCISPH) to allow for better incompressibility constraints M. Ihmsen et al., 2010, introduce boundary handling and adaptive time-stepping for...