Strömungsbeschleunigung

Strömungsbeschleunigung, or flow acceleration, is a central quantity in fluid dynamics describing how the velocity of a fluid element changes with time as it moves through a flow field. It combines local and convective contributions: a = Du/Dt = ∂u/∂t + (u · ∇)u, where u is the velocity vector field. The local (temporal) term ∂u/∂t accounts for changes at a fixed point, while the convective term (u · ∇)u accounts for changes due to movement through spatial variations in the velocity field. The material derivative Du/Dt follows a specific fluid parcel, contrasting with Eulerian descriptions that fix a point in space.

In the Navier-Stokes framework, the acceleration of a Newtonian fluid is related to forces by ρ Du/Dt = -∇p + μ∇²u + f, where ρ is density, p pressure, μ dynamic viscosity, and f body forces. This links flow acceleration to pressure gradients, viscous stresses, and external forces. In compressible flows, density variations couple with velocity changes; in incompressible flows (ρ constant), the equation simplifies accordingly.

Measurement and computation: acceleration can be obtained directly from time-resolved velocity fields using particle image velocimetry (PIV) or velocity gradient data, or inferred from numerical simulations via Du/Dt. Applications span aerodynamics, hydrodynamics, meteorology, and physiology, including the analysis of turbulence, wake dynamics, and cardiovascular blood flow.

See also: Navier-Stokes equations, Euler equations, turbulence, convection, local and convective acceleration.