Navier–Stokes equations

An example of convection. Though the flow may be steady (time-independent), the fluid decelerates as it moves down the diverging duct (assuming incompressible or subsonic compressible flow), hence there is an acceleration happening over position.

Visualization of a) parallel flow and b) radial flow.

Some of the flow lines along a Hopf fibration.

In physics, the Navier–Stokes equations /nævˈjeɪ stoʊks/, named after Claude-Louis Navier and George Gabriel Stokes, describe the motion of viscous fluid substances. These balance equations arise from applying Newton's second law to fluid motion, together with the assumption that the stress in the fluid is the sum of a diffusing viscous term (proportional to the gradient of velocity) and a pressure term—hence describing viscous flow. The main difference between them and the simpler Euler equations for inviscid flow is that Navier–Stokes equations also in the Froude limit (no external field) are not conservation equations, but rather a dissipative system, in the sense that they cannot be put into the quasilinear homogeneous form:

单词	Convective acceleration
释义	Convective acceleration 英语百科 Navier–Stokes equations In physics, the Navier–Stokes equations /nævˈjeɪ stoʊks/, named after Claude-Louis Navier and George Gabriel Stokes, describe the motion of viscous fluid substances. These balance equations arise from applying Newton's second law to fluid motion, together with the assumption that the stress in the fluid is the sum of a diffusing viscous term (proportional to the gradient of velocity) and a pressure term—hence describing viscous flow. The main difference between them and the simpler Euler equations for inviscid flow is that Navier–Stokes equations also in the Froude limit (no external field) are not conservation equations, but rather a dissipative system, in the sense that they cannot be put into the quasilinear homogeneous form:
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Convective acceleration

Navier–Stokes equations