Advection

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Having a change of temperature and the material density by the movement of the material in the space in a point with the space that is uneven in temperature or material density with the advection (is Riyu British: advection) (physical quantity is carried in space). Relations are close in in physics particularly hydrodynamics. The way of thinking that started from the space mentioned above is assumed an oiler-like way of thinking, and a Lagrange-like way of thinking that started from the material adversely is spoken as follows (I refer to continuum mechanics # material indication and space indication).

An example includes cold air in the sky of a certain point and does it when there is warm air to the west. An advection means that warm air is carried here by fall wind, and a rise in temperature is observed at the point (oiler description). The west, cold air exist warm air on the east side, and, as for the cold air, the air which is warm from the point that there is to the east side moves to the point with the east side by fall wind (Lagrange description).

Advection equation

Partial differential equation expressing an advection is called an advection equation. The advection equation to express that physical quantity ψ(t, x) do an advection in speed c is expressed as follows:

${\displaystyle {\frac {\partial \psi (t,{\boldsymbol {x}})}{\partial t}}=-{\boldsymbol {c}}\cdot {\boldsymbol {\nabla }}\psi (t,{\boldsymbol {x}})}$

,∇ expresses space differential calculus here.

In the case of one dimension, the advection equation is as follows:

${\displaystyle {\frac {\partial \psi (t,x)}{\partial t}}+c{\frac {\partial \psi (t,x)}{\partial x}}=0}$

I can solve this equation analytically and am expressed as follows using any function f:

${\displaystyle \psi (t,{\boldsymbol {x}})=f({\boldsymbol {x}}-{\boldsymbol {c}}t)}$

Allied item

• Diffusion
• Advection-diffusion equation
• Consecutive equations
• Wave equation

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