Physical meaning of 3 order spatial derivative?

[jollage]

Hi

Does anybody know the physics meaning of the following equation

\frac{\partial u}{\partial t}+\bar{U}\frac{\partial u}{\partial x}=D\frac{\partial ^3 u}{\partial x^3}

Is there any physical system can be described by this equation?

Thanks.

 

[Simon Bridge]

The 1st order is the gradient
The 2nd order is the curvature
The third order is... ? That the jist of the question ?

note - you normally find the equation from the physics, not the other way around.
There are probably, after all, many situations where you'd want to find the gradient of the curvature.

 

[Andy Resnick]

Hi

Does anybody know the physics meaning of the following equation

\frac{\partial u}{\partial t}+\bar{U}\frac{\partial u}{\partial x}=D\frac{\partial ^3 u}{\partial x^3}

Is there any physical system can be described by this equation?

Thanks.

That is one form (the linearized form) of the Korteweg-deVries equation, and can be used to model surface waves. Other 'flavors' of the KdV equation are used to model nonlinear waves in a dispersive-dissipative medium. Including other spatial dimensions allows you to model unsteady hydrodynamic boundary layers.

 

[Chestermiller]

If u is the concentration of a diffusing species, this equation describes the transient 1D convection and diffusion of the species in a flowing stream. In this application, U is the velocity of the stream in which the species is dissolved, and D is the diffusion coefficient. The flow is in the x-direction. The problem is set up using an Eulerian frame of reference.

Chet