# Physical meaning of 3 order spatial derivative?

1. Jul 1, 2013

### 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.

2. Jul 2, 2013

### 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.

3. Jul 2, 2013

### Andy Resnick

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.

4. Jul 2, 2013

### Staff: Mentor

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