<p>I was reading a <a href="http://onlinelibrary.wiley.com/doi/10.1029/2006WR005155/full" rel="nofollow noreferrer">paper</a> (equation 1 in linked paper) where they used 'linearized Boussinesq' equation to model groundwater in unconfined aquifer.  The linearized Boussinesq equation described in the paper was $$\frac{\partial h}{\partial t} = \frac{kh^*}{\phi} \frac{\partial^2 h}{\partial x^2}$$ where $k$ is hydraulic conductivity $h^*$ is average height of water table and $\phi$ is specific yield. This equation is very much similar to diffusion equation used normally to model groundwater flow in confined aquifer as defined below.$$\frac{\partial h}{\partial t} = \frac{kd}{S} \frac{\partial^2 h}{\partial x^2}$$ where $d$ is thickness and $s$ is storativity of confined aqufier.  When I googled about Boussinest equation, it is noway similar to what I have presented above. My question is is 'linearized form of Boussinesq equation similar to diffusion equation in this case? If yes then how?</p>

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2017-05-12T21:05:12.773Z
@gansub how? The partial derivative w.r.t time is second derivative in the given link? Also the term on right hand side of equation 1 in link as no corresponding term in the equation that I have given here.
Ather Cheema
<models><hydrology><groundwater><water-table>
Linear Boussinesq Equation for groundwater flow in inconfined aquifer?
Ather Cheema
# Linear Boussinesq Equation for groundwater flow in inconfined aquifer?

(Asked by: username_0 on 2017-05-09)

I was reading a [paper](http://onlinelibrary.wiley.com/doi/10.1029/2006WR005155/full) (equation 1 in linked paper) where they used 'linearized Boussinesq' equation to model groundwater in unconfined aquifer. The linearized Boussinesq equation described in the paper was $$\frac{\partial h}{\partial t} = \frac{kh^\*}{\phi} \frac{\partial^2 h}{\partial x^2}$$ where $k$ is hydraulic conductivity $h^\*$ is average height of water table and $\phi$ is specific yield. This equation is very much similar to diffusion equation used normally to model groundwater flow in confined aquifer as defined below.$$\frac{\partial h}{\partial t} = \frac{kd}{S} \frac{\partial^2 h}{\partial x^2}$$ where $d$ is thickness and $s$ is storativity of confined aqufier. When I googled about Boussinest equation, it is noway similar to what I have presented above. My question is is 'linearized form of Boussinesq equation similar to diffusion equation in this case? If yes then how?

**Tags:** models, hydrology, groundwater, water-table

> **Comments:**
> **username_0**: @gansub how? The partial derivative w.r.t time is second derivative in the given link? Also the term on right hand side of equation 1 in link as no corresponding term in the equation that I have given here.  

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## 0 answers

