## Setting up an Amazon EC2 instance LAMP stack

Script to set up a LAMP stack to run a PHP website from an Amazon EC2 instance:

Script to set up a LAMP stack to run a PHP website from an Amazon EC2 instance:

The governing equations in geophysical fluid dynamics can be simplified somewhat if the horizontal length and velocity scales are much larger than the vertical length and velocity scales, respectively.

They are commonly used to describe both the ocean and atmosphere, as well as estuaries, rivers and channels.

According to Riddaway and Hortal, the set of coupled non-linear partial differential equations solved in numerical weather prediction (NWP) describe three important dynamical processses:

- Advection
- Diffusion
- Adjustment

The first two are familiar to the non-meteorologist more used to working with
the general equations of fluid motion. The third, *adustment*, is described as
'how the mass and wind fields adjust to one another'.

Consider the *inhomogeneous Fredholm integral equation*:

\[ H \psi(\mu) = \lambda \int_a^b \sigma(\mu, \mu') \psi(\mu') d\mu'
+ S(\mu) \]

The unknown to be solved for is \(\psi(\mu)\) where \(a \le \mu \le b\) is the
independent variable, and the known function \(\sigma(\mu, \mu')\) is known as
the *kernel*. This is an *inhomogeneous* equation because the known function
\(S(\mu) \ne 0\).