
Variation of the square root of turbulent kinetic energy at the Værnes airport along the flight path
HOW NORWEGIANS AIRPORTS ARE DIFFERENT FROM OTHER EUROPEAN AIRPORTS ?
Norway is one of the world’s most northerly countries, and one of Europe’s most mountainous countries with large areas dominated by the Scandinavian Mountains. Average elevation is 460 m and 32% of the mainland is located above the tree line. The country is also characterized by fjords penetrating deep into country’s mainland. Because of its peculiar terrain most of the airports are located near a fjord or in valleys. Look at the pictures below. Compared to Amsterdam airport (right) which is located on a flat terrain, the Norwegian airports like Forde are surrounded by water and hills. The irregular terrain generates intense turbulence near the airport and poses real danger to the flights operating in the region. There have been incidents on one of the airports where the plane went of the run way because of the turbulence. Avoiding such turbulent conditions require accurate forecast of turbulence in the vicinity of the airport. Applied Mathematics group in SINTEF ICT have developed a geophysical flow modeling tool called SIMRA which is coupled to the Norwegian Weather Forecasting model and gives the hourly prediction of turbulence and updates the results on www.ipcc.no. Presently the model is operating on 12 Norwegian airports. So, next time when you travel do not forget to visit this website. You will have a fair idea of the turbulence you will expect.

Left: Forde, Right: CDF, Paris airport
Here I am giving a demonstration of the tool. Since, I live in Trondheim I have taken the Værnes airport as the test case. You can see in the figure below that it is a “typical” Norwegian airport surrounded by hills and water.

Værnes Airport
GOVERNING EQUATIONS
Digitalized Terrain data for Værnes Airport
Mass Conservation Equation: 
Momentum Conservation Equation: 
Energy Conservation Equation: 
TKE Equation: 
EDR Equation: 
SAFETY FACTOR
The simplest meteorological variable considered most important for aviation safety is called the F-factor or wind shear and what is called turbulence, represented by
. These quantities are given by the following equations:
F-factor: ![F=-\overline{\frac{c}{g}\frac{\partial u}{\partial x}+\frac{w}{c}}^{\ell_{f}}=-\frac{c}{g \ell_{f}}[u(x+\ell_{f}/2-u(x-\ell_{f}/2)t]+\frac{\overline{w}^{\ell_{f}}}{c} F=-\overline{\frac{c}{g}\frac{\partial u}{\partial x}+\frac{w}{c}}^{\ell_{f}}=-\frac{c}{g \ell_{f}}[u(x+\ell_{f}/2-u(x-\ell_{f}/2)t]+\frac{\overline{w}^{\ell_{f}}}{c}](http://s.wordpress.com/latex.php?latex=%20%20F%3D-%5Coverline%7B%5Cfrac%7Bc%7D%7Bg%7D%5Cfrac%7B%5Cpartial%20u%7D%7B%5Cpartial%20x%7D%2B%5Cfrac%7Bw%7D%7Bc%7D%7D%5E%7B%5Cell_%7Bf%7D%7D%3D-%5Cfrac%7Bc%7D%7Bg%20%5Cell_%7Bf%7D%7D%5Bu%28x%2B%5Cell_%7Bf%7D%2F2-u%28x-%5Cell_%7Bf%7D%2F2%29t%5D%2B%5Cfrac%7B%5Coverline%7Bw%7D%5E%7B%5Cell_%7Bf%7D%7D%7D%7Bc%7D%20%20%20&bg=000000&fg=ffffff&s=2)
Turbulence: 
Here c is the fly path, g is the acceleration due to gravity, u is the wind component along the fly path, w is the vertical wind component,
is the turbulent dissipation, K is turbulent kinetic energy,
turbulent length scale and
is the minimum response distance for landing configuration and is of the order of
, which corresponds to a time interval of about
. Averaging over this distance is indicated by the overline. Coefficient
is given by
.
Prevalence of the two conditions
and
correspond to severe turbulence for commercial aircrafts and represent potential danger. These conditions are easily met when
.
DIGITALIZED TERRAIN DATA AND MESHED DOMAIN



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