A simple method to estimate the eddy dissipation rate from SODAR/RASS measurements

Wake vortices generated by aircraft may cause a potential hazard to a following aircraft. Therefore, separation standards were established to avoid the wake hazard. Today, wake vortices more and more influence the traffic throughput at major airport due to these prescribed separation standards. Those standards most of the time are over-conservative. Therefore wake vortex avoidance systems are under development which aim at monitoring and predicting the wake vortex behavior in the terminal area. The goal is to safely reduce aircraft separations and to increase capacity. Save and reliable wake vortex predictions require high quality weather observations and predictions which must at least cover the whole glide path. Atmospheric turbulence significantly influences the decay of wake vortices generated by aircraft. Today, all state-of-the-art wake vortex models parameterize the decay due to turbulence in terms of the turbulent eddy dissipation rate. Measurements of wake vortices in the atmosphere indicate the correlation between eddy dissipation rate and wake vortex life time. Long lived vortices have been observed up to five minutes under conditions of weak turbulence and neutral stratification. It is obvious that in particular those long-lived vortices have to be monitored and predicted in an operational environment due to the potential risk for following aircraft.

This paper compares dissipation rates determined from a combination of SODAR/RASS and sonic anemometer measurements with measurements of a pulsed 2 µm LIDAR system. Data from two European measurement campaigns in 2002 and 2003 are used for comparison. The experiments were dedicated to characterize the wake vortex of a large transport conditions in calm atmospheric conditions in order to identify the effect of flight configuration on wake vortex characteristics. Flight tests were carried out in the residual layer during evening hours.

We apply and modify an approach proposed by Kramar and Kouznetsov (2002) who employ a simple TKE budget model to estimate the dissipation rate from SODAR/RASS. In our approach this estimate is combined with sonic anemometer measurements. The dissipation rate determined from the LIDAR system is based on the second order structure function (Banakh and Smalikho, 1997).

In a first step we analyze the eddy dissipation rate determined from sonic anemometer measurements. We consider 10 minute data samples applying structure functions. The underlying requirements such as local isotropy are evaluated. The uncertainty of the dissipation rate estimates is quantified considering subsample and larger averaging intervals. The high resolution sonic measurements are used to scale the turbulent kinetic energy determined from SODAR. We use a multi resolution filter (Howell and Mahrt, 1997) to explicitly consider length scales of the flow which are most amenable to trigger instability mechanisms and a subsequent wake vortex decay. This scaling appears necessary in a weakly turbulent atmosphere where the SODAR determined standard deviations of the wind components are dominated by wave activity. Length scales up to approximately 200 m are considered. The commonly observed Crow instability is triggered at a length scale 8.6 times the initial vortex spacing where the initial vortex spacing of a large transport aircraft is on the order of 40 m.

The analysis of 57 cases indicates a good agreement between the two measurements. The RMS error of normalized dissipation rate is 4*10^-4 m^2/s^3. For weakly stable cases this RMS error reduces to 2.2*10^4 m^2/s^3 and increases to 5.7*10-4 m^2/s^3 for weakly unstable cases. Average dissipation rate from SODAR is 4.1*10^-4 m^2/s^3 (weakly unstable) and 2.1*10^-4 m^2/s^3 (weakly stable).