Does the aircraft direction of movement affect its response to (moderate or greater) turbulence?

Bob LunnonEx UK Met Office/Univ of Reading

Introductory comments

• I presented a poster at the AMS annual meeting this year entitled “How useful is it to represent CAT by sequences of vortices?”

• It can be shown that for an idealised aircraft encountering an idealised vortex, the aircraft experiences an acceleration proportional to the vector product of the air velocity vector with the vorticity vector

• This implies that aircraft direction of travel is highly significant

More realistic derivation of dependency on direction of travel

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Figure shows load factor (normal acceleration squared) as a function of angle of encounter with a wake vortex (theoretical calculation)

Can naturally occurring turbulence be thought of in terms of vortices?

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Figure shows reconstructed vorticity field using aircraft data in case of severe turbulence encounter

Comments on previous slide• Parks et al (1985) reported a second case where it was possible to

diagnose a similar vortex array. As would be expected there were violent normal accelerations stemming from the two vortices directly intersected by the flight path in the figure, but not for the other 3 vortices in the figure. This clearly indicates that for this case, the sequence of vortices is a useful way to represent the atmospheric conditions.

• The well known turbulence encounter reported in Clark et al (2000) was associated with horizontal vortices, in that case parallel to the prevailing wind. Although a single encounter does not constitute rigorous confirmation that this is a useful general approach, it encourages further research on the question.

Numerically simulated field of flow around decaying wake vortices

Comments on previous slide

• The success of the application of the aircraft separations applied during final approach implies that wake vortices, which consist of very well defined vortices, pose a threat of a significant normal acceleration but the more 3-D turbulence surrounding the vortices does not pose such a significant threat.

• The conclusion is that it is plausible that 2-D turbulence is more likely on average to constitute a threat then 3-D turbulence, and that representing turbulent flows by sequences of vortices may well provide useful guidance of the threat posed by the turbulence.

Feasibility of forecasting vortex characteristics

Comments on previous slide

• A seminal paper on prediction of CAT was Roach (1970), which focussed on Kelvin Helmholtz instability. The derived CAT predictor was essentially rate of change (with respect to time) of Richardson Number. If the terms in this expression which are independent of temperature are examined, it can be shown that the terms represent the effect of large scale deformation on vorticity about a horizontal axis. This is illustrated in slide.

Definition of Lunnon predictor

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Different causes of turbulence

The applicability of sequences of vortices to the representation of turbulence may well depend on the meteorological mechanism causing the turbulence. For both Kelvin Helmholtz instability and flow normal to a quasi 2-D mountain ridge, the representation by vortices seems relatively attractive. For more general flow over orography, and for convection, representation by vortices seems less attractive. All mechanisms causing turbulence need to be considered. Algorithms reflecting all the main causes of turbulence are represented in Sharman et al (2006).

Use of Eddy Dissipation Rate/Turbulent Kinetic Energy

• A contrasting approach to the quantification of turbulence is the use of turbulent kinetic energy and eddy dissipation rate. Converting from one to the other required the use of a length scale and if the turbulence is quasi 2-D then it is by no means clear what length scale is appropriate. However it is noted that reasonable correlation has been obtained between aircraft acceleration and eddy dissipation rate. In Cornman and Meymaris (2010) it is stated “Statistical and case study analyses will be presented to show that the conversion is an accurate method that can valuable tactical and strategic information to the pilot.”

Philosophical point

• There is a philosophical point here too. Note the following quote from Davidson (2004):“Engineers, mathematicians and physicists tend to view turbulence in rather different ways, and even within each discipline there are many disparate groups. Some groups emphasise the role of coherent vortices, while others downplay the importance of such structures and advocate the use of purely statistical methods of attack.” It is argued that the approach advocated in this poster is a “coherent vortices” approach whilst the use of EDR/TKE is a more statistical approach.

The effect of different scales of turbulence

• An issue is the dependency of aircraft response to different scales of turbulence.

• An aircraft will be relatively unaffected by vortices having a characteristic scale much smaller than the aircraft dimensions, because, assuming the aircraft is essentially rigid, it will integrate out the effect of these wind variations.

• Intentional movement of aircraft control surfaces will enable the aircraft to mitigate the effects of relatively large scale wind fluctuations.

• Therefore between these two scales there exists a scale where the effect of, say, a single isolated vortex on the aircraft motion will be maximum. It is potentially very useful to say something about the scale of vortices.

The effect of vertical vortices

• For the normal (near vertical) component of aircraft acceleration, vortices with a horizontal axis of rotation are relevant, but vertical vortices will cause horizontal accelerations. This issue was explored by Knox (1997) – the vortices are associated with inertial instability, which in turn is associated with strongly anticyclonic flows.

• Again, the aircraft acceleration will be approximately proportional to half the product of the vorticity and the airspeed. Given that vertical vorticity in the atmosphere is smaller in magnitude than horizontal vorticity, it follows that aircraft horizontal accelerations will be smaller than normal accelerations. However, transverse accelerations can be potential disruptive and injurious to passengers and cabin crew, so it is desirable to forecast these.

Concluding remarks

• More work needs to be done to show that forecasts taking aircraft direction of movement into account generate better verification statistics than isotropic forecasts

• If this is shown, the aviation community needs to be educated so that they can be prepared for an intermediate step in diagnosing forecast aircraft normal (and horizontal) accelerations for a particular envisaged trajectory

• A similar step may be needed for icing forecasts