How useful is it to represent CAT by sequences of vortices?

The severity of an aircraft encounter with turbulence is most commonly quantified by reference to the aircraft normal acceleration. For an encounter between an idealised aircraft and an idealised vortex, the acceleration vector is equal to the cross product of half the vorticity vector with air velocity vector. More realistic expressions for the aircraft acceleration have been derived in the context of aircraft encounters with wake vortices, and, although the scale of wake vortices is smaller than that of naturally occurring vortices, the broad methodology is broadly applicable. 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, and this will be discussed.

Questions that arise are: 1. To what extent is a sequence of vortices an accurate representation of turbulence in the atmosphere? 2. How well can we predict the significant properties of vortices? 3. How well can we predict aircraft behaviour given the characteristics of the vortices?

I will attempt to answer these questions through reference to the published literature on the subject.

A question which is linked to the feasibility of representing turbulence by sequences of vortices is: is the turbulence which causes highest amplitude aircraft accelerations quasi two-dimensional?

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.

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.

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.

Note that it is accepted that, for the foreseeable future, it will not be possible to explicitly forecast individual vortices that pose a threat to aircraft, at least not on the global scale. However there is some evidence that it is already possible to forecast forcing mechanisms, and this is one of the grounds for optimism. It is anticipated that it will be possible to forecast discrete volumes of the atmosphere in which there can be expected to be a finite number of vortices with certain characteristics, e.g. orientation, separation.