Stably Stratified Boundary Layer

last modified June 2002, Frank Holzäpfel

All 3 vorticity components of a wake vortex in a weakly stably stratified atmosphere.
Baroclinically produced vorticity induces verticalvorticity which is intensified by vortex stretching.
Subsequently, vortex tilting transfers verticalvorticity into lateral vorticity and vice versa.
Streamline indicates efficient transport between the primary vortices -
this effect is prerequisite for rapid decay mechanisms.

Paper 1:

Two-Dimensional Wake Vortex Physics in the Stably Stratified Atmosphere.

F. Holzäpfel, T. Gerz
Aerospace Science and Technology 5 (1999) 261-270.

The effects of stable stratification on aircraft wake vortices are investigated
by means of high-resolution two-dimensional simulations.  The simulations
elucidate that the vortices first decelerate and then accelerate their descent,
where they largely conserve their circulation.  However, for very stable
stratification the tip vortices may rise again to the flight path.  The
underlying physical mechanisms are revealed by means of a point vortex method
and are examined complementarily by balancing the impulse of the wake vortices.
It is shown that the prominant effects, deceleration, detrainment and
acceleration, are caused by the kinematic interaction of the vorticity generated
by baroclinity and the primary vorticity.  Furthermore, it is found that the
impulse of the whole system, including the detrained secondary vorticity,
is oscillating with the Brunt-Väisälä frequency which implies that the
wingtip vortices themselves do not.  Finally, a local shear--number is proposed
which takes into account the interaction of primary and secondary vorticity and
can describe the instantaneous tendency of wake vortices to accelerate or to

Paper 2:

The turbulent decay of trailing vortex pairs
 in stably stratified environments

Frank Holzäpfel, Thomas Gerz, Robert Baumann
Aerospace Science and Technology 5 (2001) 95-108

The decay of trailing vortex pairs in thermally stably stratified environments is
investigated by means of large eddy simulations.  Results of in-situ measurements
in the wakes of different aircraft are used to find appropriate intitializations for the
simulation of wake turbulence in the quiescent atmosphere.  Furthermore, cases
with weak atmospheric turbulence are investigated.  It is shown that the early
development of the vortices is not affected by turbulence and develops almost
identically as in 2D simulations of wake vortices in stably stratified environments.
In a quiescent atmosphere the subsequent vortex decay is controlled
by the interaction of short-wave disturbances, owing to the aircraft
induced turbulence, and baroclinic vorticity, owing to stable stratification.
As a consequence, vertical vorticity streaks between the vortices are induced
which are substantially intensified by vortex stretching and finally lead to
rapid turbulent wake--vortex decay.  When in addition also atmospheric
turbulence is present, the long-wave instability is dominantly promoted.  For
very strong stratification ($Fr<1$) it is observed that wake vortices may
rebound but lose most of their strength before reaching the flight level.
Finally, the simulation results are compared to the predictive capabilities of
Greene's approximate model.

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(warning: the letters are of good quality only when the paper is printed)

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