Abstracts - KTH Mechanics

On the generation of diagonal ‘rib’ vortices in the braid region
of a mixing layer
Jimmy Philip ∗ and Jacob Cohen ∗
The three-dimensional (3D) structure of a plane turbulent mixing layer is characterized
by the presence of secondary quasi-streamwise counter-rotating vortices (ribs),
connecting the bottom of the primary upstream spanwise vortex (roller) with the top
of the downstream one. 1 The flow region generated between the two rollers is that
of a plane stagnation flow. A similar field has been also observed between the heads
of two consecutive hairpin vortices in a turbulent boundary layer. 2 We show that a
3D localized disturbance embedded in this plane stagnation flow can develop into the
rib vortices which have been widely observed in turbulent mixing layers. We use the
fluid impulse (FI) of the disturbance to analytically predict its growth for an arbitrary
initial amplitude. The predictions are confirmed by numerical simulations.
Accordingly, an initial dipole Gaussian vorticity distribution is placed in an external,
unbounded, irrotational plane stagnation flow represented by U =(Ay, Ax, 0).
The viscous disturbance vorticity equation is integrated analytically. The results show
that the FI associated with such disturbances decays and grows exponentially along
the principal axes x = y (figure 1a) and x = −y (figure 1b), respectively. Numerical
simulations for both linear and nonlinear disturbances confirm the above predictions.
The resulting structure is that of a counter-rotating vortex pair as seen in figure 1(c),
which is similar to that of ribs vortices observed in turbulent mixing layers. Furthermore,
it is shown that the FI, the disturbance kinetic energy and enstrophy follow the
same trend, i.e. when the FI increases with time so does the kinetic energy and enstrophy,
and vice-versa. The correspondence between them suggests the use of the fluid
impulse to predict stability of plane stagnation flow to such localized disturbances.
∗ Faculty of Aerospace Engineering, Technion - Israel Institute of Technology, Haifa 32000, Israel.
1 Bernal and Roshko, J. Fluid Mech. 170, 499 (1986).
2 Adrian et al. J. Fluid Mech. 422, 1 (2000).
-5 0 5
(a) (b) (c)
Figure 1: (a) Comparison between analytical solution and numerical simulation of the
FI evolution: initial fluid impulse, p0 = px10 (b) initial FI, p0 = px20. (c) The evolved
counter-rotating vortex pair shown by iso-surfaces of the vorticity magnitude.
Y
10
0
-10
Z
-10
0
X
10
171