INSTABILITY AND TRANSIENT GROWTH FOR 2 TRAILING-VORTEX PAIRS

The stability of two vortex pairs is analysed as a model for the vorte x system generated by an aircraft in flaps-down configuration. The co- rotating vortices on the starboard and port sides tumble about one ano ther as they propagate downward. This results in a time-periodic basic state for the stability analysis. The dynamics and instability of the trailing vortices are modelled using thin vortex filaments. Stability equations are derived by matching the induced velocities from Biot-Sa vart integrals with kinematic equations obtained by temporal different iation of the vortex position vectors. The stability equations are sol ved analytically as an eigenvalue problem, using Floquet theory, and n umerically as an initial value problem. The instabilities are periodic along the axes of the vortices with wavelengths that are large compar ed to the size of the vortex cores. The results show symmetric instabi lities that are linked to the long-wavelength Crow instability. In add ition, new symmetric and antisymmetric instabilities are observed at s horter wavelengths. These instabilities have growth rates 60-100% grea ter than the Crow instability The system of two vortex pairs also exhi bits transient growth which can lead to growth factors of 10 or 15 in one-fifth of the time required for the same growth due to instability.