Plasma sheet bursty bulk flows often oscillate around their equilibrium position at about 10 REdowntail. The radial magnetic field, pressure, and flux tube volume profiles usually behave differently earthward and tailward of this position. Using data from five Time History of Events and Macroscale Interactions during Substorms (THEMIS) probes, we reconstruct these profiles with the help of an empirical model and apply thin filament theory to show that the oscillatory flow braking can occur in an asymmetric potential. Thus, the thin filament oscillations appear to be anharmonic, with a power spectrum exhibiting peaks at both the fundamental frequency and the first harmonic. Such anharmonic oscillatory braking can explain the presence of the first harmonic in Pi2 pulsations (frequency doubling), which are simultaneously observed by magnetometers on the ground near the conjugate THEMIS footprints.