6.6. NUMERICAL MODELING OF TIME-DEPENDENT STREAMING 59
Fig. 6.5(d) for both the analytical solution for the oscillator and the numerical solution
for the channel. The transient overshoot is a result of the mismatch between the phase of
the forcing and the phase of the oscillation. For the channel resonance, the overshoot thus
occurs when the frequency f of the boundary oscillations does not match the resonance
frequency fres, which can be determined numerically from the resonance curves shown in
Fig. 6.5(c). For the channel this may seem counter-intuitive, since the most basic understanding
of the acoustic resonance is that energy is gradually pumped into the acoustic
resonance eld until the viscous loss equals the power input, resulting in a monotonic
build-up of the energy. However, due to the oscillator behavior of the channel resonance,
the monotonic build-up of the energy only occurs when f = fres, which is also shown in
Fig. 6.5(d).
The numerical analysis in Ref. 30 Appendix E showed that the acoustic energy builds
up approximately ve times faster than the streaming ow. Since the radiation force scales
by the acoustic energy, this makes the radiation force more dominant in the transient
regime of approximately one millisecond compared to the steady-state. Applying a pulsed
actuation did not improve the ratio of radiation force and streaming-induced drag force.
On the contrary, the conclusion was that it would never be advantages to turn o the
actuation, since this causes the energy and thus the radiation force to decay fast, while the
magnitude of the streaming ow decays much slower.