The Hydrodynamic Behavior of Vortex Shedding behind Circular Cylinder in the Presence of Group Focused Waves

Vortex shedding behind an elastically mounted circular cylinder in the presence of group focused waves propagating upstream was investigated using a classical approach (time series and FFT) and nonclassical approach (complex 2D Morlet wavelets). Wavelet analysis emerged as a novel solution in this regard. Our results include wave trains with different nonlinearities propagating in different water depths and derived from three types of spectra (Pierson–Moskowitz, JONSWAP (γ = 3.3 or γ = 7)). It was found that the generated wave trains could modify regimes of shedding behind the cylinder, and subharmonic frequency lock-in could arise in particular situations. The occurrence of a lock-in regime in the case of wave trains propagating in intermediate water locations was shown experimentally even for small nonlinearities. Moreover, the application of time-localized wavelet analysis was found to be a powerful approach. In fact, the frequency lock-in regime and its duration could be readily identified from the wavelet-based energy and its corresponding ridges.

A systematic analysis of the phase lags associated with the type-C quasi-periodic oscillation in GRS 1915+105

ABSTRACT We present a systematic analysis of the phase lags associated with the type-C quasi-periodic oscillations (QPOs) in GRS 1915+105 using RXTE data. Our sample comprises 620 RXTE observations with type-C QPOs ranging from ∼0.4 to ∼6.3 Hz. Based on our analysis, we confirm that the QPO phase lags decrease with QPO frequency, and change sign from positive to negative at a QPO frequency of ∼2 Hz. In addition, we find that the slope of this relation is significantly different between QPOs below and above 2 Hz. The relation between the QPO lags and QPO rms can be well fitted with a broken line: as the QPO lags go from negative to positive, the QPO rms first increases, reaching its maximum at around zero lag, and then decreases. The phase-lag behaviour of the subharmonic of the QPO is similar to that of the QPO fundamental, where the subharmonic lags decrease with subharmonic frequency and change sign from positive to negative at a subharmonic frequency of ∼1 Hz; on the contrary, the second harmonic of the QPO shows a quite different phase-lag behaviour, where all the second harmonics show hard lags that remain more or less constant. For both the QPO and its (sub)harmonics, the slope of the lag–energy spectra shows a similar evolution with frequency as the average phase lags. This suggests that the lag–energy spectra drive the average phase lags. We discuss the possibility for the change in lag sign, and the physical origin of the QPO lags.

Pulsed Control of Thermoacoustic Instabilities: Analysis and Experiment

Thermoacoustic instabilities in combustors have been suppressed using phase-shift algorithms pulsing an on-off actuator at the limit cycle frequency (flc) or at the subharmonics of flc. It has been suggested that control at a subharmonic rate may extend the actuator lifetime and possibly require less actuator bandwidth. This paper examines the mechanism of subharmonic control in order to clarify the principles of operation and subsequently identify potential advantages for combustion control. Theoretical and experimental arguments show that there must be a Fourier component of the subharmonic control signal at flc in order to stabilize the limit cycling behavior. It is also demonstrated that the magnitude of that Fourier component must be equivalent to the signal magnitude for a linear phase-shift controller that operates directly at flc. The concept of variable-subharmonic control is introduced whereby the actuator is pulsed at the instability frequency to initially stabilize the system and then is pulsed at a subharmonic frequency to maintain stability. These results imply that an actuator used for subharmonic control cannot be effective unless its bandwidth spans the instability frequency. The advantage of reduced cycling may still be realized but will require higher control authority to produce the same effect as an actuator pulsed at the instability frequency.

SYNCHRONIZATION OF MULTISTABLE SYSTEMS

We present the detailed study of synchronization of two unidirectionally coupled identical systems with coexisting chaotic attractors and analyze system dynamics observed on the route from asynchronous behavior to complete synchronization when the coupling strength is increased. We distinguish three stages of synchronization depending on the coupling strength which can be conventionally divided into three intervals. A relatively weak coupling induces asynchronous intermittent jumps between coexisting attractors and anticipating phase synchronization within windows where the systems stay in similar attractors; an intermediate coupling creates combined attractors that give rise to generalized synchronization in the form of subharmonic frequency entrainment; and a strong coupling results in complete synchronization. The results of numerical simulations are in good agreement with experiments carried out with piecewise-linear Rössler-like electronic circuits.