Effects of phase difference between instability modes on boundary-layer transition

Phase effect on the modal interaction of flow instabilities is investigated for laminar-to-turbulent transition in a flat-plate boundary-layer flow. Primary and secondary three-dimensional (3-D) oblique waves at various initial phase differences between these two instability modes. Three numerical methods are used for a systematic approach for the entire transition process, i.e. before the onset of transition well into fully turbulent flow. Floquet analysis predicts the subharmonic resonance where a subharmonic mode locally resonates for a given basic flow composed of the steady laminar flow and the fundamental mode. Because Floquet analysis is limited to the resonating subharmonic mode, nonlinear parabolised stability equation analysis (PSE) is conducted with various phase shifts of the subharmonic mode with respect to the given fundamental mode. The application of PSE offers insights on the modal interaction affected by the phase difference up to the weakly nonlinear stage of transition. Large-eddy simulation (LES) is conducted for a complete transition to turbulent boundary layer because PSE becomes prohibitively expensive in the late nonlinear stage of transition. The modulation of the subharmonic resonance with the initial phase difference leads to a significant delay in the transition location up to $\Delta Re_{x, tr} \simeq 4\times 10^5$ as predicted by the current LES. Effects of the initial phase difference on the spatial evolution of the modal shape of the subharmonic mode are further investigated. The mechanism of the phase evolution is discussed, based on current numerical results and relevant literature data.

Dynamics of Plane Waves in the Fractional Nonlinear Schrödinger Equation with Long-Range Dispersion

We analytically and numerically investigate the stability and dynamics of the plane wave solutions of the fractional nonlinear Schrödinger (NLS) equation, where the long-range dispersion is described by the fractional Laplacian (−Δ)α/2. The linear stability analysis shows that plane wave solutions in the defocusing NLS are always stable if the power α∈[1,2] but unstable for α∈(0,1). In the focusing case, they can be linearly unstable for any α∈(0,2]. We then apply the split-step Fourier spectral (SSFS) method to simulate the nonlinear stage of the plane waves dynamics. In agreement with earlier studies of solitary wave solutions of the fractional focusing NLS, we find that as α∈(1,2] decreases, the solution evolves towards an increasingly localized pulse existing on the background of a “sea” of small-amplitude dispersive waves. Such a highly localized pulse has a broad spectrum, most of whose modes are excited in the nonlinear stage of the pulse evolution and are not predicted by the linear stability analysis. For α≤1, we always find the solution to undergo collapse. We also show, for the first time to our knowledge, that for initial conditions with nonzero group velocities (traveling plane waves), an onset of collapse is delayed compared to that for a standing plane wave initial condition. For defocusing fractional NLS, even though we find traveling plane waves to be linearly unstable for α<1, we have never observed collapse. As a by-product of our numerical studies, we derive a stability condition on the time step of the SSFS to guarantee that this method is free from numerical instabilities.

Effect of Nonreciprocal Forces on the Stability of Dust Clusters

Results are presented from studies of the stability of the plane dust clusters in the form of a regular polygon with the number of particles from two to five. It is assumed that the particles are placed in the plasma consisting of Maxwellian electrons and a directed flow of cold ions. It is shown that, in such clusters, the oscillatory instabilities can develop along with the aperiodic instabilities. The ranges of plasma parameters are determined, within which the oscillatory instability of the five-particle cluster becomes saturated at the weakly nonlinear stage. As a result, the cluster forms a time crystal, which can be a chiral crystal.

Влияние ангармонизма на тепловыделение и упрочнение металлов при квазистатическом растяжении

In this paper, we present the analysis of results of experimental studies of energy dissipation and variations of the transverse strain coefficients under quasistatic tensile stress of metals. The nature of changes in these processes at different stages of deformation is considered: elastic, nonlinear, transition from elastic to developed plastic flow, and developed plastic flow. It is shown that at all stages there is a correlation of changes in independently measured strain parameters: temperature, transverse strain coefficients, and hardening. The decisive effect of the interaction potential anharmonicity on the nature of the processes of changes in modules and dissipation at the nonlinear stage of deformation is discussed.

Control of Nonlinear Stage of the Laminar-Turbulent Transition on an Airfoil by Distributed Suction through a Finely Perforated Surface

The results of experimental investigations of the influence of distributed suction through a finely perforated surface on the spatial development of perturbations of the straight wing boundary layer at the nonlinear stage of its evolution are presented in this article. It was found that distributed suction reduces the intensity of integral pulsations for natural disturbances by 90 times. A spectral analysis of disturbances showed a decrease in the intensity of high-frequency fluctuations in a narrow frequency band by two orders of magnitude for natural and forced disturbances generated by an external acoustic field. It was found that the distributed suction affects the average flow, namely, when the suction is on, the turbulent state of the boundary layer is eliminated, its separation near the trailing edge of the wing and the laminar flow is defined in the boundary layer.

AZIMUTHAL STABILITY OF TRICHEL PULSES AND CATHODE DIRECTED STREAMERS

The numerical simulations of negative corona discharge in Trichel pulse mode are carried out with the calculation of evolution of azimuthal perturbations. It is found the azimuthal instability with increment corresponding to avalanche development. This instability is suppressed at the nonlinear stage and does not lead to the process branching. The result is also applicable to the azimuthal instability of the cathode directed streamer, found earlier. The difference in their increments is followed from the difference in courses of the processess, which is discuss.

Attenuation Characteristics of Stress Wave Peak in Sandstone Subjected to Different Axial Stresses

To investigate the effect of axial stress on the attenuation characteristics of stress wave peaks, stress wave propagation experiments with small disturbance of a sandstone bar were carried out by a modified split Hopkinson pressure bar test system. Then, effects of axial stress on the waveform, attenuation rate, temporal-spatial attenuation characteristics, and attenuation sensitivity factor of the peak were studied. The results showed that the presence or absence of axial stress has a significant effect on the waveform. With axial stress loading, both temporal and spatial attenuation rates undergo similar development stages, “nonlinear stage + linear stage,” in which the demarcation stress (σ/σc) is 30%. Under the same axial stress, the peak decreases exponentially with the propagation time and distance with different attenuation intensities. With increasing axial stress, the temporal and spatial response intensities also experience “nonlinear stage + linear stage.” However, the temporal and spatial attenuation coefficients undergo three stages, first a dramatic decrease, then gentle development, and finally a sharp increase, in which demarcation stresses (σ/σc) are 30% and 55%. The defined attenuation sensitivity factor can well describe the attenuation sensitivity of peaks to different axial stresses. The conclusions can provide a theoretical reference for rock mass stability analysis in blasting excavation.