Quantum properties near the instability boundary in optomechanical system

The properties of the system near the instability boundary are very sensitive to external disturbances, which is important for amplifying some physical effects or improving the sensing accuracy. In this paper, the quantum properties near the instability boundary in a simple optomechanical system have been studied by numerical simulation. Calculations show that the transitional region connecting the Gaussian states and the ring states when crossing the boundary is sometimes different from the region centered on the boundary line, but it is more essential. The change of the mechanical Wigner function in the transitional region directly reflects its bifurcation behavior in classical dynamics. Besides, quantum properties, such as mechanical second-order coherence function and optomechanical entanglement, can be used to judge the corresponding bifurcation types and estimate the parameter width and position of the transitional region. The non-Gaussian transitional states exhibit strong entanglement robustness, and the transitional region as a boundary ribbon can be expected to replace the original classical instability boundary line in future applications.

The effect of G?rtler instability on hypersonic boundary layer transition

The evolution of Gortler vortices and its interaction with other instabilities are investigated in this paper. Both the Mack mode and the Gortler mode exist in hypersonic boundary-layer flows over concave surfaces, and their interactions are crucially important in boundary layer transition. We carry out a direct numerical simulation to explore the interaction between the GOrtler and the oblique Mack mode. The results indicate that the interaction between the forced Gortler mode and the oblique Mack mode promotes the onset of the transition. The forced oblique Mack mode is susceptible to nonlinear interaction. Because of the development of the GOrtler mode, the forced Mack mode and other harmonic modes are excited.

Selective enhancement of oblique waves caused by finite amplitude second mode in supersonic boundary layer

Nonlinear interactions of the two-dimensional （2D） second mode with oblique modes are studied numerically in a Mach 6.0 fiat-plate boundary layer, focusing on its selective enhancement effect on amplification of different oblique waves. Evolution of oblique modes with various frequencies and spanwise wavenumbers in the presence of 2D second mode is simulated successively, using a modified parabolized stability equation （PSE） method, which is able to simulate interaction of two modes with different frequen- cies efficiently. Numerical results show that oblique modes in a broad band of frequencies and spanwise wavenumbers can be enhanced by the finite amplitude 2D second mode instability wave. The enhancement effect is accomplished by interaction of the 2D second mode, the oblique mode, and a forced mode with difference frequency. Two types of oblique modes are found to be more amplified, i.e., oblique modes with frequency close to that of the 2D second mode and low-frequency first mode oblique waves. Each of them may correspond to one type of transition routes found in transition experiments. The spanwise wavenumber of the oblique wave preferred by the nonlinear interaction is also determined by numerical simulations.

Finescale Spiral Rainbands Modeled in a High-Resolution Simulation of Typhoon Rananim (2004)

Finescale spiral rainbands associated with Typhoon Rananim （2004） with the band length ranging from 10 to nearly 100 km and band width varying from 5 to 15 km are simulated using the Fifth-Generation NCAR/Penn State Mesoscale Model （MM5）. The finescale rainbands have two types： one intersecting the eyewall and causing damaging wind streaks, and the other distributed azimuthally along the inner edge of the eyewall with a relatively short lifetime. The formation of the high-velocity wind streaks results from the interaction of the azimuthal flow with the banded vertical vorticity structure triggered by tilting of the horizontal vorticity. The vertical advection of azimuthal momentum also leads to acceleration of tangential flow at a relatively high Mtitude. The evolution and structures of the bands are also examined in this study. Further investigation suggests that the boundary inflection points are related tightly to the development of the finescale rainbands, consistent with previous findings using simple symmetric models. In particular; the presence of the level of inflow reversal in the boundary layer is a crucial factor controlling the formation of these bands. The near-surface wavy peaks of vertical vorticity always follow the inflection points in radial flow. The mesoscale vortices and associated convective updrafts in the eyewall are considered to strengthen the activity of finescale bands, and the updrafts can trigger the formation of the bands as they reside in the environment with inflow reversal in the boundary layer.

EFFECTS OF BOUNDARY LAYER FRICTION AND TOPOGRAPHY ON THE INSTABILITY OF BAROCLINIC WAVES

In this paper,the simultaneous effects of boundary layer and topography on the instability of Eady wave are investigated by using a new parameterization of the vertical velocity at the top of PBL and the influences of the stratification of the PBL,roughness and the slope of terrain are shown.Furthermore,the effects of the boundary layer friction and topography on generalized Eady wave are also investigated.

On Parametric Instability Boundaries of Axially Moving Beams with Internal Resonance

In this paper, the instability boundaries of an axially moving viscoelastic beam due to parametric resonance are revisited for the internal resonance case. The relation between the time-dependent tension and the time-dependent axial speed is constructed, which provides a new model in the study of axially moving material with pulsation parameters. The instability boundaries caused by the combination of parametric and internal resonances are studied using the method of multiple time scales. Some strange instability boundaries are detected when the internal resonance is considered. The phenomenon of local zigzag boundary contour is explained from the viewpoint of modal interactions.

Generation of acoustic waves in the hypersonic boundary layer over a wavy wall

The effects of a wavy wall on a hypersonic boundary layer of a flared cone are investigated using experimental measurements and direct numerical simulations(DNSs). Non-contact optical measurements using a focused laser differential interferometer(FLDI) show that a wavy wall can significantly suppress the second mode, and multiple perturbations of new frequencies are generated over the wavy surface, which agrees well with numerical results. Using Lagrangian tracking of marked particles, it is demonstrated that the wavy wall geometry can induce mean flow oscillations while exciting acoustic waves. The frequencies of the excited disturbances over a wavy wall agree with the classical Rossiter model. The superposition of a disturbance propagating downstream and an acoustic wave propagating upstream at the same frequency but with different amplitudes and propagation velocities results in a spatial distribution with a streamwise-oscillatory pattern over the wavy surface. A simple two-wave superposition model that takes into account the phase velocities and wavenumbers of the convective disturbance and acoustic wave can well describe the modal behavior of excited disturbances over a wavy wall.

Linear stability analysis of interactions between mixing layer and boundary layer flows

The linear instabilities of incompressible confluent mixing layer and boundary layer were analyzed.The mixing layers include wake,shear layer and their combination.The mean velocity profile of confluent flow is taken as a superposition of a hyperbolic and exponential function to model a mixing layer and the Blasius similarity solution for a flat plate boundary layer.The stability equation of confluent flow was solved by using the global numerical method.The unstable modes associated with both the mixing and boundary layers were identified.They are the boundary layer mode,mixing layer mode 1（nearly symmetrical mode）and mode 2（nearly anti-symmetrical mode）.The interactions between the mixing layer stability and the boundary layer stability were examined.As the mixing layer approaches the boundary layer,the neutral curves of the boundary layer mode move to the upper left,the resulting critical Reynolds number decreases,and the growth rate of the most unstable mode increases.The wall tends to stabilize the mixing layer modes at low frequency.In addition,the mode switching behavior of the relative level of the spatial growth rate between the mixing layer mode 1 and mode 2 with the velocity ratio is found to occur at low frequency.

Feedback control of boundary layer Tollmien-Schlichting waves using a simple model-based controller

The attenuation of spatially evolving instability Tollmien-Schlichting(T-S)waves in the boundary layer of a flat plate with zero pressure gradients using an active feedback control scheme is theoretically and numerically investigated.The boundary layer is excited artificially by various perturbations to create a three-dimensional field of instability waves.Arrays of actuators and sensors are distributed locally at the wall surface and connected together via a feedback controller.The key elements of this feedback control are the determination of the dynamic model of the flat plate boundary layer between the actuators and the sensors,and the design of the model-based feedback controller.The dynamic model is established based on the linear stability calculation which simulates the three-dimensional input-output behaviour of the boundary layer.To simplify the control problem,an uncoupled control mode of the dynamic model is made to capture only those dynamics that have greatest influences on the input-output behaviour.A Proportional-Integral-Derivative(PID)controller,i.e.a lead-lag compensator,combining with a standard Smith predictor is designed based on the system stability criterion and the specifications using frequency-response methods.Good performance of the feedback control with the uncoupled control mode is demonstrated by the large reduction of the three-dimensional disturbances in the boundary layer.This simple feedback control is realistic and competitive in a practical implementation of T-S wave cancellation using a limited number of localised sensors and actuators.