Linear Analysis of Longshore Currents Instability over Mild Slopes

Longshore current instability is important to nearshore hydrodynamic and sediment transport. This paper investigates the longshore current instability growth model based experimental data with different velocity profiles of slopes1:100 and 1:40 by adopting a linear shear instability model with the bottom friction effects. The results show that:(1)Only backshear mode exists in the instability of longshore current for slope 1:40 and frontshear and backshear modes may exist slope 1:100.(2) The peaks of linear instability growth mode for slope 1:100 correspond to three cases: the dominant peak is formed by the joint action of both frontshear and backshear, or by backshear alone without the existence of the smaller peak or formed by either the frontshear or backshear.(3) Bottom friction can decrease the corresponding unstable growth rate but it cannot change the unstable fluctuation period. The results of fluctuation period, wavelength and spatial variation obtained by the analysis of linear shear instability are in good agreement with experimental results.

Gyroscopic modes decoupling method in parametric instability analysis of gyroscopic systems

Traditional procedures to treat vibrations of gyroscopic continua involve direct application of perturbation methods to a system with both a strong gyroscopic term and other weakly coupled terms.In this study,a gyroscopic modes decoupling method is used to obtain an equivalent system with decoupled gyroscopic modes having only weak couplings.Taking the axially moving string as an example,the instability boundaries in the vicinity of parametric resonances are detected using both the traditional coupled gyroscopic system and our system with decoupled gyroscopic modes,and the results are compared to show the advantages and disadvantages of each method.

Effect of wall-cooling on Mack-mode instability in high speed flat-plate boundary layers

The instability of the Mack mode is destabilized by wall-cooling in a high speed boundary layer. The aim of this paper is to study the mechanism of the wall cooling effect on the Mack mode instability by numerical methods. It is shown that the wall-cooling can destabilize the Mack mode instability, similar to the previous conclusions with the exception that the Mack mode instability can be stabilized by wall-cooling if the wall temperature is extremely low. The reversed wall temperature is related to a freestream condition. If the Mach number increases to a large enough value, e.g., about 7, the reversed wall temperature will tend to be zero. It seems that the Mack mode instability is determined by the region between the boundary layer edge and the critical layer. When the wall temperature decreases, this region becomes wider, and the boundary layer becomes more unstable. Additionally, a relative supersonic unstable mode can be observed when the velocity of the critical layer is less than 1 - liMa or is cancelled by the wall-cooling effect. These results provide a deeper understanding on the wall-cooling effect in high speed boundary layers.

Mode coupling in nonlinear Kelvin-Helmholtz instability

This paper investigates the interaction of a small number of modes in the two-fluid Kelvin-Helmholtz instability at the nonlinear regime by using a two-dimensional hydrodynamic code. This interaction is found to be relatively long range in wave-number space and also it acts in both directions, i.e. short wavelengths affect long wavelengths and vice versa. There is no simple equivalent transformation from a band of similar modes to one mode representing their effective amplitude. Three distinct stages of interaction have been identified.

Generation of VLF Mode Instability by Generalized Distribution Function in the Presence of Parallel AC Electric Field in Uranus

VLF （very low frequency） mode instability with parallel AC electric field was studied for generalized loss-cone distribution with an index j, which is reducible to bi-Maxwellian, loss- cone and delta function for j = 0, 1 and co. The particle trajectories and dispersion relation are obtained through a kinetic approach and method of characteristic solutions. The calculations are compared with the observations of low frequency waves of Voyager 2. The growth rate of plasma parameters suited to magnetosphere of Uranus is obtained. It is inferred that the magnitude as well as frequency of AC （alternating current） field increases the growth rate and widen the band width significantly. In addition to temperature anisotropy, particles in plasma having generalized loss-cone distribution provide an additional source of energy.

Experiments of Brittle-Plastic Transition and Instability Modes of Juyongguan Granite at Different Temperatures and Pressures

Three groups of experiments on brittle-plastic transition and instability modes of granite were performed in a triaxial vessel with solid pressure medium at high temperature and high pressure. The results of experiments show that brittle faulting is the major failure mode at temperature <300℃, but crystal-plastic deformation is dominate at temperature >800℃, and there is a transition with increasing temperature from semi-brittle faulting to cataclastic flow and semi-brittle flow at temperatures of 300～800℃. So, temperature is the most influential factor in brittle-plastic transition of granite and confining pressure is the second factor. The results also show that progressive failure of granite occurs at lower pressure or high temperature where there is crystal plasticity, and sudden instability occurs at room temperature and high pressure (>300MPa) or high temperature and great pressure(550℃600MPa ～650℃700MPa), and a broad regime of quasi-sudden instability exists between the T-P condition of progressive failure and sudden instability. So, instability modes of granite depend simultaneously on the pressure and temperature.

Effects of resonant magnetic perturbation on the instability of single tearing mode with non-shear flow

Non-shear flow can change the O-point position of a magnetic island, and thus it may play an important role in the effects of resonant magnetic perturbation(RMP) on the single tearing mode. We employ the nonlinear magnetohydrodynamics model in a slab geometry to investigate how RMP affects the single tearing mode instability with non-shear flow. It is found that the driving and suppressing effects of RMP on single tearing mode instability will appear alternately. When the flow velocity is small, the suppressing effect plays a major role through the development of the mode, and the tearing mode instability will be suppressed. With the flow velocity increasing, the driving effect will increase, while the suppressing effect will decrease. When the two effects reach equilibrium, the tearing mode will become stable.

Discrete modulational instability and bright localized spin wave modes in easy-axis weak ferromagnetic spin chains involving the next-nearest-neighbor coupling

We report a theoretical work on the properties of modulational instability and bright type nonlinear localized modes in one-dimensional easy-axis weak ferromagnetic spin lattices involving next-nearest-neighbor couplings.With a linear stability analysis, we calculate the growth rates of the modulational instability, and plot the instability regions.When the strength of the next-nearest-neighbor coupling is large enough, two new asymmetric modulational instability regions appear near the boundary of the first Brillouin zone.Furthermore, analytical forms of the bright nonlinear localized modes are constructed by means of a quasi-discreteness approach.The influence of the next-nearest-neighbor coupling on the Brillouin zone center mode and boundary mode are discussed.In particular, we discover a reversal phenomenon of the propagation direction of the Brillouin zone boundary mode.

Phase Effect on Mode Coupling in Kelvin—Helmholtz Instability for Two-Dimensional Incompressible Fluid

This paper studies the phase effect in mode coupling of Kelvin-Helmholtz instability in two-dimensionalincompressible fluid.It is found that there is an important growth phenomenon of every mode in the mode couplingprocess.The growth changes periodically with phase difference and in the condition of our simulation the period is about0.7π.The period characteristic is apparent in all stage of the mode coupling process,especially in the relatively laterstage.

Application of Galerkin spectral method for tearing mode instability

Magnetic reconnection and tearing mode instability play a critical role in many physical processes.The application of Galerkin spectral method for tearing mode instability in two-dimensional geometry is investigated in this paper.A resistive magnetohydrodynamic code is developed,by the Galerkin spectral method both in the periodic and aperiodic directions.Spectral schemes are provided for global modes and local modes.Mode structures,resistivity scaling,convergence and stability of tearing modes are discussed.The effectiveness of the code is demonstrated,and the computational results are compared with the results using Galerkin spectral method only in the periodic direction.The numerical results show that the code using Galerkin spectral method individually allows larger time step in global and local modes simulations,and has better convergence in global modes simulations.

Prediction of Instability Separation Modes and Its Application in Practical Dynamic Security Region

The transient critical boundary of dynamic security region (DSR) can be approximated by a few hyper planes correlated with instability separation modes. A method to fast predict instability separation modes is proposed for DSR calculation in power injection space. The method identifies coherent generation groups by the developed K-medoids algorithm, taking a similarity matrix derived from the reachability Grammian as the index. As an experimental result, reachability Grammian matrices under local injections are approximately invariant. It indicates that the generator coherency identifications are nearly consistent for different injections. Then instability separation modes can be predicted at the normal operating point, while average initial acceleration is considered as the measure of the critical generator group to amend the error. Moreover, based on these predicted instability separation modes, a critical point search strategy for DSR calculation is illustrated in the reduced injection space of the critical generators. The proposed method was evaluated using New England Test System, and the computation accuracy and speed in determining the practical DSR were improved.

On the mechanism by which nose bluntness suppresses second-mode instability

A physical mechanism by which nose bluntness suppresses second-mode instability is proposed.Considered are 7 degree half-angle straight cones with nose bluntness radii of 0.15 mm, 3.556 mm,5 mm, 9.525 mm, 12.7 mm and 25.4 mm at tunnel conditions relevant to the AFOSR-Notre Dame Large Mach 6 Quiet Tunnel. It is shown that second-mode suppression is achieved via entropy layer modulation of the basic state density gradient. A weakening of the density gradient disrupts the acoustic resonance necessary to sustain second-mode growth. These results are consistent with the thermoacoustic interpretation which posits that second-mode instability can be modeled as thermoacoustic resonance of acoustic energy trapped within an acoustic impedance well.Furthermore, the generalized inflection point criterion of Lees and Lin is applied to develop a criterion for the existence of second-mode instability based on the strength of the basic state density gradient.

INSTABILITY OF HAGEN-POISEUILLE FLOW FOR NON-AXISYMMETRIC MODE

An investigation is described for instability problem of flow through a pipe of circular cross section. As a disturbance motion, we consider a general non-axisym-metric mode. An associated amplitude or modulation equation has been derived for this disturbance motion. This equation belongs to a diffusion type.The coefficient of it can be negative while Reynolds number increases, because of the complex interaction between molecular diffusion and convection. The negative diffusivity, when it occurs, causes a concentration and focussing of energy within decaying slugs, acting as a role of reversing natural decays.

Mode-Coupling Analysis of Parametric Decay Instability in Magnetized Plasmas

In this paper, derived from Maxwell and fluid equations of plasmas, unified nonlinear wave equations are used to describe the parametric decay instability （PDI） in magnetized plasmas, and in view of mode-coupling, we can obtain all the possible PDI channels. By solving the nonlinear equations with a mode-coupling method, we obtain the growth rate of the PDI, of which all of the three waves are ordinary mode （O-mode） or extraordinary mode （X-mode） wave. Under the dipole approximation, an explicit formula of the growth rate of the X-mode and the condition of the equilibrium density scale are obtained. According to the existence conditions of three X-mode waves, this kind of instability might exist in ECRH with the second harmonic X-mode wave.

Power of all-fiber amplifier increasing from 1030 W to 2280 W through suppressing mode instability by increasing the seed power

In this work, we investigate suppressing mode instability in detail by varying the seed power in a large mode area all-fiber amplifier with a fiber core diameter of 25 μm. The transverse mode instability(TMI) thresholds are systematically measured for different seed power. Our experimental results reveal that increasing the seed power has a positive influence on enhancing the output power before the TMI effect appears, and finally the TMI threshold is approximately doubled from1030 W to 2280 W when the seed power is increased from 27 W to 875 W. Almost 84.7% slope efficiency is reached with different seed power before the TMI threshold power. During our operation, we also find that in this type of LMA fiber the beam quality of the amplifier is degraded gradually instead of a sudden change as the pump power increases.

Magnetic diagnostics for magnetohydrodynamic instability research and the detection of locked modes in J-TEXT

Magnetohydrodynamic(MHD)instabilities are widely observed during tokamak plasma operation.Magnetic diagnostics provide important information which supports the understanding and control of MHD instabilities.This paper presents the current status of the magnetic diagnostics dedicated to measuring MHD instabilities at the J-TEXT tokamak;the diagnostics consist of five Mirnov probe arrays for measuring high-frequency magnetic perturbations and two saddle-loop arrays for low-frequency magnetic perturbations,such as the locked mode.In recent years,several changes have been made to these arrays.The structure of the probes in the poloidal Mirnov arrays has been optimized to improve their mechanical strength,and the number of in-vessel saddle loops has also been improved to support better spatial resolution.Due to the installation of high-field-side(HFS)divertor targets in early 2019,some of the probes were removed,but an HFS Mirnov array was designed and installed behind the targets.Owing to its excellent toroidal symmetry,the HFS Mirnov array has,for the first time at J-TEXT,provided valuable new information about the locked mode and the quasi-static mode(QSM)in the HFS.Besides,various groups of magnetic diagnostics at different poloidal locations have been systematically used to measure the QSM,which confirmed the poloidal mode number m and the helical structure of the QSM.By including the HFS information,the 2/1 resonant magnetic perturbation(RMP)-induced locked mode was measured to have a poloidal mode number m of~2.

Instability of the interface in two-layer flows with large viscosity contrast at small Reynolds numbers

The Kelvin-Helmholtz instability is believed to be the dominant instability mechanism for free shear flows at large Reynolds numbers. At small Reynolds numbers, a new instability mode is identified when the temporal instability of parallel viscous two fluid mixing layers is extended to current-fluid mud systems by considering a composite error function velocity profile. The new mode is caused by the large viscosity difference between the two fluids. This interfacial mode exists when the fluid mud boundary layer is sufficiently thin. Its performance is different from that of the Kelvin-Helmholtz mode. This mode has not yet been reported for interface instability problems with large viscosity contrasts. These results are essential for further stability analysis of flows relevant to the breaking up of this type of interface.

Three-Dimensional Instability of Flow Around Two Circular Cylinders in Tandem Arrangement

The spatial evolution of vortices and transition to three-dimensionality in the wake of two circular cylinders in tandem arrangement have been numerically studied. An improved virtual body method developed from the virtual boundary method is used here. A Reynolds number range between 220 and 270 has been considered, and the spacing between two cylinders is selected as L/D=3 and L/D=3.5. When L/D=3, the secondary vortices of Mode-A are seen to appear at Re=240 and persist over the range of the Reynolds number of 240～270. When L/D=3.5, the similar critical Reynolds number has been found at Re=250. No obvious discontinuity has been found in the Strouhal-Reynolds number relationship, and this is different from three-dimensional flow around a single cylinder at the critical Reynolds number. The spanwise wavelength is about four times the diameter of the cylinder, and it is the characteristic wavelength for Mode-A instability. This paper can give some foremost insight into the three-dimensional instability of flow by complicated geometrical configuration.

ON SECONDARY INSTABILITY WITH RESPECT TO THREE DIMENSIONAL SUBHARMONIC DISTURBANCES IN BOUNDARY LAYER

The general equations of secondary instability with respect to three-dimensional subharmonic disturbances are derived and applied to Blasius boundary layer in the present paper.The theoretical results of evolution and spatial distribution of subharmonic disturbances are compared with experimental data.The re- suits show the important role of the process of route to transition in low-disturbance environments,and indi- cate that spatial mode is more rational than temporal mode.

Parametric Instability Analysis of Deepwater Top-Tensioned Risers Considering Variable Tension Along the Length

Parametric instability of a riser is caused by fluctuation of its tension in time due to the heave motion of floating platform. Many studies have tackled the problem of parametric instability of a riser with constant tension. However, tension in the riser actually varies linearly from the top to the bottom due to the effect of gravity. This paper presents the parametric instability analysis of deepwater top-tensioned risers(TTR) considering the linearly varying tension along the length. Firstly, the governing equation of transverse motion of TTR under parametric excitation is established. This equation is reduced to a system of ordinary differential equations by using the Galerkin method. Then the parametric instability of TTR for three calculation models are investigated by applying the Floquet theory. The results show that the natural frequencies of TTR with variable tension are evidently reduced, the parametric instability zones are significantly increased and the maximum allowable amplitude of platform heave is much smaller under the same damping; The nodes and antinodes of mode shape are no longer uniformly distributed along the axial direction and the amplitude also changes with depth, which leads to coupling between the modes. The combination resonance phenomenon occurs as a result of mode coupling, which causes more serious damage.