The mode number dependence of neutral stability of cross-waves

1990 ◽  
Vol 9 (3) ◽  
pp. 148-152 ◽  
Author(s):  
L. Shemer ◽  
S. Lichter
Keyword(s):  
Mode Number ◽  
Neutral Stability ◽  
Cross Waves

Mode-number shifting of nonlinear cross-waves

1987 ◽  
Vol 35 (12) ◽  
pp. 5282-5284 ◽  
Author(s):  
Seth Lichter ◽  
William B. Underhill
Keyword(s):  
Mode Number ◽  
Cross Waves

On the neutral stability of cross‐waves

1989 ◽  
Vol 1 (7) ◽  
pp. 1128-1132 ◽  
Author(s):  
E. Kit ◽  
L. Shemer
Keyword(s):  
Neutral Stability ◽  
Cross Waves

scholarly journals Modulated, frequency-locked, and chaotic cross-waves

1991 ◽  
Vol 225 ◽  
pp. 371-394 ◽  
Author(s):  
William B. Underhill ◽  
Seth Lichter ◽  
Andrew J. Bernoff
Keyword(s):  
Modulational Instability ◽  
Rectangular Channel ◽  
Wave Structure ◽  
Mode Analysis ◽  
Spanwise Direction ◽  
Neutral Stability ◽  
Coupled Mode ◽  
Weakly Coupled ◽  
Arnold Tongues ◽  
Cross Waves

Measurements were made of the wave height of periodic, quasi-periodic, and chaotic parametrically forced cross-waves in a long rectangular channel. In general, three frequencies (and their harmonics) may be observed: the subharmonic frequency and two slow temporal modulations — a one-mode instability associated with streamwise variation and a sloshing motion associated with spanwise variation. Their interaction, as forcing frequency, f, and forcing amplitude, a, were varied, produced a pattern of Arnold tongues in which two or three frequencies were locked. The overall picture of frequency-locked and -unlocked regions is explained in terms of the Arnold tongues predicted by the circle-map theory describing weakly coupled oscillators. Some of the observed tongues are apparently folded by a subcritical bifurcation, with the tips of the tongues lying on the unstable manifold folded under the observed stable manifold. Near the intersection of the neutral stability curves for two adjacent modes, a standing wave localized on one side of the tank was observed in agreement with the coupled-mode analysis of Ayanle, Bernoff & Lichter (1990). At large cross-wave amplitudes, the spanwise wave structure apparently breaks up, because of modulational instability, into coherent soliton-like structures that propagate in the spanwise direction and are reflected by the sidewalls.

scholarly journals Magnetoelastic Coupling and Delta-E Effect in Magnetoelectric Torsion Mode Resonators

Sensors ◽  
2021 ◽  
Vol 21 (6) ◽  
pp. 2022
Author(s):  
Benjamin Spetzler ◽  
Elizaveta V. Golubeva ◽  
Ron-Marco Friedrich ◽  
Sebastian Zabel ◽  
Christine Kirchhof ◽  
...  
Keyword(s):  
Low Frequency ◽  
High Sensitivity ◽  
Element Model ◽  
Mode Number ◽  
Frequency Change ◽  
General Description ◽  
Resonance Modes ◽  
Field Sensor ◽  
Magnetic Sensitivity ◽  
Bending Modes

Magnetoelectric resonators have been studied for the detection of small amplitude and low frequency magnetic fields via the delta-E effect, mainly in fundamental bending or bulk resonance modes. Here, we present an experimental and theoretical investigation of magnetoelectric thin-film cantilevers that can be operated in bending modes (BMs) and torsion modes (TMs) as a magnetic field sensor. A magnetoelastic macrospin model is combined with an electromechanical finite element model and a general description of the delta-E effect of all stiffness tensor components Cij is derived. Simulations confirm quantitatively that the delta-E effect of the C66 component has the promising potential of significantly increasing the magnetic sensitivity and the maximum normalized frequency change ∆fr. However, the electrical excitation of TMs remains challenging and is found to significantly diminish the gain in sensitivity. Experiments reveal the dependency of the sensitivity and ∆fr of TMs on the mode number, which differs fundamentally from BMs and is well explained by our model. Because the contribution of C11 to the TMs increases with the mode number, the first-order TM yields the highest magnetic sensitivity. Overall, general insights are gained for the design of high-sensitivity delta-E effect sensors, as well as for frequency tunable devices based on the delta-E effect.

scholarly journals Analysis of the unstable Tollmien–Schlichting mode on bodies with a rounded leading edge using the parabolized stability equation

2009 ◽  
Vol 623 ◽  
pp. 167-185
Author(s):  
M. R. TURNER ◽  
P. W. HAMMERTON
Keyword(s):  
Asymptotic Theory ◽  
Free Stream ◽  
Leading Edge ◽  
Adverse Pressure Gradient ◽  
Reynolds Numbers ◽  
Neutral Stability ◽  
S Wave ◽  
Stability Equation ◽  
Stability Point ◽  
Tollmien Schlichting

The interaction between free-stream disturbances and the boundary layer on a body with a rounded leading edge is considered in this paper. A method which incorporates calculations using the parabolized stability equation in the Orr–Sommerfeld region, along with an upstream boundary condition derived from asymptotic theory in the vicinity of the leading edge, is generalized to bodies with an inviscid slip velocity which tends to a constant far downstream. We present results for the position of the lower branch neutral stability point and the magnitude of the unstable Tollmien–Schlichting (T-S) mode at this point for both a parabolic body and the Rankine body. For the Rankine body, which has an adverse pressure gradient along its surface far from the nose, we find a double maximum in the T-S wave amplitude for sufficiently large Reynolds numbers.

scholarly journals Evaluation of a global aerosol microphysics model against size-resolved particle statistics in the marine atmosphere

2007 ◽  
Vol 7 (8) ◽  
pp. 2073-2090 ◽  
Author(s):  
D. V. Spracklen ◽  
K. J. Pringle ◽  
K. S. Carslaw ◽  
G. W. Mann ◽  
P. Manktelow ◽  
...  
Keyword(s):  
Marine Boundary Layer ◽  
Geometric Mean ◽  
Carbonaceous Material ◽  
Mode Number ◽  
Anthropogenic Sources ◽  
Substantial Contribution ◽  
Particle Size Range ◽  
Accumulation Mode ◽  
Tropospheric Aerosol ◽  
Aitken Mode

Abstract. A statistical synthesis of marine aerosol measurements from experiments in four different oceans is used to evaluate a global aerosol microphysics model (GLOMAP). We compare the model against observed size resolved particle concentrations, probability distributions, and the temporal persistence of different size particles. We attempt to explain the observed sub-micrometre size distributions in terms of sulfate and sea spray and quantify the possible contributions of anthropogenic sulfate and carbonaceous material to the number and mass distribution. The model predicts a bimodal size distribution that agrees well with observations as a grand average over all regions, but there are large regional differences. Notably, observed Aitken mode number concentrations are more than a factor 10 higher than in the model for the N Atlantic but a factor 7 lower than the model in the NW Pacific. We also find that modelled Aitken mode and accumulation mode geometric mean diameters are generally smaller in the model by 10–30%. Comparison with observed free tropospheric Aitken mode distributions suggests that the model underpredicts growth of these particles during descent to the marine boundary layer (MBL). Recent observations of a substantial organic component of free tropospheric aerosol could explain this discrepancy. We find that anthropogenic continental material makes a substantial contribution to N Atlantic MBL aerosol, with typically 60–90% of sulfate across the particle size range coming from anthropogenic sources, even if we analyse air that has spent an average of >120 h away from land. However, anthropogenic primary black carbon and organic carbon particles (at the emission size and quantity assumed here) do not explain the large discrepancies in Aitken mode number. Several explanations for the discrepancy are suggested. The lack of lower atmospheric particle formation in the model may explain low N Atlantic particle concentrations. However, the observed and modelled particle persistence at Cape Grim in the Southern Ocean, does not reveal a diurnal cycle consistent with a photochemically driven local particle source. We also show that a physically based cloud drop activation scheme better explains the observed change in accumulation mode geometric mean diameter with particle number.

A Research of Intra Prediction Coding with Variance of Prediction Mode Number

2015 ◽  
Vol 719-720 ◽  
pp. 1177-1183
Author(s):  
Wei Zheng ◽  
Long Ye ◽  
Jing Ling Wang ◽  
Qin Zhang
Keyword(s):  
State Of The Art ◽  
Intra Prediction ◽  
Mode Number ◽  
Bit Rate ◽  
Rate Reduction ◽  
Directional Information ◽  
Mode Index ◽  
Residual Image ◽  
Prediction Mode ◽  
Direction Information

Intra prediction is a key step in H.264/AVC to improve the coding performance with the idea that removing the directional redundancy among neighboring blocks. In order to cover more directional information existed in the image frames, there are usually many prediction modes can be selected in the state-of-the-art coding frameworks, but more bits are also needed to encode the prediction mode index information, then how to achieve the maximum overall bit-rate reduction became a problem. In this paper, 16 kinds of prediction modes are adopted by considering the direction information for 8x8 image blocks. Through calculating the bit-rate both for the mode index and residual image under different number of prediction modes, we obtain the most suitable prediction mode number relatively from the graphs. Experimental results show that, with the increase of prediction mode number, the residual information decreases obviously, and the sum of residual information and prediction mode index information also decreases but levels off after reaching a certain mode number, even has an obviously rising trend.

Effect of poloidal equilibrium flow and pressure gradient on the m/n = 2/1 tearing mode

2022 ◽  
Author(s):  
Yue Ming ◽  
Deng Zhou ◽  
Jinfang Wang
Keyword(s):  
Pressure Gradient ◽  
Stability Index ◽  
Plasma Pressure ◽  
Mode Number ◽  
Pressure Perturbation ◽  
Equilibrium Flow ◽  
Tearing Mode ◽  
Mode Instability ◽  
Mode Stability ◽  
Adverse Influence

Abstract The effect of equilibrium poloidal flow and pressure gradient on the m/n = 2/1 (m is the poloidal mode number and n is the toroidal mode number) tearing mode instability for tokamak plasmas is investigated. Based on the condition of ≠0 ( is plasma pressure), the radial part of motion equation is derived and approximately solved for large poloidal mode numbers (m). By solving partial differential equation (Whittaker equation) containing second order singularity, the tearing mode stability index Δ′ is obtained. It is shown that, the effect of equilibrium poloidal flow and pressure gradient has the adverse effect on the tearing mode instability when the pressure gradient is nonzero. The poloidal equilibrium flow with pressure perturbation partially reduces the stability of the classical tearing mode. But the larger pressure gradient in a certain poloidal flow velocity range can abate the adverse influence of equilibrium poloidal flow and pressure gradient. The numerical results do also indicate that the derivative of pressure gradient has a significant influence on the determination of instability region of the poloidal flow with pressure perturbation.

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