The effect of initial amplitude and convergence ratio on instability development and deposited fluctuating kinetic energy in the single-mode Richtmyer–Meshkov instability in spherical implosions

AbstractThe Agulhas Current intermittently undergoes dramatic offshore excursions from its mean path because of the downstream passage of mesoscale solitary meanders or Natal pulses. New observations and analyses are presented of the variability of the current and its meanders using mooring observations from the Agulhas Current Time-Series Experiment (ACT) near 34°S. Using a new rotary EOF method, mesoscale meanders and smaller-scale meanders are differentiated and each captured in a single mode of variance. During mesoscale meanders, an onshore cyclonic circulation and an offshore anticyclonic circulation act together to displace the jet offshore, leading to sudden and strong positive conversion of kinetic energy from the mean flow to the meander via nonlinear interactions. Smaller meanders are principally represented by a single cyclonic circulation spanning the entire jet that acts to displace the jet without extracting kinetic energy from the mean flow. Synthesizing in situ observations with altimeter data leads to an account of the number of mesoscale meanders at 34°S: 1.6 yr−1 on average, in agreement with a recent analysis by Rouault and Penven (2011) and significantly less than previously understood. The links between meanders and the arrival of Mozambique Channel eddies or Madagascar dipoles at the western boundary upstream are found to be robust in the 20-yr altimeter record. Yet, only a small fraction of anomalies arriving at the western boundary result in meanders, and of those, two-thirds can be related to ring shedding. Most Agulhas rings are shed independently of meanders.

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Modulational Interactions of Two Monochromatic Waves and Packets of Random Waves

Australian Journal of Physics ◽

10.1071/ph940375 ◽

1994 ◽

Vol 47 (4) ◽

pp. 375 ◽

Cited By ~ 4

Author(s):

SV Vladimirov ◽

SI Popel

Keyword(s):

Modulational Instability ◽

Single Mode ◽

Maximum Effect ◽

Random Wave ◽

Random Waves ◽

Third Order ◽

Langmuir Waves ◽

Coupled Equations ◽

Instability Development ◽

Field Correlation

The modulational instability of Langmuir waves in unmagnetised plasmas is reviewed for the cases when a pump consist of two monochromatic or a large number of random modes. It is demonstrated that the correct theory for the modulational instability operates with 'renormalised' equations for the linear dielectric function as well as for the effective third-order plasma response. This renormalisation is due to so-called interference terms. The appearance of interference terms is a specific feature of the multi-mode modulational instability in comparison with the well-known instability of a single mode. All calculations use a simple and universal formalism including new methods developed for description of the modulational effects in arbitrary media. The modulational instability of two pump Langmuir modes is considered for the case of comparatively small instability rates, when 'renormalised' expressions for linear and nonlinear plasma polarisation responses provide the maximum effect on the instability development. For instabilities of the broad spectra of random waves, the integral equations are presented for perturbations of wave field correlation functions. In the description of the modulational instability of random wave packets these equations play the same role as the set of coupled equations for the fields of modulational perturbations in the case of two monochromatic pumps. Rates and thresholds of the instabilities are found in various limits.

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Richtmyer–Meshkov instability on a quasi-single-mode interface

Journal of Fluid Mechanics ◽

10.1017/jfm.2019.416 ◽

2019 ◽

Vol 872 ◽

pp. 729-751 ◽

Cited By ~ 7

Author(s):

Yu Liang ◽

Zhigang Zhai ◽

Juchun Ding ◽

Xisheng Luo

Keyword(s):

Nonlinear Model ◽

Small Amplitude ◽

Linear Growth ◽

Single Mode ◽

High Order ◽

Initial Amplitude ◽

Previous Theory ◽

Weakly Nonlinear ◽

Nonlinear Stage ◽

Amplitude Growth

Experiments on Richtmyer–Meshkov instability of quasi-single-mode interfaces are performed. Four quasi-single-mode air/$\text{SF}_{6}$ interfaces with different deviations from the single-mode one are generated by the soap film technique to evaluate the effects of high-order modes on amplitude growth in the linear and weakly nonlinear stages. For each case, two different initial amplitudes are considered to highlight the high-amplitude effect. For the single-mode and saw-tooth interfaces with high initial amplitude, a cavity is observed at the spike head, providing experimental evidence for the previous numerical results for the first time. For the quasi-single-mode interfaces, the fundamental mode is the dominant one such that it determines the amplitude linear growth, and subsequently the impulsive theory gives a reasonable prediction of the experiments by introducing a reduction factor. The discrepancy in linear growth rates between the experiment and the prediction is amplified as the quasi-single-mode interface deviates more severely from the single-mode one. In the weakly nonlinear stage, the nonlinear model valid for a single-mode interface with small amplitude loses efficacy, which indicates that the effects of high-order modes on amplitude growth must be considered. For the saw-tooth interface with small amplitude, the amplitudes of the first three harmonics are extracted from the experiment and compared with the previous theory. The comparison proves that each initial mode develops independently in the linear and weakly nonlinear stages. A nonlinear model proposed by Zhang & Guo (J. Fluid Mech., vol. 786, 2016, pp. 47–61) is then modified by considering the effects of high-order modes. The modified model is proved to be valid in the weakly nonlinear stage even for the cases with high initial amplitude. More high-order modes are needed to match the experiment for the interfaces with a more severe deviation from the single-mode one.

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XI.—Correlations in alpha-Particle-accompanied fission

Proceedings of the Royal Society of Edinburgh Section A Mathematical and Physical Sciences ◽

10.1017/s0080454100008633 ◽

1971 ◽

Vol 69 (2) ◽

pp. 149-164

Author(s):

N. Feather

Keyword(s):

Kinetic Energy ◽

Single Mode ◽

Neutron Number ◽

Particle Energy ◽

Ternary Fission ◽

Classical Description ◽

Independent Variables ◽

The Moment ◽

Electrostatic Potential Energy ◽

Nuclear Configuration

SynopsisThe attempt is made to exhibit the necessary correlations between fragment excitation (or prompt neutron number), fragment kinetic energy, and a-particle energy, in α-particle-accompanied ternary fission. Treating a single mode of mass and charge division on the assumption that the ternary process develops directly out of an intermediate binary phase, and using the mutual electrostatic potential energy of the nascent binary fragments of this phase and the additional kinetic energy developed at the moment of α-particle emission as independent variables, various formal results are obtained and discussed in the light of the experimental evidence.In terms of a classical description, it appears likely that (for a given mode of division) the nuclear configuration at a-particle release in ternary fission is subject to much smaller variations than is the nuclear configuration at scission in binary fission in the corresponding mode. Possible inadequacies of this classical description are very briefly discussed.

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An experimental study of the high Mach number and high initial-amplitude effects on the evolution of the single-mode Richtmyer–Meshkov instability

Laser and Particle Beams ◽

10.1017/s0263034603213082 ◽

2003 ◽

Vol 21 (3) ◽

pp. 341-346 ◽

Cited By ~ 8

Author(s):

O. SADOT ◽

A. RIKANATI ◽

D. ORON ◽

G. BEN-DOR ◽

D. SHVARTS

Keyword(s):

Shock Wave ◽

Experimental Study ◽

Mach Number ◽

Small Amplitude ◽

Single Mode ◽

Incident Shock ◽

Initial Amplitude ◽

High Mach Number ◽

High Mach ◽

Late Stages

The present article describes an experimental study that is a part of an integrated theoretical (Rikanatiet al.2003) and experiential investigation of the Richtmyer–Meshkov (RM) hydrodynamic instability that develops on a perturbed contact surface by a shock wave. The Mach number and the high initial-amplitude effects on the evolution of the single-mode shock-wave-induced instability were studied. To distinguish between the above-mentioned effects, two sets of shock-tube experiments were conducted: high initial amplitudes with a low-Mach incident shock and small amplitude initial conditions with a moderate-Mach incident shock. In the high-amplitude experiments a reduction of the initial velocity with respect to the linear prediction was measured. The results were compared to those predicted by a vorticity deposition model and to previous experiments with moderate and high Mach numbers done by others and good agreement was found. The result suggested that the high initial-amplitude effect is the dominant one rather than the high Mach number effect as suggested by others. In the small amplitude–moderate Mach numbers experiments, a reduction from the impulsive theory was noted at late stages. It is concluded that while high Mach number effect can dramatically change the behavior of the flow at all stages, the high initial-amplitude effect is of minor importance at the late stages. That result is supported by a two-dimensional numerical simulation.

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Transient spectrum of sin2-pulsed driven harmonic oscillator

Journal of Nonlinear Optical Physics & Materials ◽

10.1142/s0218863514500520 ◽

2014 ◽

Vol 23 (04) ◽

pp. 1450052

Author(s):

S. S. Hassan ◽

R. A. Alharbey ◽

H. Al-Zaki

Keyword(s):

Coherent State ◽

Harmonic Oscillator ◽

Pulse Shape ◽

Coupled System ◽

Single Mode ◽

Central Peak ◽

Hole Burning ◽

Initial Amplitude ◽

Fluorescent Spectrum ◽

Initial Excitation

Exact analytical results are derived for the coupled system of nondissipative single mode quantized harmonic oscillator (HO) and arbitrary pulse shape. Specifically, for a sin2-pulse shape, the transient fluorescent spectrum is obtained in the general case of initial coherent state |α〉 of the HO. The dominant central Lorentzian is surrounded by weak oscillations due to the larger number of sequential pulses which get amplified asymmetrically in the nonresonant case as a result of balancing and interference processes between the initial excitation (|α2|) and the strength of the exciting pulse. Further pronounced oscillations is noticed with "hole burning" structure in the central peak due to nonzero phase of the initial amplitude (α).

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