scholarly journals Explosive instability due to flow over a rippled bottom

2019 ◽  
Vol 26 (3) ◽  
pp. 283-290
Author(s):  
Anirban Guha ◽  
Raunak Raj
Keyword(s):  
Normal Mode ◽  
Internal Waves ◽  
Large Amplitude ◽  
Tidal Flow ◽  
Negative Energy ◽  
The Other ◽  
Bragg Resonance ◽  
Explosive Instability ◽  
Shear Instabilities ◽  
The Waves

Abstract. In this paper, we study Bragg resonance, i.e., the triad interaction between surface and/or interfacial waves with a bottom ripple, in the presence of background velocity. We show that when one of the constituent waves of the triad has negative energy, the amplitudes of all the waves grow exponentially. This is very different from classic Bragg resonance in which one wave decays to cause the growth of the other. The instabilities we observe are “explosive” and are different from normal mode shear instabilities since our velocity profiles are linearly stable. Our work may explain the existence of large-amplitude internal waves over periodic bottom ripples in the presence of tidal flow observed in oceans and estuaries.

scholarly journals Explosive instability due to flow over a rippled bottom

2019 ◽  
Author(s):  
Raunak Raj ◽  
Anirban Guha
Keyword(s):  
Normal Mode ◽  
Internal Waves ◽  
Large Amplitude ◽  
Tidal Flow ◽  
Negative Energy ◽  
The Other ◽  
Bragg Resonance ◽  
Explosive Instability ◽  
Shear Instabilities ◽  
The Waves

Abstract. In this paper, we study Bragg resonance, i.e. the triad interaction between surface and/or interfacial waves with bottom ripple, in the presence of background velocity. We show that when one of the constituent waves of the triad has negative energy, the amplitudes of all the waves grow exponentially. This is very different from classic Bragg resonance in which one wave decays to cause the growth of the other. The instabilities we observe are explosive and are different from normal mode shear instabilities since our velocity profiles are linearly stable. Our work may explain the existence of large amplitude internal waves over periodic bottom ripples in the presence of tidal flow observed in oceans and estuaries.

Finite-amplitude internal wavepacket dispersion and breaking

2001 ◽  
Vol 429 ◽  
pp. 343-380 ◽  
Author(s):  
BRUCE R. SUTHERLAND
Keyword(s):  
Numerical Simulations ◽  
Internal Waves ◽  
Large Amplitude ◽  
Finite Amplitude ◽  
Critical Amplitude ◽  
Fully Nonlinear ◽  
Weakly Nonlinear ◽  
The Stability ◽  
The Waves ◽  
Horizontal Wavelength

The evolution and stability of two-dimensional, large-amplitude, non-hydrostatic internal wavepackets are examined analytically and by numerical simulations. The weakly nonlinear dispersion relation for horizontally periodic, vertically compact internal waves is derived and the results are applied to assess the stability of weakly nonlinear wavepackets to vertical modulations. In terms of Θ, the angle that lines of constant phase make with the vertical, the wavepackets are predicted to be unstable if [mid ]Θ[mid ] < Θc, where Θc = cos−1 (2/3)1/2 ≃ 35.3° is the angle corresponding to internal waves with the fastest vertical group velocity. Fully nonlinear numerical simulations of finite-amplitude wavepackets confirm this prediction: the amplitude of wavepackets with [mid ]Θ[mid ] > Θc decreases over time; the amplitude of wavepackets with [mid ]Θ[mid ] < Θc increases initially, but then decreases as the wavepacket subdivides into a wave train, following the well-known Fermi–Pasta–Ulam recurrence phenomenon.If the initial wavepacket is of sufficiently large amplitude, it becomes unstable in the sense that eventually it convectively overturns. Two new analytic conditions for the stability of quasi-plane large-amplitude internal waves are proposed. These are qualitatively and quantitatively different from the parametric instability of plane periodic internal waves. The ‘breaking condition’ requires not only that the wave is statically unstable but that the convective instability growth rate is greater than the frequency of the waves. The critical amplitude for breaking to occur is found to be ACV = cot Θ (1 + cos2 Θ)/2π, where ACV is the ratio of the maximum vertical displacement of the wave to its horizontal wavelength. A second instability condition proposes that a statically stable wavepacket may evolve so that it becomes convectively unstable due to resonant interactions between the waves and the wave-induced mean flow. This hypothesis is based on the assumption that the resonant long wave–short wave interaction, which Grimshaw (1977) has shown amplifies the waves linearly in time, continues to amplify the waves in the fully nonlinear regime. Using linear theory estimates, the critical amplitude for instability is ASA = sin 2Θ/(8π2)1/2. The results of numerical simulations of horizontally periodic, vertically compact wavepackets show excellent agreement with this latter stability condition. However, for wavepackets with horizontal extent comparable with the horizontal wavelength, the wavepacket is found to be stable at larger amplitudes than predicted if Θ [lsim ] 45°. It is proposed that these results may explain why internal waves generated by turbulence in laboratory experiments are often observed to be excited within a narrow frequency band corresponding to Θ less than approximately 45°.

Internal wave excitation from stratified flow over a thin barrier

1998 ◽  
Vol 377 ◽  
pp. 223-252 ◽  
Author(s):  
BRUCE R. SUTHERLAND ◽  
PAUL F. LINDEN
Keyword(s):  
Internal Wave ◽  
Numerical Simulations ◽  
Internal Waves ◽  
Wavelet Transforms ◽  
Large Amplitude ◽  
Internal Gravity Waves ◽  
Wave Excitation ◽  
Mean Flow ◽  
Propagating Waves ◽  
The Waves

We perform laboratory experiments in a recirculating shear flow tank of non-uniform salt-stratified water to examine the excitation of internal gravity waves (IGW) in the wake of a tall, thin vertical barrier. The purpose of this study is to characterize and quantify the coupling between coherent structures shed in the wake and internal waves that radiate from the mixing region into the deep, stationary fluid. In agreement with numerical simulations, large-amplitude internal waves are generated when the mixing region is weakly stratified and the deep fluid is sufficiently strongly stratified. If the mixing region is unstratified, weak but continuous internal wave excitation occurs. In all cases, the tilt of the phase lines of propagating waves lies within a narrow range. Assuming the waves are spanwise uniform, their amplitude in space and time is measured non-intrusively using a recently developed ‘synthetic schlieren’ technique. Using wavelet transforms to measure consistently the width and duration of the observed wavepackets, the Reynolds stress is measured and, in particular, we estimate that when large-amplitude internal wave excitation occurs, approximately 7% of the average momentum across the shear depth and over the extent of the wavepacket is lost due to transport away from the mixing region by the waves.We propose that internal waves may act back upon the mean flow modifying it so that the excitation of waves of that frequency is enhanced. A narrow frequency spectrum of large-amplitude waves is observed because the feedback is largest for waves with phase tilt in a range near 45°. Numerical simulations and analytic theories are presented to further quantify this theory.

Trapped internal waves over undular topography

1991 ◽  
Vol 226 ◽  
pp. 205-217 ◽  
Author(s):  
C. Kranenburg ◽  
J. D. Pietrzak ◽  
G. Abraham
Keyword(s):  
Internal Wave ◽  
Internal Waves ◽  
Large Amplitude ◽  
Bottom Topography ◽  
Stratified Flow ◽  
Wave Mode ◽  
Finite Amplitude ◽  
Trapped Waves ◽  
Acoustic Images ◽  
The Waves

We describe observations of slowly decelerating stratified flow over undular bottom topography in an estuary. The flow, which initially was supercritical with respect to the first internal wave mode, approached a resonance after it had become subcritical. A series of acoustic images showed large-amplitude first-mode trapped waves during this phase of the tide. We derive a criterion for quasi-steady response, and present an extension of Yih's class II linear finite-amplitude solutions that accounts for the waves observed.

scholarly journals Observations of Large-Amplitude Nonlinear Internal Waves from a Drifting Array: Instruments and Methods

2010 ◽  
Vol 27 (10) ◽  
pp. 1711-1731 ◽  
Author(s):  
L. R. Centurioni
Keyword(s):  
South China Sea ◽  
Time Scales ◽  
Internal Waves ◽  
South China ◽  
Large Amplitude ◽  
The South China Sea ◽  
Nonlinear Internal Waves ◽  
China Sea ◽  
Drifting Buoy ◽  
The Waves

Abstract This paper presents a novel methodology applied to the observation of large-amplitude nonlinear internal waves in the upper ocean from an array of drifting instruments. The characteristics of the instrument used—an Autonomous Drifting Ocean Station with acoustic current profilers (ADOS-A), which is a drifting buoy with a 200-m-long thermistor chain, several profiling acoustic current meters, and a GPS—are discussed. The ADOS-A is lightweight and relatively inexpensive and can be deployed from aircrafts or from ships of opportunity. Three packets of large-amplitude, nonlinear internal waves were observed in the South China Sea. The speed and the direction of propagation of the waves are accurately determined and their characteristics and evolution over space and time scales comparable with those of the waves, as they propagate through the array, are discussed.

Experimental Research on Damages Detection of Pipeline Structure by Using PZT-Based Waves

2011 ◽  
Author(s):  
Shi Yan ◽  
Binbin He ◽  
Naizhi Zhao
Keyword(s):  
Damage Detection ◽  
Lead Zirconate Titanate ◽  
Smart Materials ◽  
Arrival Time ◽  
Mode Conversion ◽  
Guided Wave ◽  
The Other ◽  
Damage Location ◽  
The Waves ◽  
Peak Value

Pipeline structure may generate damages during its service life due to the influence of environment or accidental loading. The damages need to be detected and repaired if they are severe enough to influence the transportation work. Non-destructive detection using smart materials combined with suitable diagonal algorithms are widely used in the field of structural health monitoring (SHM). Piezoelectric ceramics (such as Lead Zirconate Titanate, PZT) is one of the smart materials to be applied in the SHM due to the piezoelectric effect. So far, the PZT-based wave method is widely used for damage detection of structures, in particular, pipeline structures. A series of piezoelectric patches are bonded on the surface of the pipeline structure to monitor the damages such as local crack or effective area reduction due to corrosion by using diagonal waves. The damage of the pipeline structure can be detected by analysis of the received diagonal waves which peak value, phase, and arriving time can be deferent from the health ones. The response of the diagonal wave is not only correlated to the damage location through estimation of the arrival time of the wave peak, but also associated with the peak value of the wave for the reduction of wave energy as the guided wave passing through the damages. Therefore, the presence of damages in the pipeline structure can be detected by investigating the parameter change of the guided waves. The change of the wave parameters represents the attenuation, deflection and mode conversion of the waves due to the damages. In addition, the guided wave has the ability of quick detecting the damage of the pipeline structure and the simplicity of generating and receiving detection waves by using PZT patches. To verify the proposed method, an experiment is designed and tested by using a steel pipe bonded the PZT patches on the surface of it. The PZT patches consist of an array to estimate the location and level of the damage which is simulated by an artificial notch on the surface of the structure. The several locations and deep heights of the notches are considered during the test. A pair of the PZT patches are used at the same time as one is used as an actuator and the other as a sensor, respectively. A tone burst of 5 cycles of wave shape is used during the experiment. A wave generator is applied to create the proposed waves, and the waves are amplified by an amplifier to actuate the PZT patch to emit the diagonal waves with appropriately enough energy. Meanwhile, the other PZT patch is used as a sensor to receive the diagonal signals which contain the information of the damages for processing. For data processing, an index of root mean square deviation (RMSD) of the received data is used to estimate the damage level by compare of the data between the damaged and the health peak valves of the received signals. The time reversal method which aimed at increasing the efficiency of the detection is also used to detect the damage location by estimating the arrival time of the reflected wave passing with a certain velocity. The proposed method experimentally validates that it is effective for application in damage detection of pipeline structure.

scholarly journals Energy Balance Indicators during the Transition Period and Early Lactation of Purebred Holstein and Simmental Cows and Their Crosses

Animals ◽  
2021 ◽  
Vol 11 (2) ◽  
pp. 309
Author(s):  
Deise Aline Knob ◽  
André Thaler Neto ◽  
Helen Schweizer ◽  
Anna C. Weigand ◽  
Roberto Kappes ◽  
...  
Keyword(s):  
Energy Balance ◽  
Milk Yield ◽  
Milk Composition ◽  
Negative Energy ◽  
The Other ◽  
Negative Energy Balance ◽  
Metabolic Energy ◽  
Genetic Groups ◽  
Significant Difference ◽  
Fat Thickness

Crossbreeding in dairy cattle has been used to improve functional traits, milk composition, and efficiency of Holstein herds. The objective of the study was to compare indicators of the metabolic energy balance, nonesterified fatty acids (NEFA), beta-hydroxybutyrate (BHBA), glucose, body condition score (BCS) back fat thickness (BFT), as well as milk yield and milk composition of Holstein and Simmental cows, and their crosses from the prepartum period until the 100th day of lactation at the Livestock Center of the Ludwig Maximilians University (Munich, Germany). In total, 164 cows formed five genetic groups according to their theoretic proportion of Holstein and Simmental genes as follows: Holstein (100% Holstein; n = 9), R1-Hol (51–99% Holstein; n = 30), first generation (F1) crossbreds (50% Holstein, 50% Simmental; n = 17), R1-Sim (1–49% Holstein; n = 81) and Simmental (100% Simmental; n = 27). The study took place between April 2018 and August 2019. BCS, BFT blood parameters, such as BHBA, glucose, and NEFA were recorded weekly. A mixed model analysis with fixed effects breed, week (relative to calving), the interaction of breed and week, parity, calving year, calving season, milking season, and the repeated measure effect of cow was used. BCS increased with the Simmental proportion. All genetic groups lost BCS and BFT after calving. Simmental cows showed lower NEFA values. BHBA and glucose did not differ among genetic groups, but they differed depending on the week relative to calving. Simmental and R1-Sim cows showed a smaller effect than the other genetic groups regarding changes in body weight, BCS, or back fat thickness after a period of a negative energy balance after calving. There was no significant difference for milk yield among genetic groups, although Simmental cows showed a lower milk yield after the third week after calving. Generally, Simmental and R1-Simmental cows seemed to deal better with a negative energy balance after calving than purebred Holstein and the other crossbred lines. Based on a positive heterosis effect of 10.06% for energy corrected milk (ECM), the F1, however, was the most efficient crossbred line.

Marguerite Yourcenar, traductrice

Babel ◽  
1994 ◽  
Vol 40 (1) ◽  
pp. 21-37
Author(s):  
Ivo R.V. Hoefkens
Keyword(s):  
The Other ◽  
Political Sphere ◽  
Negro Spirituals ◽  
Marguerite Yourcenar ◽  
Other Hand ◽  
The Aesthetic ◽  
Literary Output ◽  
Ethical Communication ◽  
The Waves ◽  
Second Period

Marguerite Yourcenar, known as an author, is also the translator of about a dozen works. My purpose here is to trace the evolution of her oeuvre in the field of translation in relation to her literary output. I have divided the former into three distinct periods, the first of which covers the closing years of the 1930s, when Marguerite Yourcenar translated Virginia Woolf's The Waves and Henry James's What Maisie Knew. Her interest in these authors is to a large extent stylistic. On the other hand, the translation of Constantin Cavafy's poetry, which was begun during the same period, reflects the intimist themes to be found in Marguerite Yourcenar's early narratives {Alexis and the others), although she was then already seeking out other thematic sources. The translation was only published in 1958. It consequently falls within a second period: that of the "présentations critiques" (critical commentaries). These major efforts in translation {Présentation critique de Constantin Cavafy, La Couronne et la Lyre, Fleuve profonde, Sombre rivière) are marked by a manifest preoccupation with the aesthetic. But themes of a more universal character and engagement in the socio-political sphere also enter into the choice of the texts for translation (negro spirituals, Présentation critique d'Hortense Flexner). These translations were contemporaneous with the creation of Marguerite Yourcenar's most important novels, namely Mémoires d'Hadrien and L'OEuvre au Noir. The last of the three periods, the 1980s, finds her tackling far less ambitious projects, the function of which tends increasingly towards ethical communication. The only one of them that bears any resemblance to the "présentations critiques" is the essay on Yukio Mishima and the translation of Cinq Nô Modernes, assuming that these are to be considered as an ensemble. Here, as elsewhere, it also emerges that Marguerite Yourcenar is largely indifferent to the existence of other translations.

Internal waves in a viscous atmosphere

1975 ◽  
Vol 72 (4) ◽  
pp. 773-786 ◽  
Author(s):  
W. L. Chang ◽  
T. N. Stevenson
Keyword(s):  
Energy Source ◽  
Incompressible Fluid ◽  
Internal Waves ◽  
Infinite Number ◽  
Similarity Solution ◽  
Small Amplitude ◽  
Horizontal Plane ◽  
Two Dimensional ◽  
The Waves ◽  
Isothermal Atmosphere

The way in which internal waves change in amplitude as they propagate through an incompressible fluid or an isothermal atmosphere is considered. A similarity solution for the small amplitude isolated viscous internal wave which is generated by a localized two-dimensional disturbance or energy source was given by Thomas & Stevenson (1972). It will be shown how summations or superpositions of this solution may be used to examine the behaviour of groups of internal waves. In particular the paper considers the waves produced by an infinite number of sources distributed in a horizontal plane such that they produce a sinusoidal velocity distribution. The results of this analysis lead to a new small perturbation solution of the linearized equations.

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