scholarly journals Generation of Wave Groups by Shear Layer Instability

Fluids ◽  
2019 ◽  
Vol 4 (1) ◽  
pp. 39 ◽  
Author(s):  
Roger Grimshaw
Keyword(s):  
Growth Rate ◽  
Group Velocity ◽  
Linear Growth ◽  
Linear Stability Theory ◽  
Linear Growth Rate ◽  
Wave Groups ◽  
Weakly Nonlinear ◽  
Complex Valued ◽  
Fundamental Requirement ◽  
Temporal Growth Rate

The linear stability theory of wind-wave generation is revisited with an emphasis on the generation of wave groups. The outcome is the fundamental requirement that the group move with a real-valued group velocity. This implies that both the wave frequency and the wavenumber should be complex-valued, and in turn this then leads to a growth rate in the reference frame moving with the group velocity which is in general different from the temporal growth rate. In the weakly nonlinear regime, the amplitude envelope of the wave group is governed by a forced nonlinear Schrödinger equation. The effect of the wind forcing term is to enhance modulation instability both in terms of the wave growth and in terms of the domain of instability in the modulation wavenumber space. Also, the soliton solution for the wave envelope grows in amplitude at twice the linear growth rate.

Resonant over-reflection of internal gravity waves from a thin shear layer

1981 ◽  
Vol 109 ◽  
pp. 349-365 ◽  
Author(s):  
R. H. J. Grimshaw
Keyword(s):  
Growth Rate ◽  
Shear Layer ◽  
Gravity Waves ◽  
Finite Time ◽  
Linear Growth ◽  
Vortex Sheet ◽  
Internal Gravity Waves ◽  
Finite Amplitude ◽  
Linear Growth Rate ◽  
Weakly Nonlinear

In a previous paper (Grimshaw 1979) the resonant over-reflection of internal gravity waves from a vortex sheet was considered in the weakly nonlinear regime. It was shown there that the time evolution of the amplitude of the vortex sheet displacement was balanced by a cubic nonlinearity. For one vortex sheet mode, symmetrical with respect to the interface, it was shown that a steady finite-amplitude wave was possible. For the other, asymmetric modes, a singularity develops in a finite time. In the present paper, that analysis is extended by replacing the vortex sheet with a thin shear layer of thickness α2, where α is the amplitude of the shear layer displacement. The effect of this extension is to introduce a linear growth rate term in the amplitude equation, which is otherwise unaltered. The linear growth rate can be computed from a formula due to Drazin & Howard (1966, p. 67). The effect on the modes is that the symmetric mode is linearly damped and requires sustained forcing to be observed, while the asymmetric modes are slightly destabilized by the linear term and, as in the vortex-sheet model, develop a singularity in finite time.

Note on weakly nonlinear stability theory of a free mixing layer

1987 ◽  
Vol 409 (1837) ◽  
pp. 351-367 ◽  
Keyword(s):  
Growth Rate ◽  
Nonlinear Evolution Equation ◽  
Linear Growth ◽  
Nonlinear Evolution ◽  
Second Harmonic ◽  
Mixing Layer ◽  
Linear Growth Rate ◽  
Mean Flow ◽  
Initial Flow ◽  
Weakly Nonlinear

This paper is concerned with an analysis of the derivation of a nonlinear evolution equation governing the dynamics of a weakly unstable pertur­bation in a mixing layer. It is demonstrated that the Landau constant has no universal character and is determined by the degree of supercriticality of perturbation, whose measure is represented by the linear growth rate of instability γ (which is proportional to the departure from neutral wavenumber). It is shown that the interaction of the fundamental harmonic of the perturbation with the associated distortion of a mean flow is the dominant nonlinear effect. It is this that makes the main contribution to the Landau constant rather than the interaction with the second harmonic as was thought previously. We examine the régimes of both a viscous and a non-stationary critical layer and calculate the Landau constant. It is shown that, except for the case when the supercriticality is very small, γ « v ( v is the inverse of the Reynolds number), the nonlinearity cannot substantially influence the exponential growth of the perturbation predicted by linear theory. When γ « v , however, the nonlinear time exceeds the time of viscous spreading of the initial flow and for a correct formulation of the problem, one has, as was first pointed out by Huerre, to introduce here an artificial force field.

Dynamics of ultra-thin two-layer films under the action of inclined temperature gradients

2009 ◽  
Vol 631 ◽  
pp. 165-197 ◽  
Author(s):  
ALEXANDER A. NEPOMNYASHCHY ◽  
ILYA B. SIMANOVSKII
Keyword(s):  
Growth Rate ◽  
Temperature Gradient ◽  
Linear Growth ◽  
Nonlinear Evolution ◽  
Temperature Gradients ◽  
Linear Stability Theory ◽  
Linear Growth Rate ◽  
Nonlinear Simulations ◽  
Inclined Temperature Gradient ◽  
Longitudinal Structures

The development of instabilities under the joint action of the van der Waals forces and Marangoni stresses in a two-layer film in the presence of an inclined temperature gradient is investigated. The problem is solved by means of a linear stability theory and nonlinear simulations. It has been found that for sufficiently large values of the ratio between the longitudinal and transverse Marangoni numbers, the real part of the linear growth rate does not depend on the direction of the wavenumber, except the case of nearly longitudinal disturbances. Numerous types of nonlinear evolution have been observed, among them are ordered systems of droplets, ‘splashes’, oblique waves, modulated transverse and longitudinal structures.

Microborings and growth in Late Ordovician halysitids and other corals

1993 ◽  
Vol 67 (6) ◽  
pp. 922-934 ◽  
Author(s):  
Robert J. Elias ◽  
Dong-Jin Lee
Keyword(s):  
Growth Rate ◽  
Linear Growth ◽  
Inverse Correlation ◽  
Weight Percent ◽  
Late Ordovician ◽  
Coral Growth ◽  
Linear Growth Rate ◽  
Skeletal Density ◽  
Rugose Coral ◽  
Endolithic Algae

Microborings in the Late Ordovician tabulate corals Catenipora rubra (a halysitid) and Manipora amicarum (a cateniform nonhalysitid) and in an epizoic solitary rugose coral differ from nearly all of those previously reported in Paleozoic corals. These microborings were formed within the coralla by endolithic algae and fungi located beneath living polyps. Comparable structures in the Late Ordovician tabulate Quepora ?agglomeratiformis (a halysitid) represent algal microborings, not spicules, and halysitids are corals, not sponges as suggested by Kaźmierczak (1989).Endolithic algae in cateniform tabulates relied primarily on light entering through the outer walls of the ranks rather than through the polyps; lacunae within coralla permitted appropriate levels of light to reach many corallites. The direction of boring was determined by corallum microstructure and possibly also by the distribution of organic matter within the skeleton. There is an apparent inverse correlation between boring activity and coral growth rate.The location and relative abundance of pyritized microborings within calcareous coralla can be established quantitatively and objectively from electron microprobe determinations of weight percent sulfur along appropriate traverses of the coral skeleton. The distribution of such microborings in Catenipora rubra and Manipora amicarum is comparable to algal banding in modern corals; this is the first report of such banding in the interiors of Paleozoic corals. Change in the intensity of boring within each corallum was evidently a response to variation in the linear growth rate of the coral, or to fluctuation in an environmental factor (perhaps light intensity) that could control both algal activity and growth rate in these corals. Change in the algal boring intensity and linear growth rate of the coral was generally but not always seasonal and usually but not invariably associated with change in the density of coral skeletal deposition.Cyclic bands of boring abundance maxima within fossil colonial corals provide a measure of annual linear growth comparable to the widely accepted method based on skeletal density bands. Algal bands are more sporadically developed than density bands within and among coralla, thus increasing the difficulty of interpretation. Fluctuations in the abundance of algal microborings apparently provide a detailed record of changes in the linear growth rate of colonies and of individuals within colonies. Combined analyses of microboring abundance and skeletal density will contribute significantly to our understanding of the biological and environmental factors involved in endolithic activity and coral growth.

scholarly journals <sup>210</sup>Pb-<sup>226</sup>Ra chronology reveals rapid growth rate of <i>Madrepora oculata</I> and <i>Lophelia pertusa</i> on world's largest cold-water coral reef

2011 ◽  
Vol 8 (6) ◽  
pp. 12247-12283
Author(s):  
P. Sabatier ◽  
J.-L. Reyss ◽  
J. M. Hall-Spencer ◽  
C. Colin ◽  
N. Frank ◽  
...  
Keyword(s):  
Growth Rate ◽  
Coral Reef ◽  
Linear Growth ◽  
Cold Water ◽  
Optimal Growth ◽  
Growth Conditions ◽  
Age And Growth ◽  
Linear Growth Rate ◽  
Lophelia Pertusa ◽  
Water Coral

Abstract. Here we show the use of the 210Pb-226Ra excess method to determine the growth rate of corals from one of the world's largest known cold-water coral reef, the Røst Reef off Norway. Two large branching framework-forming cold-water coral specimens, one Lophelia pertusa and one Madrepora oculata were collected alive at 350 m water depth from the Røst Reef at ~67° N and ~9° E. Pb and Ra isotopes were measured along the major growth axis of both specimens using low level alpha and gamma spectrometry and the corals trace element compositions were studied using ICP-QMS. Due to the different chemical behaviors of Pb and Ra in the marine environment, 210Pb and 226Ra were not incorporated the same way into the aragonite skeleton of those two cold-water corals. Thus to assess of the growth rates of both specimens we have here taken in consideration the exponential decrease of initially incorporated 210Pb as well as the ingrowth of 210Pb from the decay of 226Ra. Moreover a~post-depositional 210Pb incorporation is found in relation to the Mn-Fe coatings that could not be entirely removed from the oldest parts of the skeletons. The 226Ra activities in both corals were fairly constant, then assuming constant uptake of 210Pb through time the 210Pb-226Ra chronology can be applied to calculate linear growth rate. The 45.5 cm long branch of M. oculata reveals an age of 31 yr and a~linear growth rate of 14.4 ± 1.1 mm yr−1, i.e. 2.6 polyps per year. However, a correction regarding a remaining post-depositional Mn-Fe oxide coating is needed for the base of the specimen. The corrected age tend to confirm the radiocarbon derived basal age of 40 yr (using 14C bomb peak) with a mean growth rate of 2 polyps yr−1. This rate is similar to the one obtained in Aquaria experiments under optimal growth conditions. For the 80 cm-long specimen of L. pertusa a remaining contamination of metal-oxides is observed for the middle and basal part of the coral skeleton, inhibiting similar accurate age and growth rate estimates. However, the youngest branch was free of Mn enrichment and this 15 cm section reveals a growth rate of 8 mm yr−1 (~1 polyp every two to three years). However, the 210Pb growth rate estimate is within the lowermost ranges of previous growth rate estimates and may thus reflect that the coral was not developing at optimal growth conditions. Overall, 210Pb-226Ra dating can be successfully applied to determine the age and growth rate of framework-forming cold-water corals, however, removal of post-depositional Mn-Fe oxide deposits is a prerequisite. If successful, large branching M. oculata and L. pertusa coral skeletons provide unique oceanographic archive for studies of intermediate water environmentals with an up to annual time resolution and spanning over many decades.

scholarly journals Wavelength dependence of the linear growth rate of the <I>E<sub>s</sub></I> layer instability

2007 ◽  
Vol 25 (6) ◽  
pp. 1311-1322 ◽  
Author(s):  
R. B. Cosgrove
Keyword(s):  
Growth Rate ◽  
Electric Fields ◽  
Large Scale ◽  
Linear Growth ◽  
Three Dimensional ◽  
Generalized Derivation ◽  
Wavelength Dependence ◽  
Meridional Wind ◽  
Linear Growth Rate ◽  
Significant Wavelength

Abstract. It has recently been shown, by computation of the linear growth rate, that midlatitude sporadic-E (Es) layers are subject to a large scale electrodynamic instability. This instability is a logical candidate to explain certain frontal structuring events, and polarization electric fields, which have been observed in Es layers by ionosondes, by coherent scatter radars, and by rockets. However, the original growth rate derivation assumed an infinitely thin Es layer, and therefore did not address the short wavelength cutoff. Also, the same derivation ignored the effects of F region loading, which is a significant wavelength dependent effect. Herein is given a generalized derivation that remedies both these short comings, and thereby allows a computation of the wavelength dependence of the linear growth rate, as well as computations of various threshold conditions. The wavelength dependence of the linear growth rate is compared with observed periodicities, and the role of the zeroth order meridional wind is explored. A three-dimensional paper model is used to explain the instability geometry, which has been defined formally in previous works.

scholarly journals Evaluation of Biomass and Chitin Production of Morchella Mushrooms Grown on Starch-Based Substrates

Foods ◽  
2019 ◽  
Vol 8 (7) ◽  
pp. 239 ◽  
Author(s):  
Aikaterini Papadaki ◽  
Panagiota Diamantopoulou ◽  
Seraphim Papanikolaou ◽  
Antonios Philippoussis
Keyword(s):  
Growth Rate ◽  
Linear Growth ◽  
Biomass Yield ◽  
Linear Growth Rate ◽  
Waste Streams ◽  
Mycelium Growth ◽  
Potato Dextrose Broth ◽  
Polysaccharide Content ◽  
Potato Peels ◽  
Mycelium Growth Rate

Morchella sp. is one of the most expensive mushrooms with a high nutritional profile. In this study, the polysaccharide content of Morchella species was investigated. Specifically, mycelium growth rate, biomass production, sclerotia formation, and glucosamine and total polysaccharides content of six Morchella species grown on a starch-based media were evaluated. Submerged fermentations in potato dextrose broth resulted in a glucosamine content of around 3.0%. In solid-state fermentations (SSF), using potato dextrose agar, a high linear growth rate (20.6 mm/day) was determined. Increased glucosamine and total polysaccharides content were observed after the formation of sclerotia. Biomass and glucosamine content were correlated, and the equations were used for the indirect estimation of biomass in SSF with agro-industrial starch-based materials. Wheat grains (WG), potato peels (PP), and a mixture of 1:1 of them (WG–PP) were evaluated as substrates. Results showed that the highest growth rate of 9.05 mm/day was determined on WG and the maximum biomass yield (407 mg/g) on WG–PP. The total polysaccharide content reached up to 18.4% of dried biomass in WG–PP. The results of the present study proved encouraging for the efficient bioconversion of potato and other starch-based agro-industrial waste streams to morel biomass and sclerotia eliciting nutritional and bioactive value.

Effect of prolonged uterine blood flow reduction on fetal growth in sheep

1996 ◽  
Vol 270 (1) ◽  
pp. R246-R253 ◽  
Author(s):  
D. W. Boyle ◽  
S. Lecklitner ◽  
E. A. Liechty
Keyword(s):  
Growth Rate ◽  
Blood Flow ◽  
Fetal Growth ◽  
Linear Growth ◽  
Arterial Oxygen ◽  
Linear Growth Rate ◽  
Uterine Blood Flow ◽  
Arterial Oxygen Content ◽  
Flow Reduction ◽  
Blood Flow Reduction

The purpose of the present investigation was to study the effect of 7 days of uterine blood flow reduction on fetal growth. Reduction in uterine blood flow was accomplished by external occlusion of the terminal aorta in 20 pregnant sheep. Linear growth was monitored daily by means of a crown-rump length measuring device. The deliveries of oxygen, glucose, and lactate to the fetus, as well as their uptakes by the fetus, were determined before and after 7 days of uterine blood flow reduction and correlated with rates of fetal growth. Identical studies were conducted in nine control animals. Uterine blood flow reduction resulted in a significant decrease in fetal oxygen delivery and fetal arterial oxygen content. Linear growth rate decreased by 38% in the occluded animals during hypoxemia. In addition, there was a 20% reduction in daily weight gain in occluded animals compared with controls. There were no differences in the uptakes of oxygen, glucose, and lactate by the fetus. Positive correlations were found between linear growth rate and fetal arterial oxygen content (r2 = 0.25, P = 0.0001) and between linear growth rate and fetal oxygen delivery (r2 = 0.21, P = 0.0006). The correlations between linear growth rate and fetal oxygenation provide strong evidence of the central role of oxygen in the regulation of fetal growth.

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