scholarly journals Triad Instability of Planetary Rossby Waves

2007 ◽  
Vol 37 (8) ◽  
pp. 2158-2171 ◽  
Author(s):  
Yu Zhang ◽  
Joseph Pedlosky
Keyword(s):  
Growth Rate ◽  
Large Scale ◽  
Rossby Waves ◽  
Maximum Growth ◽  
Maximum Growth Rate ◽  
Coriolis Parameter ◽  
Planetary Scale ◽  
Baroclinic Waves ◽  
Eastern Boundary ◽  
Ray Path

Abstract The triad instability of the large-scale, first-mode, baroclinic Rossby waves is studied in the context of the planetary scale when the Coriolis parameter is to its lowest order varying with latitude. Accordingly, rather than remain constant as in quasigeostrophic theory, the deformation radius also changes with latitude, yielding new and interesting features to the propagation and triad instability processes. On the planetary scale, baroclinic waves vary their meridional wavenumbers along group velocity rays while they conserve both frequencies and zonal wavenumbers. The amplitudes of both barotropic and baroclinic waves would change with latitude along a ray path in the same way that the Coriolis parameter does if effects of the nonlinear interaction are ignored. The triad interaction for a specific triad is localized within a small latitudinal band where the resonance conditions are satisfied and quasigeostrophic theory is applicable locally. Using the growth rate from that theory as a measure, at each latitude along the ray path of the basic wave, a barotropic wave and a secondary baroclinic wave are picked up to form the most unstable triad and the distribution of this maximum growth rate is examined. It is found to increase southward under the assumption that triad interactions do not cause a noticeable decrease in the quantity of the basic wave’s amplitude divided by the Coriolis parameter. Different barotropic waves that maximize the growth rate at different latitudes have almost the same meridional length scale, on the order of the deformation radius. With many rays starting from different latitudes on the eastern boundary and with wavenumbers on each of them satisfying the no-normal-flow condition, the resulting two-dimensional distribution of the growth rate is a complicated function of the relative relations of zonal wavenumbers or frequencies on different rays and the orientation of the eastern boundary. In general, the growth rate is largest on rays originating to the north.

Rossby-wave driven zonal flows in the ionospheric E-layer

2007 ◽  
Vol 73 (1) ◽  
pp. 131-140 ◽  
Author(s):  
T. D. KALADZE ◽  
D. J. WU ◽  
O. A. POKHOTELOV ◽  
R. Z. SAGDEEV ◽  
L. STENFLO ◽  
...  
Keyword(s):  
Large Scale ◽  
Rossby Waves ◽  
Maximum Growth ◽  
Present Theory ◽  
Finite Amplitude ◽  
Maximum Growth Rate ◽  
Small Scale ◽  
Reynolds Stresses ◽  
Zonal Flows ◽  
Coupled Equations

Abstract.A novel mechanism for the generation of large-scale zonal flows by small-scale Rossby waves in the Earth's ionospheric E-layer is considered. The generation mechanism is based on the parametric excitation of convective cells by finite amplitude magnetized Rossby waves. To describe this process a generalized Charney equation containing both vector and scalar (Korteweg–de Vries type) nonlinearities is used. The magnetized Rossby waves are supposed to have arbitrary wavelengths (as compared with the Rossby radius). A set of coupled equations describing the nonlinear interaction of magnetized Rossby waves and zonal flows is obtained. The generation of zonal flows is due to the Reynolds stresses produced by finite amplitude magnetized Rossby waves. It is found that the wave vector of the fastest growing mode is perpendicular to that of the magnetized Rossby pump wave. Explicit expression for the maximum growth rate as well as for the optimal spatial dimensions of the zonal flows are obtained. A comparison with existing results is carried out. The present theory can be used for the interpretation of the observations of Rossby-type waves in the Earth's ionosphere.

Filamentation of a laser beam in a strongly ionized magnetoplasma

1978 ◽  
Vol 19 (1) ◽  
pp. 55-61 ◽  
Author(s):  
L. A. Pitale
Keyword(s):  
Magnetic Field ◽  
Growth Rate ◽  
Laser Beam ◽  
Spatial Scale ◽  
Large Scale ◽  
Maximum Growth ◽  
Mean Free Path ◽  
Maximum Growth Rate ◽  
Main Beam ◽  
Small Scale

On a time-scale of the order of the energy relaxation time, a high power laser beam, propagating in a strongly ionized magnetoplasma is shown to be unstable for small scale fluctuations. In the domain r0 < [mi/m]½ λm. v2/[ω2c + v2] (r0, λm, v, ωc, and m being respectively the spatial scale of the perturbation, electron mean free path, collision frequency, cyclotron frequency and mass and mi being the ion mass) the main loss of excess electron energy is due to thermal conduction; in the other limit collisional loss dominates. It is shown that for small scale fluctuations the growth rate increases with (i) increasing magnetic field and (ii) increasing r0. For large scale fluctuations the magnetic field does not show any effect; the growth rate, however, diminishes with increasing spatial scale. A maximum growth rate is obtained both for some optimum value of scale length and for intensity of the main beam.

Drift wave driven zonal flows in electron–positron–ion plasmas

2010 ◽  
Vol 76 (3-4) ◽  
pp. 635-643 ◽  
Author(s):  
T. D. KALADZE ◽  
O. A. POKHOTELOV ◽  
M. SHAD
Keyword(s):  
Growth Rate ◽  
Large Scale ◽  
Maximum Growth ◽  
Finite Amplitude ◽  
Maximum Growth Rate ◽  
Small Scale ◽  
Drift Waves ◽  
Zonal Flows ◽  
Electron Positron ◽  
Spatial Dimensions

AbstractThe generation of large-scale zonal flows by small-scale electrostatic drift waves in electron–positron–ion (EPI) plasma is considered. The generation mechanism is based on the parametric excitation of convective cells by finite amplitude drift waves. To describe this process, the Hasegawa–Mima equation generalized for the case of EPI plasma is used. Explicit expressions for the maximum growth rate as well as for the optimal spatial dimensions of the zonal flows are obtained. Dependence of the growth rate on the spectrum purity of the wave packet is also investigated. The relevant instability conditions are determined.

A note on growth curves of rabbit lines selected on growth rate or litter size

1993 ◽  
Vol 57 (2) ◽  
pp. 332-334 ◽  
Author(s):  
A. Blasco ◽  
E. Gómez
Keyword(s):  
Growth Rate ◽  
Litter Size ◽  
Growth Curves ◽  
Live Weight ◽  
Maximum Growth ◽  
Maximum Growth Rate ◽  
Standard Errors ◽  
Adult Weight ◽  
Weight Growth ◽  
Using Data

Two synthetic lines of rabbits were used in the experiment. Line V, selected on litter size, and line R, selected on growth rate. Ninety-six animals were randomly collected from 48 litters, taking a male and a female each time. Richards and Gompertz growth curves were fitted. Sexual dimorphism appeared in the line V but not in the R. Values for b and k were similar in all curves. Maximum growth rate took place in weeks 7 to 8. A break due to weaning could be observed in weeks 4 to 5. Although there is a remarkable similarity of the values of all the parameters using data from the first 20 weeks only, the higher standard errors on adult weight would make 30 weeks the preferable time to take data for live-weight growth curves.

Reassessment of Maximum Growth Rates for C3 and C4 Crops

1978 ◽  
Vol 14 (1) ◽  
pp. 1-5 ◽  
Author(s):  
J. L. Monteith
Keyword(s):  
Growth Rate ◽  
Growth Rates ◽  
Growing Season ◽  
Maximum Growth ◽  
Maximum Growth Rate ◽  
Crop Growth ◽  
Close Inspection ◽  
Similar Difference ◽  
Photosynthetic Efficiencies

SUMMARYFigures for maximum crop growth rates, reviewed by Gifford (1974), suggest that the productivity of C3 and C4 species is almost indistinguishable. However, close inspection of these figures at source and correspondence with several authors revealed a number of errors. When all unreliable figures were discarded, the maximum growth rate for C3 stands fell in the range 34–39 g m−2 d−1 compared with 50–54 g m−2 d−1 for C4 stands. Maximum growth rates averaged over the whole growing season showed a similar difference: 13 g m−2 d−1 for C3 and 22 g m−2 d−1 for C4. These figures correspond to photosynthetic efficiencies of approximately 1·4 and 2·0%.

Interpretation of Experimental Data with Regard to the Activated Sludge Model No.1 and Calibration of the Model for Municipal Wastewater Treatment Plants

1992 ◽  
Vol 25 (6) ◽  
pp. 167-183 ◽  
Author(s):  
H. Siegrist ◽  
M. Tschui
Keyword(s):  
Experimental Data ◽  
Growth Rate ◽  
Activated Sludge ◽  
Municipal Wastewater ◽  
Wastewater Treatment Plants ◽  
Treatment Plant ◽  
Maximum Growth ◽  
Maximum Growth Rate ◽  
Municipal Wastewater Treatment ◽  
Activated Sludge Model

The wastewater of the municipal treatment plants Zürich-Werdhölzli (350000 population equivalents), Zürich-Glatt (110000), and Wattwil (20000) have been characterized with regard to the activated sludge model Nr.1 of the IAWPRC task group. Zürich-Glatt and Wattwil are partly nitrifying treatment plants and Zürich-Werdhölzli is fully nitrifying. The mixing characteristics of the aeration tanks at Werdhölzli and Glatt were determined with sodium bromide as a tracer. The experimental data were used to calibrate hydrolysis, heterotrophic growth and nitrification. Problems arising by calibrating hydrolysis of the paniculate material and by measuring oxygen consumption of heterotrophic and nitrifying microorganisms are discussed. For hydrolysis the experimental data indicate first-order kinetics. For nitrification a maximum growth rate of 0.40±0.07 d−1, corresponding to an observed growth rate of 0.26±0.04 d−1 was calculated at 10°C. The half velocity constant found for 12 and 20°C was 2 mg NH4-N/l. The calibrated model was verified with experimental dam of me Zürich-Werdhölzli treatment plant during ammonia shock load.

Dietary Protein Requirements of Fishes — A Reassessment

1987 ◽  
Vol 44 (11) ◽  
pp. 1995-2001 ◽  
Author(s):  
Stephen H. Bowen
Keyword(s):  
Growth Rate ◽  
Dietary Protein ◽  
Protein Concentration ◽  
Trophic Ecology ◽  
Maximum Growth ◽  
Maximum Growth Rate ◽  
Intake Rate ◽  
Protein Requirement ◽  
Fish Physiology ◽  
Protein Retention

It is widely believed that fishes require more dietary protein than other vertebrates. Many aspects of fish physiology, nutrition, and trophic ecology have been interpreted within the context of this high protein requirement. Here, fishes are compared with terrestrial homeotherms in terms of (1) protein requirement for maintenance, (2) relative protein concentration in the diet required for maximum growth rate, (3) protein intake rate required for maximum growth rate, (4) efficiency of protein retention in growth, and (5) weight of growth achieved per weight of protein ingested. The two animal groups compared differ only in relative protein concentration in the diet required for maximum growth rate. This difference is explained in terms of homeotherms' greater requirement for energy and does not reflect absolute differences in protein requirement. The remaining measures of protein requirement suggest that fishes and terrestrial homeotherms are remarkably similar in their use of protein as a nutritional resource. Reinterpretation of the role of protein in fish physiology, nutrition, and trophic ecology is perhaps in order.

Allometric scaling and taxonomic variation in nutrient utilization traits and maximum growth rate of phytoplankton

2012 ◽  
Vol 57 (2) ◽  
pp. 554-566 ◽  
Author(s):  
Kyle F. Edwards ◽  
Mridul K. Thomas ◽  
Christopher A. Klausmeier ◽  
Elena Litchman
Keyword(s):  
Growth Rate ◽  
Allometric Scaling ◽  
Maximum Growth ◽  
Nutrient Utilization ◽  
Maximum Growth Rate

Instability waves on the air–sea interface

1993 ◽  
Vol 248 ◽  
pp. 363-381 ◽  
Author(s):  
G. H. Wheless ◽  
G. T. Csanady
Keyword(s):  
Surface Tension ◽  
Growth Rate ◽  
Maximum Growth ◽  
Maximum Growth Rate ◽  
Surface Velocity ◽  
Instability Waves ◽  
Interface Surface ◽  
Fluid Properties ◽  
Compound Matrix Method ◽  
Order Of Magnitude

We used a compound matrix method to integrate the Orr–Sommerfeld equation in an investigation of short instability waves (λ < 6 cm) on the coupled shear flow at the air–sea interface under suddenly imposed wind (a gust model). The method is robust and fast, so that the effects of external variables on growth rate could easily be explored. As expected from past theoretical studies, the growth rate proved sensitive to air and water viscosity, and to the curvature of the air velocity profile very close to the interface. Surface tension had less influence, growth rate increasing somewhat with decreasing surface tension. Maximum growth rate and minimum wave speed nearly coincided for some combinations of fluid properties, but not for others.The most important new finding is that, contrary to some past order of magnitude estimates made on theoretical grounds, the eigenfunctions at these short wavelengths are confined to a distance of the order of the viscous wave boundary-layer thickness from the interface. Correspondingly, the perturbation vorticity is high, the streamwise surface velocity perturbation in typical cases being five times the orbital velocity of free waves on an undisturbed water surface. The instability waves should therefore be thought of as fundamentally different flow structures from free waves: given their high vorticity, they are akin to incipient turbulent eddies. They may also be expected to break at a much lower steepness than free waves.

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