On the Transformations between Temporal and Spatial Growth Rates

1987 ◽  
Vol 44 (18) ◽  
pp. 2668-2673
Author(s):  
Melinda S. Peng ◽  
R. T. Williams
Keyword(s):  
Growth Rates ◽  
Spatial Growth ◽  
Temporal And Spatial

Temporal and Spatial Growth of Wind Waves

2007 ◽  
Vol 37 (1) ◽  
pp. 106-114 ◽  
Author(s):  
M. Stiassnie ◽  
Y. Agnon ◽  
P. A. E. M. Janssen
Keyword(s):  
Growth Rates ◽  
Water Waves ◽  
Wind Profile ◽  
Wind Waves ◽  
Shear Velocity ◽  
Spatial Growth ◽  
Wave Celerity ◽  
Temporal And Spatial ◽  
Distinct Maximum ◽  
Logarithmic Wind Profile

Abstract A solution of Rayleigh’s instability equation, which circumvents the apparent critical-layer singularity, is provided. The temporal and spatial growth rates of water waves exposed to a logarithmic wind profile are calculated and discussed. The findings are similar to previously published results, except for shear velocity–to–wave celerity ratios larger than 2, where the newly calculated growth rates start to decrease after having reached a distinct maximum. The ratio of the spatial to temporal growth rates is examined. It is shown to deviate by up to 20% from the leading-order value of 2. The implications of the growth rate to the modal distributions of energy input from wind to waves, for young and mature seas, and in temporal/spatial growth scenarios, are analyzed.

Experimental study of the initial stages of wind waves' spatial evolution

2011 ◽  
Vol 681 ◽  
pp. 462-498 ◽  
Author(s):  
DAN LIBERZON ◽  
LEV SHEMER
Keyword(s):  
Energy Transfer ◽  
Growth Rates ◽  
Water Surface ◽  
Wind Waves ◽  
Pressure Fluctuations ◽  
Theoretical Models ◽  
Small Scale ◽  
Wave Flume ◽  
Spatial Growth ◽  
The Mean

Despite a significant progress and numerous publications over the last few decades a comprehensive understanding of the process of waves' excitation by wind still has not been achieved. The main goal of the present work was to provide as comprehensive as possible set of experimental data that can be quantitatively compared with theoretical models. Measurements at various air flow rates and at numerous fetches were carried out in a small scale, closed-loop, 5 m long wind wave flume. Mean airflow velocity and fluctuations of the static pressure were measured at 38 vertical locations above the mean water surface simultaneously with determination of instantaneous water surface elevations by wave gauges. Instantaneous fluctuations of two velocity components were recorded for all vertical locations at a single fetch. The water surface drift velocity was determined by the particle tracking velocimetry (PTV) method. Evaluation of spatial growth rates of waves at various frequencies was performed using wave gauge records at various fetches. Phase relations between various signals were established by cross-spectral analysis. Waves' celerities and pressure fluctuation phase lags relative to the surface elevation were determined. Pressure values at the water surface were determined by extrapolating the measured vertical profile of pressure fluctuations to the mean water level and used to calculate the form drag and consequently the energy transfer rates from wind to waves. Directly obtained spatial growth rates were compared with those obtained from energy transfer calculations, as well as with previously available data.

Experimental study of the stability of boundary-layer flow along a heated, inclined plate

1998 ◽  
Vol 367 ◽  
pp. 1-25 ◽  
Author(s):  
E. J. ZUERCHER ◽  
J. W. JACOBS ◽  
C. F. CHEN
Keyword(s):  
Boundary Layer ◽  
Growth Rates ◽  
Growth Curves ◽  
Leading Edge ◽  
Heated Plate ◽  
Inclined Plate ◽  
Double Pass ◽  
Longitudinal Vortices ◽  
Spatial Growth ◽  
Layer Flow

Experiments are conducted to study the longitudinal vortices that develop in the boundary layer on the upper surface of an inclined, heated plate. An isothermal plate in water is inclined at angles ranging from 20 to 60 degrees (from the vertical) while the temperature difference is varied from 2 to 23°C. A double-pass Schlieren system is used to visualize the vortices and particle image velocimetry (PIV) is used to measure velocities. In addition, a unique method is developed such that both the Schlieren visualization and PIV can be performed simultaneously. The wavelengths of the vortices and the critical modified Reynolds numbers (R˜) for the onset, merging, and breakup of the vortices are determined from Schlieren images for Pr=5.8. The critical values for R˜ and the critical wavelengths are compared to results of previous experiments and stability analyses. The spatial growth rates of vortices are determined by using the PIV measurements to determine how the circulation in the vortices grows with distance from the leading edge. This is the first time that the growth rate of the vortices have been found using velocity measurements. These spatial growth rates are compared to the results of Iyer & Kelly (1974) and found to be in general agreement. By defining a suitable circulation threshold, the critical R˜ for the onset of the vortices can be found from the growth curves.

Plasma waves in hot relativistic beam-plasma systems. Part 2. Kinetic and hydrodynamic instabilities

1990 ◽  
Vol 44 (2) ◽  
pp. 213-229 ◽  
Author(s):  
Alain Magneville
Keyword(s):  
Growth Rates ◽  
Unusual Case ◽  
Plasma Waves ◽  
Hydrodynamic Instabilities ◽  
Plasma System ◽  
Beam Velocity ◽  
Relativistic Beam ◽  
Beam Plasma ◽  
Temporal And Spatial ◽  
Kinetic Instabilities

Temporal and spatial hydrodynamical instabilities and kinetic instabilities of plasma waves are considered for a relativistic beam–plasma System. The beam and plasma temperatures, and the beam velocity, may be relativistic. Instability conditions and growth rates are evaluated. An unusual case of kinetic stability inversion, for relativistic or dense beams, is discussed.

Anchovy foraging: simulating spatial and temporal match/mismatches with zooplankton

2000 ◽  
Vol 57 (10) ◽  
pp. 2044-2053 ◽  
Author(s):  
Éva E Plagányi ◽  
Larry Hutchings ◽  
John G Field
Keyword(s):  
South African ◽  
Growth Rates ◽  
Predator Avoidance ◽  
Spatial Arrangement ◽  
Fish Growth ◽  
School Structure ◽  
The West ◽  
Temporal And Spatial ◽  
Mismatch Hypothesis ◽  
Temporal Overlap

Prey abundance is only a useful correlate of fish growth rate if it is considered within a match/mismatch hypothesis framework. We developed a model to explore the extent to which the growth rates of juvenile anchovies (Engraulis capensis) are influenced by temporal and spatial match/mismatches with the copepod Calanoides carinatus, a major component of their diet. The distributions of copepods and anchovies are dynamic, so that predation by anchovy may dramatically impact on its prey's spatial distribution. Predation rates by resident fish were commensurate with the average and maximum specific copepod production rates at fish densities of approximately 1 and 3.5 t·km-2, respectively. The spatial arrangement of fish biomass and the temporal overlap between fish and copepod abundances substantially modified both anchovy and copepod growth estimates. Predicted optimal shoal sizes suggest that additional factors such as predator avoidance or the energetics of maintaining school structure may be important. The model emulated observed variability in anchovy growth rates and confirmed the prediction that the availability of high-sustained abundances of food along the West Coast may be a critical "bottleneck" contributing to the strength of recruitment to the South African pelagic purse-seine fishery.

Temporal and spatial variation in the growth rates of Baltic herring (Clupea harengus membras L.) larvae during summer

2003 ◽  
Vol 142 (1) ◽  
pp. 25-33 ◽  
Author(s):  
T. Hakala ◽  
M. Viitasalo ◽  
H. Rita ◽  
E. Aro ◽  
J. Flinkman ◽  
...  
Keyword(s):  
Spatial Variation ◽  
Growth Rates ◽  
Clupea Harengus ◽  
Temporal And Spatial Variation ◽  
Baltic Herring ◽  
Temporal And Spatial
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