Spatial stability of the non-parallel Bickley jet

1981 ◽  
Vol 102 ◽  
pp. 127-140 ◽  
Author(s):  
Vijay K. Garg
Keyword(s):  
Growth Rate ◽  
Energy Density ◽  
Critical Reynolds Number ◽  
Transverse Velocity ◽  
Parallel Flow ◽  
Wave Number ◽  
Amplitude Wave ◽  
Spatial Stability ◽  
Rate Dependent ◽  
Neutral Curves

The spatial stability of the plane, two-dimensional jet flow to infinitesimal disturbances is investigated by taking into account the effects of transverse velocity component and the streamwise variations of the basic flow and of the disturbance amplitude, wave-number and spatial growth rate. This renders the growth rate dependent on the flow variable as well as on the transverse and streamwise co-ordinates. Growth rates for the energy density of the disturbance and the associated neutral curves are provided as a function of the streamwise co-ordinate. Variation of growth rate of the disturbance stream function and streamwise component of velocity with the transverse co-ordinate is also given for different disturbance frequencies and streamwise locations. Results are compared with those for the parallel-flow stability analysis, and also with those for an analysis that accounts for only some of the non-parallel effects. It is found that the critical Reynolds number based on the growth of energy density of the disturbance depends on the streamwise co-ordinate and lies within the range (around 20) found experimentally, while the parallel-flow theory yields a rather low value of 4·0.

Stability of Nonparallel Developing Flow in an Annulus to Asymmetric Disturbances

1982 ◽  
Vol 49 (2) ◽  
pp. 436-439
Author(s):  
V. K. Garg
Keyword(s):  
Reynolds Number ◽  
Critical Reynolds Number ◽  
Flow Theory ◽  
Diameter Ratio ◽  
Parallel Flow ◽  
Wave Number ◽  
Spatial Stability ◽  
Concentric Annulus ◽  
Developing Flow ◽  
Azimuthal Wave Number

Linear spatial stability of the nonparallel developing flow in a concentric annulus shows that the asymmetric disturbance with an azimuthal wave number equal to unity is more unstable than the axisymmetric disturbance at all axial locations. Also, in the near entry region, the critical Reynolds number corresponding to the parallel flow theory is as much as three times that due to the nonparallel theory for some values of the annular diameter ratio.

scholarly journals Study of Oblique Propagating Whistler Mode Waves in Presence of Parallel DC Electric Field in Magnetosphere of Saturn

2017 ◽  
Vol 6 (2) ◽  
pp. 26 ◽  
Author(s):  
R. Kaur ◽  
R. S. Pandey
Keyword(s):  
Growth Rate ◽  
Distribution Function ◽  
Energy Density ◽  
Wave Number ◽  
Number Density ◽  
Temperature Anisotropy ◽  
Loss Cone ◽  
Whistler Mode ◽  
Whistler Mode Waves ◽  
Magnetosphere Of Saturn

In this paper whistler mode waves have been investigated in magnetosphere of Saturn. The derivation for perturbed distribution function, dispersion relation and growth rate have been determined by using the method of characteristic and kinetic approach. Analytical expressions for growth rate and real frequency of whistlers propagating oblique to magnetic field direction are attained. Calculations have been performed at 6 radial distances in plasma sheet region of Saturn’s magnetosphere as per data provided by Cassini. Work has been extended for bi-Maxwellian as well as Loss-cone distribution function. Parametric analysis show that temperature anisotropy, increase in number density, energy density and angle of propagation increases the growth rate of whistler waves along with significant shift in wave number. In case of Loss-cone distribution, increase in growth rate of whistlers is significantly more than for bi-Maxwellian distribution function. Generation of second harmonics can also be seen in the graphs plotted. It is concluded that parallel DC field stabilizes the wave and temperature anisotropy, angle of propagation, number density and energy density of electrons enhances the growth rate. Thus the results are of importance in analyzing observed VLF emissions over wide spectrum of frequency range in Saturnian magnetosphere. The analytical model developed can also be used to study various types of instabilities in planetary magnetospheres. 

Stability of Developing Flow in a Pipe—Nonparallel Effects

1981 ◽  
Vol 48 (2) ◽  
pp. 243-248 ◽  
Author(s):  
V. K. Garg ◽  
S. C. Gupta
Keyword(s):  
Growth Rate ◽  
Reynolds Number ◽  
Critical Reynolds Number ◽  
Flow Region ◽  
Flow Theory ◽  
Parallel Flow ◽  
Integration Scheme ◽  
Developing Flow ◽  
Critical Reynolds Numbers ◽  
Pass Through

A theoretical investigation into the linear, spatial instability of the developing flow in a rigid circular pipe, incorporating the effects of nonparallelism of the main flow, has been made at several axial locations. The velocity profile in the developing flow region is obtained by a finite-difference method assuming uniform flow at the entry to the pipe. For the stability analysis, the continuity and momentum equations have been integrated separately using fourth-order Runge-Kutta integration scheme and applying selectively the Gram-Schmidt orthonormalization procedure to circumvent the parasitic error-growth problem. It is found that the critical frequency, obtained from different growth rates, decreases first sharply and then gradually with increasing X, where X = x/aR = X/R; x being the streamwise distance measured from the pipe inlet, a being the radius of the pipe, and R the Reynolds number based on a and average velocity of flow. However, the critical Reynolds number versus X curves pass through a minima. The minimum critical Reynolds number corresponding to gψ(X, O), the growth rate of stream function at the pipe axis, to gE(X), the growth rate of energy density, and to the parallel flow theory are 9700 at X = 0.00325, 11,000 at X = 0.0035, and 11,700 at X = 0.0035, respectively. It is found that the actual developing flow remains unstable over a larger inlet length of the pipe than its parallel-flow approximate. The first instability of the flow on the basis of gψ(X, O), gE(X) and the parallel flow theory, is found to occur in the range 30 ≤ X ≤ 36, 35 ≤ X ≤ 43, and 36 ≤ X ≤ 45, respectively. The critical Reynolds numbers obtained on the basis of gψ(X, O) are closest to the experimental values.

Saturation mechanism and generated viscosity in gravito-turbulent accretion disks

2020 ◽  
Vol 640 ◽  
pp. A53
Author(s):  
L. Löhnert ◽  
S. Krätschmer ◽  
A. G. Peeters
Keyword(s):  
Growth Rate ◽  
Numerical Simulations ◽  
Accretion Disks ◽  
Gravitational Instability ◽  
Turbulent Viscosity ◽  
Radial Distance ◽  
Maximum Growth ◽  
Wave Number ◽  
Radiative Cooling ◽  
Mixing Length

Here, we address the turbulent dynamics of the gravitational instability in accretion disks, retaining both radiative cooling and irradiation. Due to radiative cooling, the disk is unstable for all values of the Toomre parameter, and an accurate estimate of the maximum growth rate is derived analytically. A detailed study of the turbulent spectra shows a rapid decay with an azimuthal wave number stronger than ky−3, whereas the spectrum is more broad in the radial direction and shows a scaling in the range kx−3 to kx−2. The radial component of the radial velocity profile consists of a superposition of shocks of different heights, and is similar to that found in Burgers’ turbulence. Assuming saturation occurs through nonlinear wave steepening leading to shock formation, we developed a mixing-length model in which the typical length scale is related to the average radial distance between shocks. Furthermore, since the numerical simulations show that linear drive is necessary in order to sustain turbulence, we used the growth rate of the most unstable mode to estimate the typical timescale. The mixing-length model that was obtained agrees well with numerical simulations. The model gives an analytic expression for the turbulent viscosity as a function of the Toomre parameter and cooling time. It predicts that relevant values of α = 10−3 can be obtained in disks that have a Toomre parameter as high as Q ≈ 10.

Stability of thermocapillary flows in non-cylindrical liquid bridges

2002 ◽  
Vol 458 ◽  
pp. 35-73 ◽  
Author(s):  
CH. NIENHÜSER ◽  
H. C. KUHLMANN
Keyword(s):  
Reynolds Number ◽  
Prandtl Number ◽  
Critical Reynolds Number ◽  
Volume Fraction ◽  
Thermocapillary Flow ◽  
Surface Shape ◽  
Liquid Bridges ◽  
Gravity Level ◽  
Neutral Curves ◽  
Prandtl Numbers

The thermocapillary flow in liquid bridges is investigated numerically. In the limit of large mean surface tension the free-surface shape is independent of the flow and temperature fields and depends only on the volume of liquid and the hydrostatic pressure difference. When gravity acts parallel to the axis of the liquid bridge the shape is axisymmetric. A differential heating of the bounding circular disks then causes a steady two-dimensional thermocapillary flow which is calculated by a finite-difference method on body-fitted coordinates. The linear-stability problem for the basic flow is solved using azimuthal normal modes computed with the same discretization method. The dependence of the critical Reynolds number on the volume fraction, gravity level, Prandtl number, and aspect ratio is explained by analysing the energy budgets of the neutral modes. For small Prandtl numbers (Pr = 0.02) the critical Reynolds number exhibits a smooth minimum near volume fractions which approximately correspond to the volume of a cylindrical bridge. When the Prandtl number is large (Pr = 4) the intersection of two neutral curves results in a sharp peak of the critical Reynolds number. Since the instabilities for low and high Prandtl numbers are markedly different, the influence of gravity leads to a distinctly different behaviour. While the hydrostatic shape of the bridge is the most important effect of gravity on the critical point for low-Prandtl-number flows, buoyancy is the dominating factor for the stability of the flow in a gravity field when the Prandtl number is high.

A screen for Neurospora knockout mutants displaying growth rate dependent branch density

2011 ◽  
Vol 115 (3) ◽  
pp. 296-301 ◽  
Author(s):  
Michael K. Watters ◽  
Michael Boersma ◽  
Melodie Johnson ◽  
Ciara Reyes ◽  
Evan Westrick ◽  
...  
Keyword(s):  
Growth Rate ◽  
Rate Dependent ◽  
Knockout Mutants ◽  
Branch Density

Growth-rate dependent regulation of mRNA stability in Escherichia coli

Nature ◽  
1984 ◽  
Vol 312 (5989) ◽  
pp. 75-77 ◽  
Author(s):  
G. Nilsson ◽  
J. G. Belasco ◽  
S. N. Cohen ◽  
A. von Gabain
Keyword(s):  
Escherichia Coli ◽  
Growth Rate ◽  
Mrna Stability ◽  
Rate Dependent

Bio-Inspired Robotic Undulatory Stingray

2016 ◽  
Author(s):  
Emily Studebaker ◽  
William Ermlick ◽  
Rickey Warner ◽  
Brandon Hart ◽  
Aanand Pandey ◽  
...  
Keyword(s):  
Qualitative Agreement ◽  
Wave Speed ◽  
Wave Amplitude ◽  
Wave Number ◽  
Computational Results ◽  
Cfd Simulations ◽  
Amplitude Wave ◽  
And Control ◽  
Undulating Fin

The purpose of this study was to investigate fin undulation as a form of locomotion. The analysis generated CFD simulations and models that identify characteristics that are known to indicate propulsive forces. A mechanical undulating fin was designed and built to experimentally validate these computational results. Comparing thrust data from the mechanical fin with the CFD results yielded qualitative agreement with various parameters including wave amplitude, wave speed, and wave number. Quantifying these characteristics are necessary towards understanding the mechanics of undulation and will aid in the design and control of underwater undulating robotics.

Effect of Velocity Profile on the Stability of Liquid Sheet

2014 ◽  
Vol 694 ◽  
pp. 288-291
Author(s):  
Run Ze Duan ◽  
Zhi Ying Chen ◽  
Li Jun Yang
Keyword(s):  
Growth Rate ◽  
Velocity Profile ◽  
Linear Analysis ◽  
Liquid Sheet ◽  
Wave Number ◽  
Flat Plates ◽  
Chebyshev Spectral Collocation ◽  
The Stability ◽  
The Relationship ◽  
Temporal Growth Rate

An electrified liquid sheet injected into a dielectric moving through a viscous gas bounded by two horizontal parallel flat plates of a transverse electric field is investigated with the linear analysis method. The liquid sheet velocity profile and the gas boundary layer thickness are taken into account. The relationship between temporal growth rate and the wave number was obtained using linear stability analysis and solved using the Chebyshev spectral collocation method. The effects of the velocity profile on the stability of the electrified liquid sheet were revealed for both sinuous mode and varicose mode. The results show that the growth rate of the electrified Newtonian liquid is greater than that of corresponding Newtonian one under the same condition, and the growth rate of the sinuous mode is greater than that of the varicose mode. Keywords: instability; planar liquid sheet; velocity profile;spectral method;linear analysis

Sign in / Sign up

Export Citation Format

Share Document