Finite amplitude analysis of non-isothermal parallel flow in a vertical channel filled with a highly permeable porous medium

2018 ◽  
Vol 857 ◽  
pp. 469-507 ◽  
Author(s):  
Abhishek K. Sharma ◽  
Manish K. Khandelwal ◽  
P. Bera
Keyword(s):  
Porous Medium ◽  
Energy Spectrum ◽  
Kinetic Energy ◽  
Critical Point ◽  
Bifurcation Point ◽  
Vertical Channel ◽  
Finite Amplitude ◽  
Parallel Flow ◽  
Kinetic Energy Spectrum ◽  
Nonlinear Kinetic

This paper addresses the finite amplitude instability of stably stratified non-isothermal parallel flow in a vertical channel filled with a highly permeable porous medium. A cubic Landau equation is derived to study the limiting value of growth of instabilities under nonlinear effects. The non-Darcy model is considered to describe the flow instabilities in a porous medium. The nonlinear results are presented for air as well as water. The analysis is carried out in the vicinity of as well as away from the critical point (bifurcation point). It is found that when the medium is saturated by water then supercritical bifurcation is the only type of bifurcation at and beyond the bifurcation point. However, for air, depending on the strength of the flow and permeability of the medium, both supercritical and subcritical bifurcations are observed. The influence of nonlinear interaction of different harmonics on the heat transfer rate, friction coefficient, nonlinear kinetic energy spectrum and disturbance flow is also studied in both supercritical as well as subcritical regimes. The variation of neutral stability curves of parallel mixed convection flow of air with wavenumber reveals that a bifurcation that is supercritical for some wavenumber may be subcritical orvice versaat other nearby wavenumbers. The analysis of the nonlinear kinetic energy spectrum of the fundamental disturbance also supports the existence of supercritical/subcritical bifurcation at and away from the critical point. The effect of different harmonics on the pattern of secondary flow, based on linear stability theory, is also studied and a significant influence is found, especially in the subcritical regime.

scholarly journals Calculating Energy Spectra from Drifters

2016 ◽  
Author(s):  
Joseph H. LaCasce
Keyword(s):  
Energy Spectrum ◽  
Kinetic Energy ◽  
Structure Function ◽  
Two Dimensions ◽  
Longitudinal Structure ◽  
Kinetic Energy Spectrum ◽  
Longitudinal Structure Function ◽  
Large Pair ◽  
Non Local ◽  
Lagrangian Data

The relations between the kinetic energy spectrum and the second order longitudinal structure function in two dimensions are derived, and several examples are considered. The forward conversion (from spectrum to structure function) is illustrated first with idealized power law spectra, representing turbulent inertial ranges. The forward conversion is also applied to the zonal kinetic energy spectrum of Nastrom and Gage (1985) and the result agrees well with the longitudinal structure function of Lindborg (1999). The inverse conversion (from structure function to spectrum) is tested with data from 2D turbulence simulations. When applied to the theoretical structure function (derived from the forward conversion of the spectrum), the result closely resembles the original spectrum, except at the largest wavenumbers. However the inverse conversion is much less successful when applied to the structure function obtained from pairs of particles in the flow. This is because the inverse conversion favors large pair separations, which are typically noisy with particle data. Fitting the structure function to a polynomial improves the result, but not sufficiently to distinguish the correct inertial range dependencies. Furthermore the inversion of non-local spectra is largely unsuccessful. Thus it appears that focusing on structure functions with Lagrangian data is preferable to estimating spectra.

Kinetic energy spectrum of large-and mesoscale atmospheric processes

Nature ◽  
1984 ◽  
Vol 310 (5972) ◽  
pp. 36-38 ◽  
Author(s):  
G. D. Nastrom ◽  
K. S. Gage ◽  
W. H. Jasperson
Keyword(s):  
Energy Spectrum ◽  
Kinetic Energy ◽  
Atmospheric Processes ◽  
Kinetic Energy Spectrum

scholarly journals Comment on "Reinterpreting aircraft measurement in anisotropic scaling turbulence" by Lovejoy et al. (2009)

2010 ◽  
Vol 10 (3) ◽  
pp. 1401-1402 ◽  
Author(s):  
E. Lindborg ◽  
K. K. Tung ◽  
G. D. Nastrom ◽  
J. Y. N. Cho ◽  
K. S. Gage
Keyword(s):  
Energy Spectrum ◽  
Kinetic Energy ◽  
General Circulation ◽  
General Circulation Models ◽  
Measured Spectrum ◽  
Vertical Movements ◽  
Aircraft Measurement ◽  
Kinetic Energy Spectrum ◽  
Anisotropic Scaling ◽  
The 1960S

Abstract. Recently, Lovejoy et al. (2009) argued that the steep ~k−3 atmospheric kinetic energy spectrum at synoptic scales (≥1000 km) observed by aircraft is a spurious artefact of aircraft following isobars instead of isoheights. Without taking into account the earth's rotation they hypothesise that the horizontal atmospheric energy spectrum should scale as k−5/3 at all scales. We point out that the approximate k−3-spectrum at synoptic scales has been observed by a number of non-aircraft means since the 1960s and that general circulation models and other current models have successfully produced this spectrum. We also argue that the vertical movements of the aircraft are far too small to cause any strong effect on the measured spectrum at synoptic scales.

Decrypting the charge-resolved kinetic-energy spectrum in the Coulomb explosion of argon clusters

2012 ◽  
Vol 85 (2) ◽  
Author(s):  
R. Rajeev ◽  
K. P. M. Rishad ◽  
T. Madhu Trivikram ◽  
V. Narayanan ◽  
T. Brabec ◽  
...  
Keyword(s):  
Energy Spectrum ◽  
Kinetic Energy ◽  
Coulomb Explosion ◽  
Kinetic Energy Spectrum ◽  
Argon Clusters

Kinetic energy spectrum and polarization of neutrons from the reaction 12C(p,n)X at 590 MeV

1998 ◽  
Vol 2 (4) ◽  
pp. 411-415 ◽  
Author(s):  
J. Arnold ◽  
B. van den Brandt ◽  
M. Daum ◽  
M. Finger ◽  
M. Finger ◽  
...  
Keyword(s):  
Energy Spectrum ◽  
Kinetic Energy ◽  
Kinetic Energy Spectrum

The mixing layer and its coherence examined from the point of view of two-dimensional turbulence

1988 ◽  
Vol 192 ◽  
pp. 511-534 ◽  
Author(s):  
Marcel Lesieur ◽  
Chantal Staquet ◽  
Pascal Le Roy ◽  
Pierre Comte
Keyword(s):  
Energy Spectrum ◽  
Kinetic Energy ◽  
White Noise ◽  
Mixing Layer ◽  
Finite Size ◽  
Spanwise Direction ◽  
Computational Domain ◽  
Two Dimensional ◽  
Infinite Domain ◽  
Kinetic Energy Spectrum

A two-dimensional numerical large-eddy simulation of a temporal mixing layer submitted to a white-noise perturbation is performed. It is shown that the first pairing of vortices having the same sign is responsible for the formation of a continuous spatial longitudinal energy spectrum of slope between k−4 and k−3. After two successive pairings this spectral range extends to more than 1 decade. The vorticity thickness, averaged over several calculations differing by the initial white-noise realization, is shown to grow linearly, and eventually saturates. This saturation is associated with the finite size of the computational domain.We then examine the predictability of the mixing layer, considering the growth of decorrelation between pairs of flows differing slightly at the first roll-up. The inverse cascade of error through the kinetic energy spectrum is displayed. The error rate is shown to grow exponentially, and saturates together with the levelling-off of the vorticity thickness growth. Extrapolation of these results leads to the conclusion that, in an infinite domain, the two fields would become completely decorrelated. It turns out that the two-dimensional mixing layer is an example of flow that is unpredictable and possesses a broadband kinetic energy spectrum, though composed mainly of spatially coherent structures.It is finally shown how this two-dimensional predictability analysis can be associated with the growth of a particular spanwise perturbation developing on a Kelvin-Helmholtz billow: this is done in the framework of a one-mode spectral truncation in the spanwise direction. Within this analogy, the loss of two-dimensional predictability would correspond to a return to three-dimensionality and a loss of coherence. We indicate also how a new coherent structure could then be recreated, using an eddy-viscosity assumption and the linear instability of the mean inflexional shear.

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