1,575 research outputs found
Microscopic laws vs. Macroscopic laws: Perspectives from kinetic theory and hydrodynamics
Reductionism is a prevalent viewpoint in science according to which all
physical phenomena can be understood from fundamental laws of physics. Anderson
[Science, 177, 393 (1972)], Laughlin and Pines [PNAS, 97, 28 (2000)], and
others have countered this viewpoint and argued in favour hierarchical
structure of the universe and laws. In this paper we advance the latter
perspective by showing that some of the complex flow properties derived using
hydrodynamic equations (macroscopic laws) are very difficult, if not
impossible, to describe in microscopic framework---kinetic theory. These
properties include Kolmogorov's theory of turbulence, turbulence dissipation
and diffusion, and dynamic pressure. We also provide several other examples of
hierarchical description
Variable energy flux in quasi-static magnetohydrodynamic turbulence
Experiments and numerical simulations show that the energy spectrum of the
magnetohydrodynamic turbulence in the quasi-static limit deviates from
Kolmogorov's spectrum as the external magnetic field, or
equivalently the interaction parameter, is increased. To explain this
phenomena, we construct an analytical turbulence model with variable energy
flux that arises due to the Lorentz-force induced dissipation. The energy
spectra computed using our model for various interaction parameters are in
qualitative agreement with earlier experimental and numerical results.Comment: 12 page
Contrasting turbulence in stably stratified flows and thermal convection
In this paper, the properties of stably stratified turbulence (SST) and
turbulent thermal convection are contrasted. A key difference between these
flows is the sign of the kinetic energy feed by buoyancy, . For
SST, due to its stable nature; consequently, the kinetic
energy flux decreases with wavenumber that leads to a steep
kinetic energy spectrum, . Turbulent convection is
unstable, hence that leads to an increase of
with ; this increase however is marginal due to relatively weak buoyancy,
hence , similar to that in hydrodynamic turbulence. This
paper also describes the conserved fluxes for the above systems.Comment: to appear in Physica Script
On Generation of magnetic field in astrophysical bodies
In this letter we compute energy transfer rates from velocity field to
magnetic field in MHD turbulence using field-theoretic method. The striking
result of our field theoretic calculation is that there is a large energy
transfer rate from the large-scale velocity field to the large-scale magnetic
field. We claim that the growth of large-scale magnetic energy is primarily due
to this transfer. We reached the above conclusion without any linear
approximation like that in -dynamo.Comment: 4 pages, Revtex, 1 figur
Mean magnetic field renormalization and Kolmogorov's energy spectrum in MHD turbulence
In this paper we construct a self-consistent renormalization group procedure
for MHD turbulence in which small wavenumber modes are averaged out, and
effective mean magnetic field at large wavenumbers is obtained. In this scheme
the mean magnetic field scales as , while the energy spectrum scales
as similar to that in fluid turbulence. We also deduce from the
formalism that the magnitude of cascade rate decreases as the strength of the
mean magnetic field is increased.Comment: 14 pages REVTEX, 1 postscript figure, Submitted to Phys. Plasma
Turbulent Heating in the Solar Wind and in the Solar Corona
In this paper we calculate the turbulent heating rates in the solar wind
using the Kolmogorov-like MHD turbulence phenomenology with Kolmogorov's
constants calculated by {\it Verma and Bhattacharjee }[1995b,c]. We find that
the turbulent heating can not account for the total heating of the
nonAlfv\'enic streams in the solar wind. We show that dissipation due to
thermal conduction is also a potential heating source. Regarding the Alfv\'enic
streams, the predicted turbulent heating rates using the constants of {\it
Verma and Bhattacharjee }[1995c] are higher than the observed heating rates;
the predicted dissipation rates are probably overestimates because Alfv\'enic
streams have not reached steady-state. We also compare the predicted turbulent
heating rates in the solar corona with the observations; the Kolmogorov-like
phenomenology predicts dissipation rates comparable to the observed heating
rates in the corona [{\it Hollweg, }% 1984], but Dobrowoly et al.'s generalized
Kraichnan model yields heating rates much less than that required.Comment: Latex, 22 pages, no figures, submitted to Journal of Geophysical
Researc
Introduction to Statstical Theory of Fluid Turbulence
This is a brief introduction to the statistical theory of fluid turbulence,
with emphasis on field-theoretic treatment of renormalized viscosity and energy
fluxes.Comment: 40 pages; The labels in Feynman diagram missing due to tex problems.
Look at my webpage http://home.iitk.ac.in/~mkv//prof/publications.html for
proper Feynman diagram
Turbulent drag reduction: A universal perspective from energy fluxes
Injection of dilute polymer in a turbulent flow suppresses frictional drag.
This challenging and technologically important problem remains primarily
unresolved due to the complex nature of the flow. An important factor in the
drag reduction is the energy transfer from the velocity field to the polymers.
In this paper we quantify this process using energy fluxes, as well as show its
universality in diverse flows such as magnetohydrodynamics, quasi-static
magnetohydrodynamics, and bubbly turbulence. We show that in such flows, the
transfer from kinetic energy to elastic energy leads to a reduction in kinetic
energy flux compared to the corresponding hydrodynamic turbulence. This leads
to a reduction in nonlinearity of the velocity field that results into a more
ordered flow and a suppression of turbulent drag
Anisotropy in Quasi-Static Magnetohydrodynamic Turbulence
In this review we summarise the current status of the quasi-static
magnetohydrodynamic turbulence. The energy spectrum is steeper than
Kolmogorov's spectrum due to the decrease of the kinetic energy flux
with wavenumber as a result of Joule dissipation. The spectral index
decreases with the increase of interaction parameter. The flow is quasi
two-dimensional with strong at small and weak
at large , where and are the perpendicular and
parallel components of velocity relative to the external magnetic field. For
small , the energy flux of is negative, but for large ,
the energy flux of is positive. Pressure mediates the energy
transfer from to .Comment: Review articl
Direct Interaction Approximation of Magnetohydrodynamic Turbulence
In this paper we apply Kraichnan's direct interaction approximation, which is
a one loop perturbation expansion, to magnetohydrodynamic turbulence. By
substituting the energy spectra both from kolmogorov-like MHD turbulence
phenomenology and a generalization of Dobrowolny et al.'s model we obtain
Kolmogorov's and Kraichnan's constant for MHD turbulence. We find that the
constants depend of the Alfv\'en ratio and normalized cross helicity; the
dependence has been studied here. We also demonstrate the inverse cascade of
magnetic energy for Kolmogorov-like models. Our results are in general
agreement with the earlier simulation results except for large normalized cross
helicity.Comment: Revtex, 32 pages, submitted to Phys. Rev. E, 3 figures: available
upon request at [email protected]
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