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Acceleration covariance in isotropic hydromagnetic turbulence

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Abstract

The present paper deals with the turbulent flow of an incompressible, viscous and conducting fluid which is isotropic, spatially homogeneous. The expression for acceleration covariance is derived. The obtained result shows that the defining scalars α(r, t) and β(r, t) of the acceleration covariance in MHD turbulence depend on the defining scalars of Q ij , H ij , Π ij and S ik, j .

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Abbreviations

h i :

turbulence component of the magnetic field H divided by (4πρ/μ)1/2

p :

turbulent fluctuation of static pressure

r :

distance between two points

t :

time

u i :

turbulence components of the velocity field

x i :

Eulerian Cartesian Coordinates, i=1, 2, 3

P(r), Q ij , Π jl , H ij Π ik , S ik, j :

correlation tensors defined by the set of relations (12)

Π 1, Π 2, Q, H, S :

defining scalars of Π jl , Q ij , H ij and S ik, j respectively

δ ij :

Kronecker delta

ε :

dissipation by turbulence per unit of mass

λ :

(4πσμ)−1

μ :

magnetic permeability

ν :

kinematic viscosity

ξ i :

Eulerian Cartesian coordinates, i=1, 2, 3

π :

3.14159

ρ :

density

p:

time mean value of density

ρ :

turbulent fluctuation of density

σ :

electrical conductivity

ω :

turbulent fluctuation of total pressure

∂ :

partial differential operator

▽ 2 :

Laplacian operator, \(\frac{{\partial ^2 }}{{\partial \chi _i \partial \chi _i }}\)

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Authors and Affiliations

  1. Dept. of Mathematics Faculty of Science, Banaras Hindu University, Varnasi-5, India

    R. S. Mishra & N. Kishore

Authors
  1. R. S. Mishra
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  2. N. Kishore
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Mishra, R.S., Kishore, N. Acceleration covariance in isotropic hydromagnetic turbulence. Appl. Sci. Res. 24, 44–52 (1971). https://doi.org/10.1007/BF00411703

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  • DOI: https://doi.org/10.1007/BF00411703

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