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Effect of aspect ratio on the meridional circulation of a rotating homogeneous fluid

  • V. Somaraju
  • D. A. Mohandas
  • R. Balasubramanian
Article
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Abstract

The effect of aspect ratio on the meridional circulation of a homogeneous fluid is analyzed. Aspect ratio is allowed to range between zero and unity. Relationships between possible horizontal and vertical length scales are obtained by length scale analysis as well as by solving an idealized problem. It is found that whenE 1/2 ≪ Z ≪ E1/2/δ, whereE is the Ekman number, the stream lines are closely packed near the sidewall within a thickness ofO(E 1/2). The effect of stratification is unimportant within this depth range. In the depth rangeE 1/2 /δ ≪ Z ≪ 1/ the vertical boundary layer in which the streamlines are packed is ofO(EZδ) 1/3. WhenZ ≫ 1/Eδ it is shown that the circulation decays algebraically with depth as 1/Z.

Keywords

Aspect ratio meridional circulation homogeneous fluid 

List of symbols

u, v, w

Velocity components

ψ

Stream function

p

Pressure

H, L

Characteristic dimensions in vertical and horizontal directions

δ

aspect ratio

Av, Ah

Vertical and horizontal eddy coefficients of momentum

Ev, Eh

Vertical and horizontal Ekman numbers

h, l

Vertical and horizontal length scales

ξ

Vertical distance

m

Fourier transform variable

f

Coriolis parameter

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References

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    Bender C M and Orszag S A (1978) Advanced Mathematical methods for Scientists and Engineers, McGraw-Hill Book CompanyGoogle Scholar
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    Pedlosky J (1979)Geophys. Fluid Dynamics Springer VerlagGoogle Scholar
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    Stewartson K (1957) On almost rigid rotations, Part 2,J. Fluid Mech. 3 17–26MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Indian Academy of Sciences 1986

Authors and Affiliations

  • V. Somaraju
    • 1
  • D. A. Mohandas
    • 1
    • 2
  • R. Balasubramanian
    • 1
    • 2
  1. 1.S R K R Engineering CollegeBhimavaramIndia
  2. 2.P S G College of TechnologyCoimbatoreIndia

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