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Carl B. Ketchum

Abstract

A detailed survey of the temperature structure of the upper symmetric, regular wave, and irregular regimes in a differentially heated rotating annulus is presented. The results were obtained in a large gap width, ba = 15.28 cm, where a and b are the radii of the inner and outer walls of the annulus respectively, using a 4 × 4 grid of fine wire thermocouples. The principal results are:

  1. The value of Θ = gdΔρ/[ρ̄Ω(ba)], where g is the acceleration of gravity, d the depth of the fluid, Δρ the density difference corresponding to an impressed temperature difference of Δρ, ρ̄ the mean density of the fluid and Ω the rotation rate of the annulus, at the transition between the symmetric and regular wave regimes, is 3.7 for values of the Taylor number T = [4Ω(bc)4/β][(ba)/d] between 2.7 × 107 < T < 9.8 × 107, where v̄ is the mean coefficient of kinematic viscosity of the fluid.

  2. The vertical temperature difference within the fluid is almost independent of the rotation rate and flow regime, having a mean value of 0.78ΔT. The radial temperature difference outside of the side wall boundary layers exhibits more variation with the rotation rate and flow regime.

  3. The waves in the regular wave regime are a result of the baroclinic instability of the fluid and bear a qualitative resemblance to the waves obtained in Eady's model using the observed mean wave state to determine the basic state of the model. This latter result is obtained using the numerical results of Williams in conjunction with the experimental observations.

  4. The transition from the regular wave regime to the irregular regime occurs at much larger values of T than indicated by previous results using annuli with smaller gap widths and larger aspect ratios [d/(ba)].

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S. Trivikrama Rao and Carl B. Ketchum

Abstract

This paper reports the results of a statistical study of the temperature field of several examples of regular wave, vacillating flow and irregular flow in a rotating annulus with a gap width of 10 cm using a limited number of thermocouples. The primary results indicate that the regular waves produce several wavenumber harmonies through nonlinear interactions. The wavenumber harmonies decrease in the vacillating flow and are not detectable in the irregular flow. Further, the azimuthal coherence of the flow in the irregular regime decreases very rapidly in azimuth, and yet the vertical coherence is extremely high at all frequencies indicating a strong two-dimensional character of the irregular regime.

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S. Trivikrama Rao and Carl B. Ketchum

Abstract

The spectral characteristics of the temperature field associated with the baroclinic waves in a rotating annulus of water with a rigid upper surface are presented as an extension of Rao and Ketchum (1975). The results indicate a clear nonlinear maintenance of the harmonies of the fundamental wave in the equilibrated state similar to the feature observed with a free upper surface. The period of the temperature oscillation in the case of rigid upper surface is approximately four times longer than that with a free upper surface.

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