All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 1 1 1
PDF Downloads 2 2 2

An Experimental Study of Baroclinic Annulus Waves at Large Taylor Number

View More View Less
  • 1 Dept. of Geology and Geophysics, Massachusetts Institute of Technology, Cambridge 02108
Full access

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)].

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)].

Save