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  • Author or Editor: William W. Fowlis x
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William W. Fowlis and Richard L. Pfeffer

Abstract

The radial distribution of the azimuthally averaged temperature at one depth in a rotating, differentially heated annulus of fluid undergoing “amplitude vacillation” is measured with an array of 48 thermocouples suspended on fine wires in the fluid. The properties of amplitude vacillation and the feasibility of making measurements with multi-probe arrays (properly staggered in the fluid to avoid disrupting the organized flow) are discussed.

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Basil N. Antar and William W. Fowlis

Abstract

The stability of a thin fluid layer between two rotating plates which are subjected to a horizontal temperature gradient is studied. First, the solution for the stationary basic state is obtained in a closed form. This solution identifies Ekman and thermal layers adjacent to the plates and interior temperature and velocity fields which are almost linear functions of height. Then the stability of that basic state with respect to infinitesimal zonal waves is analyzed via the solution of the complete viscous linear equations for the perturbations. The character of the growth rates is found to be similar to the growth rates of the classical baroclinic waves. The neutral stability curves for these waves possessed a knee in the Rossby-Taylor number plane to the left of which all perturbations are stable. The region of instability is found to depend on the Prandtl number, the vertical stratification parameter, and both the meridional and zonal wavenumbers. It is found in general that the flow is unstable for small enough Ekman numbers and for Rossby numbers less than 10. It is also found that increased vertical stable stratification and increased Prandtl number stabilize the flow.

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Basil N. Antar and William W. Fowlis

Abstract

A Stability analysis of a thin horizontal rotating fluid layer which is subjected to arbitrary horizontal and vertical temperature gradients is presented. The basic state is a nonlinear Hadley cell which contains both Ekman and thermal boundary layers; it is given in closed form. The stability analysis is based on the linearized Navier-Stokes equations, and zonally symmetric perturbations in the form of waves propagating in the meridional direction are considered. Numerical methods were used for the stability problem. The objective of this investigation was to extend previous work on symmetric baroclinic instability with a more realistic model. Hence, the study deals with flows for which the Richardson number (based on temperature and flow gradients at mid-depth) is of order unity and less. The computations cover ranges of Prandtl number 0.2 ≤ σ ≤ 5, Rossby number 10−2 ≤ ε ≤ 102 and Ekman number 10−4 ≤ E ≤ 10−1. It was found, in agreement with previous work, that the instability sets in when the Richardson number is close to unity and that the critical Richardson number is a non-monotonic function of the Prandtl number. Further, it was found that the critical Richardson number decreases with increasing Ekman number until a critical value of the Ekman number is reached beyond which the fluid is stable. The principal of exchange of stability was not assumed and growth rates wore calculated. A wavelength of maximum growth rate was found. For our model overstability was not found. Some computations were performed for Richardson numbers less than zero. No discontinuities in growth rates are noticeable when the Richardson number changes sign. This result indicates a smooth transition from symmetric baroclinic instability to a convective instability.

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