Baroclinic waves in an air-filled thermally driven rotating annulus

In this study an experimental investigation of baroclinic waves in air in a differentially heated rotating annulus is presented. Air has a Prandtl number of 0.707, which falls within a previously unexplored region of parameter space for baroclinic instability. The flow regimes encountered include steady waves, periodic amplitude vacillations, modulated amplitude vacillations, and either monochromatic or mixed wave number weak waves, the latter being characterized by having amplitudes less than 5% of the applied temperature contrast. The distribution of these flow regimes in parameter space are presented in a regime diagram. It was found that the progression of transitions between different regimes is, as predicted by recent numerical modeling results, in the opposite sense to that usually found in experiments with high Prandtl number liquids. No hysteresis in the flow type, with respect to variations in the rotation rate, was found in this investigation.

Figure 1

Experimental setup 1—temperature measurement.

Figure 2

(Color online) Experimental setup for flow visualization.

Figure 3

Frequency spectrum for an MAV wave signal showing the drift, vacillation, modulated vacillation, and rotationally induced alias frequencies. $\Omega =2.327$ giving an aliased frequency, ${\nu }_{\mathit{\text{alias}}}\approx 0.037\mathrm{Hz}$.

Figure 4

(Color online) Regime diagram. The dominant azimuthal wave number, $m$, is indicated by a number, the flow type is indicated with letters. Numbers designated $S$ denote a steady wave state, $W$ indicates a weak wave, AV denotes amplitude vacillation, and MAV modulated amplitude vacillations. Transitions between different wave numbers are shown with solid lines, whereas transitions between regimes of the same wave number are denoted by dotted lines. The corresponding normalized wave amplitude, $A_n$, is represented by shaded contours ($A_n=A_w∕\Delta T$, where $A_w$ is the wave amplitude in °C).

Figure 5

Time variation of the temperature amplitude of the dominant azimuthal wave number for the four types of flow: (a) Steady flow, $2S$ wave, $\mathrm{Ta}=4.26\times {10}^5$ and $\Theta =1.15$; (b) amplitude vacillation, 3 AV wave, $\mathrm{Ta}=8.23\times {10}^5$ and $\Theta =0.593$; (c) modulated amplitude vacillation, 3 MAV wave, $\mathrm{Ta}=10.2\times {10}^5$ and $\Theta =0.48$; and (d) weak wave, $1WS$, $\mathrm{Ta}=2.202\times {10}^5$ and $\Theta =2.218$.

Figure 6

Experimental azimuth-time temperature contour plot of a $2S$ wave ($\mathrm{Ta}=4.26\times {10}^5$ and $\Theta =1.15$) at midheight and midradius.

Figure 7

Experimental visualization of a $2S$ wave ($\mathrm{Ta}=4.26\times {10}^5$ and $\Theta =1.15$) at midheight.

Figure 8

Azimuth-time temperature contour plot of a traveling wave with $m=3$ at midheight and midradius, showing amplitude vacillation. ($\mathrm{Ta}=8.23\times {10}^5$ and $\Theta =0.593$) at midheight and midradius.

Figure 9

Visualization of a 3 AV wave ($\mathrm{Ta}=8.23\times {10}^5$ and $\Theta =0.593$) at midheight.

Figure 10

Azimuth-time contour plot of temperature of a traveling weak wave with $m=1$. $\mathrm{Ta}=2.202\times {10}^5$ and $\Theta =2.218$ at midheight and midradius.

Figure 11

Visualization snapshot of a weak wave with $m=1$ at $\mathrm{Ta}=2.202\times {10}^5$ and $\Theta =2.218$ at midheight.

Figure 12

Time-averaged wave number spectrum of a weak wave with $m=1$ at $\mathrm{Ta}=4.250\times {10}^5$ and $\Theta =4.589$.

Figure 13

Time-averaged wave number spectrum of a weak wave with $m=1$ at $\mathrm{Ta}=8.229\times {10}^5$ and $\Theta =2.373$.

Figure 14

Time-averaged wave number spectrum of a weak wave with $m=1$ at $\mathrm{Ta}=1.025\times {10}^6$ and $\Theta =1.905$.