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For Ra = 10 9 , 1/Ro = 10: (a) u φ t,φ versus z at r = 0.95R. The inset shows the same data for 0 ≤ z ≤ H/2 in a log-plot. (b) u φ t,φ versus r at z = H/2; radial zero crossing r = r0 (solid line) and radial maximum r = r u max φ (dashed line). (c) Instantaneous thermal field at r = r u max φ versus z and φ.

For Ra = 10 9 , 1/Ro = 10: (a) u φ t,φ versus z at r = 0.95R. The inset shows the same data for 0 ≤ z ≤ H/2 in a log-plot. (b) u φ t,φ versus r at z = H/2; radial zero crossing r = r0 (solid line) and radial maximum r = r u max φ (dashed line). (c) Instantaneous thermal field at r = r u max φ versus z and φ.

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For rapidly rotating turbulent Rayleigh--B\'enard convection in a slender cylindrical cell, experiments and direct numerical simulations reveal a boundary zonal flow (BZF) that replaces the classical large-scale circulation. The BZF is located near the vertical side wall and enables enhanced heat transport there. Although the azimuthal velocity of...

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Context 1
... our conditions, Pr = 0.8, Ra = 10 9 , and 1/Ro = 10, we compute the time-and azimuthal-average azimuthal velocity u φ t,φ (normalized by the free-fall velocity u ff = αg∆/R) as a function of height z for fixed r = 0.95R and of radius r at fixed z = H/2. The height dependence of u φ t,φ , Fig. 3a, shows an anticyclonic (negative) circulation close to the top and bottom plates and an increasingly cyclonic (positive) circulation with increasing (decreasing) z from the bottom (top) plate. The radial dependence, Fig. 3b, demonstrates the sharp localization of cyclonic motion near the sidewall as parameterized by the zero-crossing r ...
Context 2
... = αg∆/R) as a function of height z for fixed r = 0.95R and of radius r at fixed z = H/2. The height dependence of u φ t,φ , Fig. 3a, shows an anticyclonic (negative) circulation close to the top and bottom plates and an increasingly cyclonic (positive) circulation with increasing (decreasing) z from the bottom (top) plate. The radial dependence, Fig. 3b, demonstrates the sharp localization of cyclonic motion near the sidewall as parameterized by the zero-crossing r 0 (solid line) and the maximum r u max φ (dashed line). Corresponding distances from the sidewall are δ 0 = R − r 0 and δ u ...
Context 3
... on maximum of rms of u z ). δ u rms z was used to define the sidewall Stewartson layer thickness in rotating convection [24], and our results for u φ t are consistent with that description. What was absolutely not expected is the strong azimuthal variation of the instantaneous temperature T shown in Fig. 3c, a feature that defines the global flow circulation, namely the spatial distribution of the heat transport which is the origin of the bimodal temperature distributions seen in the experiments and ...
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... strong variations in instantaneous temperature shown in Fig. 3c organize into anticyclonic traveling waves illustrated in the angle-time plot of T , Fig. 4a. The BZF height is order H, Fig. 3c, but is increasingly localized in the radial direction as the rotation rate increases (Ro and Ek decrease) so that δ 0 /R ≪ 1. The azimuthal mode of T is highly correlated with a corresponding mode of the ...
Context 5
... strong variations in instantaneous temperature shown in Fig. 3c organize into anticyclonic traveling waves illustrated in the angle-time plot of T , Fig. 4a. The BZF height is order H, Fig. 3c, but is increasingly localized in the radial direction as the rotation rate increases (Ro and Ek decrease) so that δ 0 /R ≪ 1. The azimuthal mode of T is highly correlated with a corresponding mode of the vertical velocity, Fig. 4b, with a resulting coherent mode-1 (m = 1) anticyclonic circulation in φ with a warm up-flow on one side ...
Context 6
... our conditions, Pr = 0.8, Ra = 10 9 , and 1/Ro = 10, we compute the time-and azimuthal-average azimuthal velocity u φ t,φ (normalized by the free-fall velocity u ff = αg∆/R) as a function of height z for fixed r = 0.95R and of radius r at fixed z = H/2. The height dependence of u φ t,φ , Fig. 3a, shows an anticyclonic (negative) circulation close to the top and bottom plates and an increasingly cyclonic (positive) circulation with increasing (decreasing) z from the bottom (top) plate. The radial dependence, Fig. 3b, demonstrates the sharp localization of cyclonic motion near the sidewall as parameterized by the zero-crossing r ...
Context 7
... = αg∆/R) as a function of height z for fixed r = 0.95R and of radius r at fixed z = H/2. The height dependence of u φ t,φ , Fig. 3a, shows an anticyclonic (negative) circulation close to the top and bottom plates and an increasingly cyclonic (positive) circulation with increasing (decreasing) z from the bottom (top) plate. The radial dependence, Fig. 3b, demonstrates the sharp localization of cyclonic motion near the sidewall as parameterized by the zero-crossing r 0 (solid line) and the maximum r u max φ (dashed line). Corresponding distances from the sidewall are δ 0 = R − r 0 and δ u ...
Context 8
... on maximum of rms of u z ). δ u rms z was used to define the sidewall Stewartson layer thickness in rotating convection [24], and our results for u φ t are consistent with that description. What was absolutely not expected is the strong azimuthal variation of the instantaneous temperature T shown in Fig. 3c, a feature that defines the global flow circulation, namely the spatial distribution of the heat transport which is the origin of the bimodal temperature distributions seen in the experiments and ...
Context 9
... strong variations in instantaneous temperature shown in Fig. 3c organize into anticyclonic traveling waves illustrated in the angle-time plot of T , Fig. 4a. The BZF height is order H, Fig. 3c, but is increasingly localized in the radial direction as the rotation rate increases (Ro and Ek decrease) so that δ 0 /R ≪ 1. The azimuthal mode of T is highly correlated with a corresponding mode of the ...
Context 10
... strong variations in instantaneous temperature shown in Fig. 3c organize into anticyclonic traveling waves illustrated in the angle-time plot of T , Fig. 4a. The BZF height is order H, Fig. 3c, but is increasingly localized in the radial direction as the rotation rate increases (Ro and Ek decrease) so that δ 0 /R ≪ 1. The azimuthal mode of T is highly correlated with a corresponding mode of the vertical velocity, Fig. 4b, with a resulting coherent mode-1 (m = 1) anticyclonic circulation in φ with a warm up-flow on one side ...

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