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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.

Source publication

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...

## Contexts in source publication

**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 ...

**Context 4**

... 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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