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Free keywords:
rotating turbulence; Taylor-Couette flow; turbulent convection
Abstract:
We provide experimental measurements for the effective scaling of the Taylor-Reynolds number within the bulk Re-lambda.bulk, based on local flow quantities as a function of the driving strength ( expressed as the Taylor number Ta), in the ultimate regime of Taylor-Couette flow. We define Re-lambda.bulk = (sigma(bulk) (u(theta)))(2) (15/nu epsilon(bulk)))(1/2), where sigma(bulk)(u(theta)) is the bulk-averaged standard deviation of the azimuthal velocity, epsilon(bulk) is the bulk-averaged local dissipation rate and nu is the liquid kinematic viscosity. The data are obtained through flow velocity field measurements using particle image velocimetry. We estimate the value of the local dissipation rate epsilon(r) using the scaling of the second-order velocity structure functions in the longitudinal and transverse directions within the inertial range - without invoking Taylor's hypothesis. We find an effective scaling of epsilon(bulk)/(nu(3)d(3))similar to Ta-1.40, (corresponding to Nu(omega,bulk) similar to Ta-0.40 for the dimensionless local angular velocity transfer), which is nearly the same as for the global energy dissipation rate obtained from both torque measurements (Nu(omega) similar to Ta-0.40) and direct numerical simulations (Nu(omega) similar to Ta-0.38). The resulting Kolmogorov length scale is then found to scale as eta(bulk)/d similar to Ta-0.35 and the turbulence intensity as I-theta,I-bulk similar to Ta-0.061. With both the local dissipation rate and the local fluctuations available we finally find that the Taylor-Reynolds number effectively scales as Re-lambda,Re-bulk similar to Ta-0.18 in the present parameter regime of 4.0 x 10(8) < Ta < 9.0 x 10(10).
