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Torque scaling in turbulent Taylor-Couette flow with co- and counterrotating cylinders.
The transport is most efficient for the counterrotating case along the diagonal in phase space with ω(o) ≈ -0.4ω(i) and the exponent 0.38 corresponds to the ultimate regime scaling for the analogous Rayleigh-Bénard system.
Multiple states in highly turbulent Taylor-Couette flow.
This result verifies the notion that bifurcations can occur in high-dimensional flows (that is, very large Re) and questions Kolmogorov's paradigm.
Optimal Taylor–Couette turbulence
Abstract Strongly turbulent Taylor–Couette flow with independently rotating inner and outer cylinders with a radius ratio of $\eta = 0. 716$ is experimentally studied. From global torque
Logarithmic boundary layers in strong Taylor-Couette turbulence.
The variance profiles of the local azimuthal velocity have a universal peak around y+≈12 and collapse when rescaled with the driving velocity, displaying a log dependence of y+ as also found for channel and pipe flows.
Optimal Taylor–Couette flow: radius ratio dependence
Abstract Taylor–Couette flow with independently rotating inner ( $i$ ) and outer ( $o$ ) cylinders is explored numerically and experimentally to determine the effects of the radius ratio $\eta $ on
Ultimate turbulent Taylor-Couette flow.
The flow structure of strongly turbulent Taylor-Couette flow with Reynolds numbers up to Re(i)=2×10(6) of the inner cylinder is experimentally examined with high-speed particle image velocimetry (PIV) and the wind Reynolds numbers Re(w) is found to scale as Re-w∝Ta(1/2), exactly as predicted by Grossmann and Lohse.
Wall roughness induces asymptotic ultimate turbulence
Turbulence governs the transport of heat, mass and momentum on multiple scales. In real-world applications, wall-bounded turbulence typically involves surfaces that are rough; however, characterizing
Taylor–Couette turbulence at radius ratio ${\it\eta}=0.5$ : scaling, flow structures and plumes
Using high-resolution particle image velocimetry, we measure velocity profiles, the wind Reynolds number and characteristics of turbulent plumes in Taylor–Couette flow for a radius ratio of 0.5 and
Statistics of turbulent fluctuations in counter-rotating Taylor-Couette flows.
The statistics of velocity fluctuations of turbulent Taylor-Couette flow are examined and the longitudinal structure function exponents are extracted and are found to weakly depend on the ratio of the rotation rates.
Newer sums of three cubes
The search of solutions of the Diophantine equation $x^3 + y^3 + z^3 = k$ for $k<1000$ has been extended with bounds of $|x|$, $|y|$ and $|z|$ up to $10^{15}$. The first solution for $k=74$ is