Testing a missing spectral link in turbulence

Multiscale Sample Entropy of Two-Dimensional Decaying Turbulence

Multiscale sample entropy analysis has been developed to quantify the complexity and the predictability of a time series, originally developed for physiological time series. In this study, the analysis was applied to the turbulence data. We measured time series data for the velocity fluctuation, in either the longitudinal or transverse direction, of turbulent soap film flows at various locations. The research was to assess the feasibility of using the entropy analysis to qualitatively characterize turbulence, without using any conventional energetic analysis of turbulence. The study showed that the application of the entropy analysis to the turbulence data is promising. From the analysis, we successfully captured two important features of the turbulent soap films. It is indicated that the turbulence is anisotropic from the directional disparity. In addition, we observed that the most unpredictable time scale increases with the downstream distance, which is an indication of the decaying turbulence.

Asymptotic turbulent friction in 2D rough-walled flows

The friction f is the property of wall-bounded flows that sets the pumping cost of a pipeline, the draining capacity of a river, and other variables of practical relevance. For highly turbulent rough-walled pipe flows, f depends solely on the roughness length scale r, and the f - r relation may be expressed by the Strickler empirical scaling f ∝ r ^1/3 Here, we show experimentally that for soap film flows that are the two-dimensional (2D) equivalent of highly turbulent rough-walled pipe flows, f ∝ r and the f - r relation is not the same in 2D as in 3D. Our findings are beyond the purview of the standard theory of friction but consistent with a competing theory in which f is linked to the turbulent spectrum via the spectral exponent α: In 3D, α = 5/3 and the theory yields f ∝ r ^1/3; in 2D, α = 3 and the theory yields f ∝ r.

Janus Spectra in Two-Dimensional Flows

In large-scale atmospheric flows, soap-film flows, and other two-dimensional flows, the exponent of the turbulent energy spectra, α, may theoretically take either of two distinct values, 3 or 5/3, but measurements downstream of obstacles have invariably revealed α=3. Here we report experiments on soap-film flows where downstream of obstacles there exists a sizable interval in which α transitions from 3 to 5/3 for the streamwise fluctuations but remains equal to 3 for the transverse fluctuations, as if two mutually independent turbulent fields of disparate dynamics were concurrently active within the flow. This species of turbulent energy spectra, which we term the Janus spectra, has never been observed or predicted theoretically. Our results may open up new vistas in the study of turbulence and geophysical flows.

Reynolds-number dependence of the longitudinal dispersion in turbulent pipe flow

In Taylor's theory, the longitudinal dispersion in turbulent pipe flows approaches, on long time scales, a diffusive behavior with a constant diffusivity K_{L}, which depends empirically on the Reynolds number Re. We show that the dependence on Re can be determined from the turbulent energy spectrum. By using the intimate connection between the friction factor and the longitudinal dispersion in wall-bounded turbulence, we predict different asymptotic scaling laws of K_{L}(Re) depending on the different turbulent cascades in two-dimensional turbulence. We also explore numerically the K_{L}(Re) dependence in turbulent channel flows with smooth and rough walls using a lattice Boltzmann method.

Predicting two-dimensional turbulence

Prediction is a fundamental objective of science. It is more difficult for chaotic and complex systems like turbulence. Here we use information theory to quantify spatial prediction using experimental data from a turbulent soap film. At high Reynolds number, Re, where a cascade exists, turbulence becomes easier to predict as the inertial range broadens. The development of a cascade at low Re is also detected.

Scaling of near-wall flows in quasi-two-dimensional turbulent channels

The law of the wall and the log law rule the near-wall mean velocity profile of three-dimensional turbulent flows. These well-known laws, which are validated by legions of experiments and simulations, may be universal. Here, using a soap-film channel, we report the first experimental test of these laws in quasi-two-dimensional turbulent channel flows under two disparate turbulent spectra. We find that despite the differences with three-dimensional flows, the laws prevail, albeit with notable distinctions: the two parameters of the log law are markedly distinct from their three-dimensional counterpart; further, one parameter (the von Kármán constant) is independent of the spectrum whereas the other (the offset of the log law) depends on the spectrum. Our results suggest that the classical theory of scaling in wall-bounded turbulence is incomplete wherein a key missing element is the link with the turbulent spectrum.