skip to main content

Title: High-Reynolds-number fractal signature of nascent turbulence during transition

Transition from laminar to turbulent flow occurring over a smooth surface is a particularly important route to chaos in fluid dynamics. It often occurs via sporadic inception of spatially localized patches (spots) of turbulence that grow and merge downstream to become the fully turbulent boundary layer. A long-standing question has been whether these incipient spots already contain properties of high-Reynolds-number, developed turbulence. In this study, the question is posed for geometric scaling properties of the interface separating turbulence within the spots from the outer flow. For high-Reynolds-number turbulence, such interfaces are known to display fractal scaling laws with a dimensionD7/3, where the 1/3 excess exponent above 2 (smooth surfaces) follows from Kolmogorov scaling of velocity fluctuations. The data used in this study are from a direct numerical simulation, and the spot boundaries (interfaces) are determined by using an unsupervised machine-learning method that can identify such interfaces without setting arbitrary thresholds. Wide separation between small and large scales during transition is provided by the large range of spot volumes, enabling accurate measurements of the volume–area fractal scaling exponent. Measurements show a dimension ofD=2.36±0.03over almost 5 decades of spot volume, i.e., trends fully consistent with high-Reynolds-number turbulence. Additional observations pertaining more » to the dependence on height above the surface are also presented. Results provide evidence that turbulent spots exhibit high-Reynolds-number fractal-scaling properties already during early transitional and nonisotropic stages of the flow evolution.

« less
; ;
Award ID(s):
Publication Date:
Journal Name:
Proceedings of the National Academy of Sciences
Page Range or eLocation-ID:
p. 3461-3468
Proceedings of the National Academy of Sciences
Sponsoring Org:
National Science Foundation
More Like this
  1. Sub-Neptunes are common among the discovered exoplanets. However, lack of knowledge on the state of matter inH2O-rich setting at high pressures and temperatures (PT) places important limitations on our understanding of this planet type. We have conducted experiments for reactions betweenSiO2andH2O as archetypal materials for rock and ice, respectively, at highPT. We found anomalously expanded volumes of dense silica (up to 4%) recovered from hydrothermal synthesis above ∼24 GPa where theCaCl2-type (Ct) structure appears at lower pressures than in the anhydrous system. Infrared spectroscopy identifiedmore »strong OH modes from the dense silica samples. Both previous experiments and our density functional theory calculations support up to 0.48 hydrogen atoms per formula unit of (Si1xH4x)O2(x=0.12). At pressures above 60 GPa,H2O further changes the structural behavior of silica, stabilizing a niccolite-type structure, which is unquenchable. From unit-cell volume and phase equilibrium considerations, we infer that the niccolite-type phase may contain H with an amount at least comparable with or higher than that of the Ct phase. Our results suggest that the phases containing both hydrogen and lithophile elements could be the dominant materials in the interiors of water-rich planets. Even for fully layered cases, the large mutual solubility could make the boundary between rock and ice layers fuzzy. Therefore, the physical properties of the new phases that we report here would be important for understanding dynamics, geochemical cycle, and dynamo generation in water-rich planets.

    « less
  2. Assessment of the global budget of the greenhouse gas nitrous oxide (N2O) is limited by poor knowledge of the oceanicN2O flux to the atmosphere, of which the magnitude, spatial distribution, and temporal variability remain highly uncertain. Here, we reconstruct climatologicalN2O emissions from the ocean by training a supervised learning algorithm with over 158,000N2O measurements from the surface ocean—the largest synthesis to date. The reconstruction captures observed latitudinal gradients and coastal hot spots ofN2O flux and reveals a vigorous global seasonal cycle. We estimate an annual meanN2O flux ofmore »4.2 ± 1.0 Tg Ny1, 64% of which occurs in the tropics, and 20% in coastal upwelling systems that occupy less than 3% of the ocean area. ThisN2O flux ranges from a low of 3.3 ± 1.3 Tg Ny1in the boreal spring to a high of 5.5 ± 2.0 Tg Ny1in the boreal summer. Much of the seasonal variations in globalN2O emissions can be traced to seasonal upwelling in the tropical ocean and winter mixing in the Southern Ocean. The dominant contribution to seasonality by productive, low-oxygen tropical upwelling systems (>75%) suggests a sensitivity of the globalN2O flux to El Niño–Southern Oscillation and anthropogenic stratification of the low latitude ocean. This ocean flux estimate is consistent with the range adopted by the Intergovernmental Panel on Climate Change, but reduces its uncertainty by more than fivefold, enabling more precise determination of other terms in the atmosphericN2O budget.

    « less
  3. Abstract

    Microfluidics has enabled a revolution in the manipulation of small volumes of fluids. Controlling flows at larger scales and faster rates, ormacrofluidics, has broad applications but involves the unique complexities of inertial flow physics. We show how such effects are exploited in a device proposed by Nikola Tesla that acts as a diode or valve whose asymmetric internal geometry leads to direction-dependent fluidic resistance. Systematic tests for steady forcing conditions reveal that diodicity turns on abruptly at Reynolds number$${\rm{Re}}\approx 200$$Re200and is accompanied by nonlinear pressure-flux scaling and flow instabilities, suggesting a laminar-to-turbulent transition that is triggered at unusually low$${\rm{Re}}$$Re.more »To assess performance for unsteady forcing, we devise a circuit that functions as an AC-to-DC converter, rectifier, or pump in which diodes transform imposed oscillations into directed flow. Our results confirm Tesla’s conjecture that diodic performance is boosted for pulsatile flows. The connections between diodicity, early turbulence and pulsatility uncovered here can inform applications in fluidic mixing and pumping.

    « less
  4. The classic picture of soft material mechanics is that of rubber elasticity, in which material modulus is related to the entropic elasticity of flexible polymeric linkers. The rubber model, however, largely ignores the role of valence (i.e., the number of network chains emanating from a junction). Recent work predicts that valence, and particularly the Maxwell isostatic point, plays a key role in determining the mechanics of semiflexible polymer networks. Here, we report a series of experiments confirming the prominent role of valence in determining the mechanics of a model system. The system is based on DNA nanostars (DNAns): multiarmed, self-assembledmore »nanostructures that form thermoreversible equilibrium gels through base pair-controlled cross-linking. We measure the linear and nonlinear elastic properties of these gels as a function of DNAns arm number, f, and concentration [DNAns]. We find that, as f increases from three to six, the gel’s high-frequency plateau modulus strongly increases, and its dependence on [DNAns] transitions from nonlinear to linear. Additionally, higher-valence gels exhibit less strain hardening, indicating that they have less configurational freedom. Minimal strain hardening and linear dependence of shear modulus on concentration at high f are consistent with predictions for isostatic systems. Evident strain hardening and nonlinear concentration dependence of shear modulus suggest that the low-f networks are subisostatic and have a transient, potentially fractal percolated structure. Overall, our observations indicate that network elasticity is sensitive both to entropic elasticity of network chains and to junction valence, with an apparent isostatic point5<fc6in agreement with the Maxwell prediction.

    « less
  5. Cosmological simulations of galaxy formation are limited by finite computational resources. We draw from the ongoing rapid advances in artificial intelligence (AI; specifically deep learning) to address this problem. Neural networks have been developed to learn from high-resolution (HR) image data and then make accurate superresolution (SR) versions of different low-resolution (LR) images. We apply such techniques to LR cosmological N-body simulations, generating SR versions. Specifically, we are able to enhance the simulation resolution by generating 512 times more particles and predicting their displacements from the initial positions. Therefore, our results can be viewed as simulation realizations themselves, rather thanmore »projections, e.g., to their density fields. Furthermore, the generation process is stochastic, enabling us to sample the small-scale modes conditioning on the large-scale environment. Our model learns from only 16 pairs of small-volume LR-HR simulations and is then able to generate SR simulations that successfully reproduce the HR matter power spectrum to percent level up to16h1Mpcand the HR halo mass function to within10%down to1011M. We successfully deploy the model in a box 1,000 times larger than the training simulation box, showing that high-resolution mock surveys can be generated rapidly. We conclude that AI assistance has the potential to revolutionize modeling of small-scale galaxy-formation physics in large cosmological volumes.

    « less