Anisotropy of Unstably Stratified Near-Surface Turbulence

Classic Monin–Obukov similarity scaling states that in a stationary, horizontally homogeneous flow, in the absence of subsidence, turbulence is dictated by the balance between shear production and buoyancy production/destruction, whose ratio is characterized by a single universal scaling parameter. An evident breakdown in scaling is observed though, through large scatter in traditional scaling relations for the horizontal velocity variances under unstable stratification, or more generally in complex flow conditions. This breakdown suggests the existence of processes other than local shear and buoyancy that modulate near-surface turbulence. Recent studies on the role of anisotropy in similarity scaling have shown that anisotropy, even if calculated locally, may encode the information about these missing processes. We therefore examine the possible processes that govern the degree of anisotropy in convective conditions. We first use the reduced turbulence-kinetic-energy budget to show that anisotropy in convective conditions cannot be uniquely described by a balance of buoyancy and shear production and dissipation, but that other terms in the budget play an important role. Subsequently, we identify a ratio of local time scales that acts as a proxy for the anisotropic state of convective turbulence. This ratio can be used to formulate a new non-dimensional group. Results show that building on this approach the role of anisotropy in scaling relations over complex terrain can be placed into a more generalized framework.

Coriolis-induced instabilities in centrifuge modeling of granular flow

Granular flows are typically studied in laboratory flumes based on common similarity scaling, which create stress fields that only roughly approximate field conditions. The geotechnical centrifuge produces stress conditions that are closer to those observed in the field, but steady conditions can be hardly achieved. Moreover, secondary effects induced by the apparent Coriolis acceleration, which can either dilate or compress the flow, often obscure scaling. This work aims at studying a set of numerical experiments where the effects of the Coriolis acceleration are measured and analyzed. Three flow states are observed: dense, dilute, and unstable. It is found that flows generated under the influence of dilative Coriolis accelerations are likely to become unstable. Nevertheless, a steady dense flow can still be obtained if a large centrifuge is used. A parametric group is proposed to predict the insurgence of instabilities; this parameter can guide experimental designs and could help to avoid damage to the experimental apparatus and model instrumentation. Graphic abstract

Impact of Geometric Features on Color Similarity Perception of Displayed 3D Tablets

To explore the effects of geometric features on the color similarity perception of displayed three-dimensional (3D) tablets designed by color 3D modeling techniques or printed by color 3D printing techniques, two subjective similarity scaling tasks were conducted for color tablets with four shape features (circular, oval, triangular-columnar, and rounded-cuboid shapes) and four notch features (straight V, straight U, crisscross V, and crisscross U shapes) displayed on a calibrated monitor using the nine-level category judgement method. Invited observers were asked to assort all displayed samples into tablet groups using six surface colors (aqua blue, bright green, pink, orange yellow, bright red, and silvery white), and all perceived similarity values were recorded and compared to original samples successively. The results showed that the similarity perception of tested tablets was inapparently affected by the given shape features and notch features, and it should be judged by a flexible interval rather than by a fixed color difference. This research provides practical insight into the visualization of color similarity perception for displayed personalized tablets to advance precision medicine by 3D printing.

Centered Polygonal Lacunary Sequences

Lacunary functions based on centered polygonal numbers have interesting features which are distinct from general lacunary functions. These features include rotational symmetry of the modulus of the functions and a notion of polished level sets. The behavior and characteristics of the natural boundary for centered polygonal lacunary sequences are discussed. These systems are complicated but, nonetheless, well organized because of their inherent rotational symmetry. This is particularly apparent at the so-called symmetry angles at which the values of the sequence at the natural boundary follow a relatively simple 4 p -cycle. This work examines special limit sequences at the natural boundary of centered polygonal lacunary sequences. These sequences arise by considering the sequence of values along integer fractions of the symmetry angle for centered polygonal lacunary functions. These sequences are referred to here as p-sequences. Several properties of the p-sequences are explored to give insight in the centered polygonal lacunary functions. Fibered spaces can organize these cycles into equivalence classes. This then provides a natural way to approach the infinite sum of the actual lacunary function. It is also seen that the inherent organization of the centered polygonal lacunary sequences gives rise to fractal-like self-similarity scaling features. These features scale in simple ways.

Helical self-similarity of tip vortex cores

The present work investigates local flow structures and the downstream evolution of the core of helical tip vortices generated by a three-bladed rotor. Earlier experimental studies have shown that the core of a helical tip vortex exhibits a local helical symmetry with a simple relation between the axial and azimuthal velocities. In the present study, a self-similarity scaling argument further describes the downstream development of the vortex core. Self-similarity has up to now only been investigated for longitudinal vortices and it is the first time that helical vortices have become the subject of such an analysis. Combining symmetry arguments from previous studies on helical vortices with novel experiments and knowledge regarding the self-similarity evolution of the core of longitudinal vortices, a new model describing what is referred to as ‘helical self-similarity’ is proposed. The generality of the model is verified and supported by experimental data. The proposed model is important for fundamental understanding of the behaviour of helical vortices, with a range of applications in both industry and nature. Examples of this are tip vortices behind aerodynamic devices, such as vortex generators, and fixed and rotary aircraft, and in combustion chambers and cyclone separators.

Blow Up of Quintic Power 1-D Nonlinear Schroedinger Equation

This work studies an adaptive finite difference approximation to the one dimensional nonlinear Schroedinger equiation with quintic power, with special emphasis on the case when the solution blows up with finite blowing-up time $T_\infty.$ The adaptivity is utilizing similarity scaling adaptive grids studied by Berger and Kohn to study numerical solution of semilinear heat equations with finite blowing-up time.Furthermore, we reports an asymptotic behavior of the blow-up solution approaching $T_\infty$ time singularity.