An official website of the United States government
Empirical evidence is provided that within the inertial sublayer (i.e. logarithmic region) of adiabatic turbulent flows over smooth walls, the skewness of the vertical-velocity component$$S_w$$displays universal behaviour, being a positive constant and constrained within the range$$S_w \approx 0.1\unicode{x2013}0.16$$, regardless of flow configuration and Reynolds number. A theoretical model is then proposed to explain this behaviour, including the observed range of variations of$$S_w$$. The proposed model clarifies why$$S_w$$cannot be predicted from down-gradient closure approximations routinely employed in large-scale meteorological and climate models. The proposed model also offers an alternative and implementable approach for such large-scale models.
more »
« less
Radial-to-axial flows in a scaled pulsed-power scheme for producing outflows resembling YSO jets
Young stellar objects (YSOs) are protostars that exhibit bipolar outflows fed by accretion disks. Theories of the transition between disk and outflow often involve a complex magnetic field structure thought to be created by the disk coiling field lines at the jet base; however, due to limited resolution, these theories cannot be confirmed with observation and thus may benefit from laboratory astrophysics studies. We create a dynamically similar laboratory system by driving a$$\sim$$1 MA current pulse with a 200 ns rise through a$$\approx$$2 mm-tall Al cylindrical wire array mounted to a three-dimensional (3-D)-printed, stainless steel scaffolding. This system creates a plasma that converges on the centre axis and ejects cm-scale bipolar outflows. Depending on the chosen 3-D-printed load path, the system may be designed to push the ablated plasma flow radially inwards or off-axis to make rotation. In this paper, we present results from the simplest iteration of the load which generates radially converging streams that launch non-rotating jets. The temperature, velocity and density of the radial inflows and axial outflows are characterized using interferometry, gated optical and ultraviolet imaging, and Thomson scattering diagnostics. We show that experimental measurements of the Reynolds number and sonic Mach number in three different stages of the experiment scale favourably to the observed properties of YSO jets with$$Re\sim 10^5\unicode{x2013}10^9$$and$$M\sim 1\unicode{x2013}10$$, while our magnetic Reynolds number of$$Re_M\sim 1\unicode{x2013}15$$indicates that the magnetic field diffuses out of our plasma over multiple hydrodynamical time scales. We compare our results with 3-D numerical simulations in the PERSEUS extended magnetohydrodynamics code.
more »
« less
- Award ID(s):
- 1943939
- PAR ID:
- 10588556
- Publisher / Repository:
- Cambridge University Press
- Date Published:
- Journal Name:
- Journal of Plasma Physics
- Volume:
- 90
- Issue:
- 6
- ISSN:
- 0022-3778
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
This study explores heat and turbulent modulation in three-dimensional multiphase Rayleigh–Bénard convection using direct numerical simulations. Two immiscible fluids with identical reference density undergo systematic variations in dispersed-phase volume fractions,$$0.0 \leq \varPhi \leq 0.5$$, and ratios of dynamic viscosity,$$\lambda _{\mu }$$, and thermal diffusivity,$$\lambda _{\alpha }$$, within the range$$[0.1\unicode{x2013}10]$$. The Rayleigh, Prandtl, Weber and Froude numbers are held constant at$$10^8$$,$$4$$,$$6000$$and$$1$$, respectively. Initially, when both fluids share the same properties, a 10 % Nusselt number increase is observed at the highest volume fractions. In this case, despite a reduction in turbulent kinetic energy, droplets enhance energy transfer to smaller scales, smaller than those of single-phase flow, promoting local mixing. By varying viscosity ratios, while maintaining a constant Rayleigh number based on the average mixture properties, the global heat transfer rises by approximately 25 % at$$\varPhi =0.2$$and$$\lambda _{\mu }=10$$. This is attributed to increased small-scale mixing and turbulence in the less viscous carrier phase. In addition, a dispersed phase with higher thermal diffusivity results in a 50 % reduction in the Nusselt number compared with the single-phase counterpart, owing to faster heat conduction and reduced droplet presence near walls. The study also addresses droplet-size distributions, confirming two distinct ranges dominated by coalescence and breakup with different scaling laws.more » « less
-
We explored the settling dynamics of vertically aligned particles in a quiescent, stratified two-layer fluid using particle tracking velocimetry. Glass spheres of$$d=4\,{\rm mm}$$diameter were released at frequencies of 4, 6 and 8 Hz near the free surface, traversing through an upper ethanol layer ($$H_1$$), whereHis height or layer thickess, varying from$$10d$$to$$40d$$and a lower oil layer. Results reveal pronounced lateral particle motion in the ethanol layer, attributed to a higher Galileo number ($$Ga = 976$$, ratio of buoyancy–gravity to viscous effects), compared with the less active behaviour in the oil layer ($$Ga = 16$$). The ensemble vertical velocity of particles exhibited a minimum just past the density interface, becoming more pronounced with increasing$$H_1$$, and suggesting that enhanced entrainment from ethanol to oil resulted in an additional buoyancy force. This produced distinct patterns of particle acceleration near the density interface, which were marked by significant deceleration, indicating substantial resistance to particle motion. An increased drag coefficient occurred for$$H_1/d = 40$$compared with a single particle settling in oil; drag reduced as the particle-release frequency ($$\,f_p$$) increased, likely due to enhanced particle interactions at closer proximity. Particle pair dispersions, lateral ($$R^2_L$$) and vertical ($$R^2_z$$), were modulated by$$H_1$$, initial separation$$r_0$$and$$f_p$$. The$$R^2_L$$dispersion displayed ballistic scaling initially, Taylor scaling for$$r_0 < H_1$$and Richardson scaling for$$r_0 > H_1$$. In contrast,$$R^2_z$$followed a$$R^2_z \sim t^{5.5}$$scaling under$$r_0 < H_1$$. Both$$R^2_L$$and$$R^2_z$$plateaued at a distance from the interface, depending on$$H_1$$and$$f_p$$.more » « less
-
Abstract Let$$\Sigma$$be an alphabet and$$\mu$$be a distribution on$$\Sigma ^k$$for some$$k \geqslant 2$$. Let$$\alpha \gt 0$$be the minimum probability of a tuple in the support of$$\mu$$(denoted$$\mathsf{supp}(\mu )$$). We treat the parameters$$\Sigma , k, \mu , \alpha$$as fixed and constant. We say that the distribution$$\mu$$has a linear embedding if there exist an Abelian group$$G$$(with the identity element$$0_G$$) and mappings$$\sigma _i : \Sigma \rightarrow G$$,$$1 \leqslant i \leqslant k$$, such that at least one of the mappings is non-constant and for every$$(a_1, a_2, \ldots , a_k)\in \mathsf{supp}(\mu )$$,$$\sum _{i=1}^k \sigma _i(a_i) = 0_G$$. In [Bhangale-Khot-Minzer, STOC 2022], the authors asked the following analytical question. Let$$f_i: \Sigma ^n\rightarrow [\!-1,1]$$be bounded functions, such that at least one of the functions$$f_i$$essentially has degree at least$$d$$, meaning that the Fourier mass of$$f_i$$on terms of degree less than$$d$$is at most$$\delta$$. If$$\mu$$has no linear embedding (over any Abelian group), then is it necessarily the case that\begin{equation*}\left | \mathop {\mathbb{E}}_{({\textbf {x}}_1, {\textbf {x}}_2, \ldots , {\textbf {x}}_k)\sim \mu ^{\otimes n}}[f_1({\textbf {x}}_1)f_2({\textbf {x}}_2)\cdots f_k({\textbf {x}}_k)] \right | = o_{d, \delta }(1),\end{equation*}where the right hand side$$\to 0$$as the degree$$d \to \infty$$and$$\delta \to 0$$? In this paper, we answer this analytical question fully and in the affirmative for$$k=3$$. We also show the following two applications of the result.1.The first application is related to hardness of approximation. Using the reduction from [5], we show that for every$$3$$-ary predicate$$P:\Sigma ^3 \to \{0,1\}$$such that$$P$$has no linear embedding, anSDP (semi-definite programming) integrality gap instanceof a$$P$$-Constraint Satisfaction Problem (CSP) instance with gap$$(1,s)$$can be translated into a dictatorship test with completeness$$1$$and soundness$$s+o(1)$$, under certain additional conditions on the instance.2.The second application is related to additive combinatorics. We show that if the distribution$$\mu$$on$$\Sigma ^3$$has no linear embedding, marginals of$$\mu$$are uniform on$$\Sigma$$, and$$(a,a,a)\in \texttt{supp}(\mu )$$for every$$a\in \Sigma$$, then every large enough subset of$$\Sigma ^n$$contains a triple$$({\textbf {x}}_1, {\textbf {x}}_2,{\textbf {x}}_3)$$from$$\mu ^{\otimes n}$$(and in fact a significant density of such triples).more » « less
-
Flow dynamics around a stationary flat plate near a free surface is investigated using time-resolved two-dimensional particle image velocimetry. The study examines variations in angle of attack ($$\theta =0^\circ {-}35^\circ {}$$), Reynolds number ($$Re$$$$\approx$$$$10^3$$$$-$$3$$\times$$$$10^4$$) and plate proximity to the free surface ($$H^*$$). Under symmetric boundary conditions ($$H^*\geqslant {15}$$), increasing$$\theta$$intensifies fluid–plate interaction, resulting in the shedding of leading-edge and trailing-edge vortices (LEV and TEV), each characterised by distinct strengths and sizes. In both symmetric ($$H^*\geqslant {15}$$) and asymmetric ($$H^*=5$$) boundary conditions at$$\theta \lt 5^\circ {}$$, fluid flow follows the contour of the plate, unaffected by Reynolds number. However, at$$H^*=5$$, three flow regimes emerge: the first Coanda effect (CI), regular shedding (RS) and the second Coanda effect (CII), each influenced by$$\theta$$and$$Re$$. The CI regime dominates at lower angles ($$5^\circ {}\leqslant \theta \leqslant 25^\circ {}$$) and$$Re \leqslant 12\,500$$, featuring a Coanda-induced jet-like flow pattern. As the Reynolds number increases, the flow transitions into the RS regime, leading to detachment from the upper surface of the plate. This detachment results in the formation of LEV and TEV in the wake, along with surface deformation, secondary vortices and wavy shear layers beneath the free surface. At$$22\,360\lt Re \leqslant 32\,200$$and$$5^\circ {} \leqslant \theta \leqslant 25^\circ {}$$, in the CII regime, significant surface deformation causes the Coanda effect to reattach the flow to the plate, forming a unique jet-like flow.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1017/s002237782400134x
