An official website of the United States government
Dynamos driven by rotating convection in the plane layer geometry are investigated numerically for a range of Ekman number ( $$E$$ ), magnetic Prandtl number ( $Pm$ ) and Rayleigh number ( $Ra$ ). The primary purpose of the investigation is to compare results of the simulations with previously developed asymptotic theory that is applicable in the limit of rapid rotation. We find that all of the simulations are in the quasi-geostrophic regime in which the Coriolis and pressure gradient forces are approximately balanced at leading order, whereas all other forces, including the Lorentz force, act as perturbations. Agreement between simulation output and asymptotic scalings for the energetics, flow speeds, magnetic field amplitude and length scales is found. The transition from large-scale dynamos to small-scale dynamos is well described by the magnetic Reynolds number based on the small convective length scale, $$\widetilde {Rm}$$ , with large-scale dynamos preferred when $$\widetilde {Rm} \lesssim O(1)$$ . The magnitude of the large-scale magnetic field is observed to saturate and become approximately constant with increasing Rayleigh number. Energy spectra show that all length scales present in the flow field and the small-scale magnetic field are consistent with a scaling of $$E^{1/3}$$ , even in the turbulent regime. For a fixed value of $$E$$ , we find that the viscous dissipation length scale is approximately constant over a broad range of $Ra$ ; the ohmic dissipation length scale is approximately constant within the large-scale dynamo regime, but transitions to a $$\widetilde {Rm}^{-1/2}$$ scaling in the small-scale dynamo regime.
more »
« less
On the universality of local dissipation scales in turbulent channel flow
Well-resolved measurements of the small-scale dissipation statistics within turbulent channel flow are reported for a range of Reynolds numbers from $$Re_{{\it\tau}}\approx 500$$ to 4000. In this flow, the local large-scale Reynolds number based on the longitudinal integral length scale is found to poorly describe the Reynolds number dependence of the small-scale statistics. When a length scale based on Townsend’s attached-eddy hypothesis is used to define the local large-scale Reynolds number, the Reynolds number scaling behaviour was found to be more consistent with that observed in homogeneous, isotropic turbulence. The Reynolds number scaling of the dissipation moments up to the sixth moment was examined and the results were found to be in good agreement with predicted scaling behaviour (Schumacher et al. , Proc. Natl Acad. Sci. USA , vol. 111, 2014, pp. 10961–10965). The probability density functions of the local dissipation scales (Yakhot, Physica D, vol. 215 (2), 2006, pp. 166–174) were also determined and, when the revised local large-scale Reynolds number is used for normalization, provide support for the existence of a universal distribution which scales differently for inner and outer regions.
more »
« less
- Award ID(s):
- 1351411
- PAR ID:
- 10183318
- Date Published:
- Journal Name:
- Journal of Fluid Mechanics
- Volume:
- 786
- ISSN:
- 0022-1120
- Page Range / eLocation ID:
- 234 to 252
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
We present high-resolution three-dimensional (3-D) direct numerical simulations of breaking waves solving for the two-phase Navier–Stokes equations. We investigate the role of the Reynolds number ( Re , wave inertia relative to viscous effects) and Bond number ( Bo , wave scale over the capillary length) on the energy, bubble and droplet statistics of strong plunging breakers. We explore the asymptotic regimes at high Re and Bo , and compare with laboratory breaking waves. Energetically, the breaking wave transitions from laminar to 3-D turbulent flow on a time scale that depends on the turbulent Re up to a limiting value $$Re_\lambda \sim 100$$ , consistent with the mixing transition in other canonical turbulent flows. We characterize the role of capillary effects on the impacting jet and ingested main cavity shape and subsequent fragmentation process, and extend the buoyant-energetic scaling from Deike et al. ( J. Fluid Mech. , vol. 801, 2016, pp. 91–129) to account for the cavity shape and its scale separation from the Hinze scale, $$r_H$$ . We confirm two regimes in the bubble size distribution, $$N(r/r_H)\propto (r/r_H)^{-10/3}$$ for $$r>r_H$$ , and $$\propto (r/r_H)^{-3/2}$$ for $$rmore » « less
-
We perform direct numerical simulations of a gas bubble dissolving in a surrounding liquid. The bubble volume is reduced due to dissolution of the gas, with the numerical implementation of an immersed boundary method, coupling the gas diffusion and the Navier–Stokes equations. The methods are validated against planar and spherical geometries’ analytical moving boundary problems, including the classic Epstein–Plesset problem. Considering a bubble rising in a quiescent liquid, we show that the mass transfer coefficient $$k_L$$ can be described by the classic Levich formula $$k_L = (2/\sqrt {{\rm \pi} })\sqrt {\mathscr {D}_l\,U(t)/d(t)}$$ , with $d(t)$ and $U(t)$ the time-varying bubble size and rise velocity, and $$\mathscr {D}_l$$ the gas diffusivity in the liquid. Next, we investigate the dissolution and gas transfer of a bubble in homogeneous and isotropic turbulence flow, extending Farsoiya et al. ( J. Fluid Mech. , vol. 920, 2021, A34). We show that with a bubble size initially within the turbulent inertial subrange, the mass transfer coefficient in turbulence $$k_L$$ is controlled by the smallest scales of the flow, the Kolmogorov $$\eta$$ and Batchelor $$\eta _B$$ microscales, and is independent of the bubble size. This leads to the non-dimensional transfer rate $${Sh}=k_L L^\star /\mathscr {D}_l$$ scaling as $${Sh}/{Sc}^{1/2} \propto {Re}^{3/4}$$ , where $${Re}$$ is the macroscale Reynolds number $${Re} = u_{rms}L^\star /\nu _l$$ , with $$u_{rms}$$ the velocity fluctuations, $L^*$ the integral length scale, $$\nu _l$$ the liquid viscosity, and $${Sc}=\nu _l/\mathscr {D}_l$$ the Schmidt number. This scaling can be expressed in terms of the turbulence dissipation rate $$\epsilon$$ as $${k_L}\propto {Sc}^{-1/2} (\epsilon \nu _l)^{1/4}$$ , in agreement with the model proposed by Lamont & Scott ( AIChE J. , vol. 16, issue 4, 1970, pp. 513–519) and corresponding to the high $Re$ regime from Theofanous et al. ( Intl J. Heat Mass Transfer , vol. 19, issue 6, 1976, pp. 613–624).more » « less
-
null (Ed.)A turbulence enrichment model for subfilter-scale motions in large eddy simulations (LES) is comprehensively evaluated in the context of a posteriori analysis. The paper further develops the Gabor mode enrichment model first introduced in Ghate & Lele (J. Fluid Mech., vol. 819, 2017, pp. 494–539) by analysing three key requisites of LES enrichment using solenoidal small-scale velocity fields: (a) consistent spectral extrapolation and improvement of resolved single- and two-point second-order correlations; (b) ability to accurately capture the flow physics responsible for temporal decorrelation at small scales; and (c) accurate representation of spatially localized and intermittent interscale energy transfer between scales resolved by the coarse-grid LES and subfilter scales. We argue that the spatially and spectrally localized Gabor wavepackets offer an optimal basis to represent small-scale turbulence within quasi-homogeneous regions, although the alignment of fine-scale vorticity with large-scale strain appears to be somewhat overemphasized. Consequently, we interpret the resulting subfilter scales as those induced by a set of spatially dispersed Burgers–Townsend vortices with orientations determined by the larger scale velocity gradients resolved by the coarse-grid LES. Enrichment of coarse-grid simulations of two high Reynolds number flow configurations, homogeneous isotropic turbulence and a rough-wall turbulent boundary layer show promising results.more » « less
-
A Lagrangian experimental study of an axisymmetric turbulent water jet is performed to investigate the highly anisotropic and inhomogeneous flow field. Measurements are conducted within a Lagrangian exploration module, an icosahedron apparatus, to facilitate optical access of three cameras. Stereoscopic particle tracking velocimetry results in three-component tracks of position, velocity and acceleration of the tracer particles within the vertically oriented jet with a Taylor-based Reynolds number $${\textit {Re}}_\lambda \simeq 230$$ . Analysis is performed at seven locations from 15 diameters up to 45 diameters downstream. Eulerian analysis is first carried out to obtain critical parameters of the jet and relevant scales, namely the Kolmogorov and large (integral) scales as well as the energy dissipation rate. Lagrangian statistical analysis is then performed on velocity components stationarised following methods inspired by Batchelor ( J. Fluid Mech. , vol. 3, 1957, pp. 67–80), which aim to extend stationary Lagrangian theory of turbulent diffusion by Taylor to the case of self-similar flows. The evolution of typical Lagrangian scaling parameters as a function of the developing jet is explored and results show validation of the proposed stationarisation. The universal scaling constant $$C_0$$ (for the Lagrangian second-order structure function), as well as Eulerian and Lagrangian integral time scales, are discussed in this context. Constant $$C_0$$ is found to converge to a constant value (of the order of $$C_0 = 3$$ ) within 30 diameters downstream of the nozzle. Finally, the occurrence of finite particle size effects is investigated through consideration of acceleration-dependent quantities.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1017/jfm.2015.664
