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Register a new userMulti-scale energy budget of inertially driven turbulence in normal and superfluid helium
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In this paper we present a novel hydrodynamic experiment using liquid $^4$He. The flow is forced inertially by a canonical oscillating grid using either its normal (He~I) or superfluid (He~II) phase, generating a statistically stationary turbulence. We characterise the turbulent properties of the flow using 2D Lagrangian Particle tracking on hollow glass micro-spheres. As expected for tracer particles, the Vorono{i} tessellation on particle positions does not show a significant departure from a random Poisson process neither in He~I nor He~II phase. Particles positions are tracked with high temporal resolution, allowing to resolve velocity fluctuations at integral and inertial scales while properly assessing the noise contribution. Additionally, we differentiate the particles positions (by convolution with Gaussian kernels) in order to access small scale quantities like acceleration. Using these measured quantities and the formalism of classical Homogeneous Isotropic Turbulence (HIT) to perform an energy budget across scales we extract the energy injection rate at the large scale, the energy flux cascading through inertial scales, down to small scales at which it is dissipated. We found that in such inertially driven turbulence, regardless of the normal or superfluid state of the fluid, estimates of energy at the different scales are compatible with each other and consistent with oscillating grid turbulence results reported for normal fluids in the literature. The largest discrepancy shows up at small scales where the signal to noise ratio is harder to control and where the 2D measurement is contaminated by the 3D nature of the flow. This motivates to focus future experimental projects towards small scales, low noise and 3D measurements.
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The 4/5-law of turbulence, which characterizes the energy cascade from large to small-sized eddies at high Reynolds numbers in classical fluids, is verified experimentally in a superfluid 4He wind tunnel, operated down to 1.56 K and up to R_lambda ~ 1640. The result is corroborated by high-resolution simulations of Landau-Tiszas two-fluid model down to 1.15 K, corresponding to a residual normal fluid concentration below 3 % but with a lower Reynolds number of order R_lambda ~ 100. Although the Karman-Howarth equation (including a viscous term) is not valid emph{a priori} in a superfluid, it is found that it provides an empirical description of the deviation from the ideal 4/5-law at small scales and allows us to identify an effective viscosity for the superfluid, whose value matches the kinematic viscosity of the normal fluid regardless of its concentration.
A relative motion of the normal and superfluid components of Helium II results in Kelvin-Helmholtz instability (KHI) at their common free surface. We found the exact solutions for the nonlinear stage of the development of that instability. Contrary to the usual KHI of the interface between two fluids, the dynamics of Helium II free surface allows decoupling of the governing equations with their reduction to the Laplace growth equation which has the infinite number of exact solutions including the formation of sharp cusps at free surface in a finite time.
Direct Numerical Simulations of turbulent channel flows at friction Reynolds number 550, 1000, 1500, are used to analyse the turbulent production, transfer and dissipation mechanisms in the compound space of scales and wall-distances by means of the Kolmogorov equation generalized to inhomogeneous anisotropic flows. Two distinct peaks of scale-energy source are identified. The first stronger one belongs to the near-wall cycle. Its location in the space of scales and physical space is found to scale in viscous units while its intensity grows slowly with $Re$, indicating a near-wall modulation. The second source peak is found further away from the wall in the putative overlap layer and it is separated from the near-wall source by a layer of significant scale-energy sink. The dynamics of the second outer source appears to be strongly dependent on the Reynolds number. The detailed scale-by-scale analysis of this source highlights well-defined features that are used to make the properties of the outer turbulent source independent of Reynolds number and wall-distance by rescaling the problem. Overall, the present results suggest a strong connection of the observed outer scale-energy source with the presence of an outer region of turbulence production whose mechanisms are well separated from the near-wall region and whose statistical features agree with the hypothesis of an overlap layer dominated by attached eddies. Inner-outer interactions between the near-wall and outer source region in terms of scale-energy fluxes are also analysed. It is conjectured that the near-wall modulation of the statistics at increasing Reynolds number can be related to a confinement of the near-wall turbulence production due to the presence of increasingly large production scales in the outer scale-energy source region.
We analyze analytically and numerically the scale invariant stationary solution to the internal wave kinetic equation. Our analysis of the resonant energy transfers shows that the leading order contributions are given (i) by triads with extreme scale separation and (ii) by triads of waves that are quasi-colinear in the horizontal plane. The contributions from other types of triads is found to be subleading. We use the modified scale invariant limit of the Garrett and Munk spectrum of internal waves to calculate the magnitude of the energy flux towards high wave numbers in both the vertical and the horizontal directions. Our results compare favorably with the finescale parametrization of ocean mixing that was proposed in [Polzin et al. (1995)].
We report a novel technique to passively create strong secondary flows at moderate to high flow rates in microchannels, accurately control them and finally, due to their deterministic nature, program them into microfluidic platforms. Based on the flow conditions and due to the presence of the pillars in the channel, the flow streamlines will lose their fore-aft symmetry. As a result of this broken symmetry the fluid is pushed away from the pillar at the center of the channel (i.e. central z-plane). As the flow needs to maintain conservation of mass, the fluid will laterally travel in the opposite direction near the top and bottom walls. Therefore, a NET secondary flow will be created in the channel cross-section which is depicted in this video. The main platform is a simple straight channel with posts (i.e. cylindrical pillars - although other pillar cross-sections should also function) placed along the channel. Channel measures were 200 mumtimes50 mum, with pillars of 100 mum in diameter. Positioning the pillars in different locations within the cross-section of the channel will result in induction of different secondary flow patterns, which can be carefully engineered. The longitudinal spacing of the pillars is another design parameter (600 mum spacing was used for this video). The device works over a wide range (moderate to high) flow rates. We used 150 muL/min in this experiment. The device has 3 inlets where a dye stream is co-flowed between two water streams. In this video, one can see the effect of the net secondary flow created by inertia in the microchannel by visualizing the cross-section of the fluorescently labeled stream. Confocal images are sequentially taken at the inlet and after 49 consecutive pillars.
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