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arXiv2013

Velocity spectra of quantum turbulence: experiments, numerics and models

Superfluid Turbulence is unusual and presents a challenge to fluid dynamicists because it consists of two coupled, inter penetrating turbulent fluids: the first is inviscid with quantised vorticity, the second is viscous with continuous vorticity. Despite this double nature, the observed spectra of the superfluid turbulent velocity at sufficiently large length scales are similar to those o ordinary turbulence. We present experimental, numerical and theoretical results which explain these similarities, and illustrate the limits of our present understanding of superfluid turbulence at smaller scales.

cond-mat.other↗
arXiv2013

Effects of Gas Dynamics on Rapidly Collapsing Bubbles

The dynamics of rapidly collapsing bubbles are of great interest due to the high degree of energy focusing that occurs withing the bubble. Molecular dynamics provides a way to model the interior of the bubble and couple the gas dynamics with the equations governing the bubble wall. While much theoretical work has been done to understand how a bubble will respond to an external force, the internal dynamics of the gas system are usually simplified greatly in such treatments. This paper shows how the gas system dynamics affect bubble collapse and illustrates what effects various modeling assumptions can have on the motion of the bubble wall. In addition, we present a method of adaptively partitioning space to improve the performance of collision intersection calculations when using an energy dependent collision cross section.

physics.comp-ph↗
arXiv2013

Are Lagrangian stochastic models at odds with statistical theories of relative dispersion?

In an article on statistical modelling of turbulent relative dispersion, Franzese & Cassiani (2007, p. 402) commented on Lagrangian stochastic models and reported some concern about the consistency between statisti- cal and stochastic modelling of turbulent dispersion. In this short article, comparison of the two approaches is performed. As far as the dependence of models from turbulence constants is concerned, the two theoretical ap- proaches are found to be in perfect agreement eliminating every possible concern.

physics.flu-dyn↗
arXiv2013

An approximate analytical solution of free convection problem for vertical isothermal plate via transverse coordinate Taylor expansion

The model under consideration is based on approximate analytical solution of two dimensional stationary Navier-Stokes and Fourier-Kirchhoff equations. Approximations are based on the typical for natural convection assumptions: the fluid noncompressibility and Bousinesq approximation. We also assume that ortogonal to the plate component (x) of velocity is neglectible small. The solution of the boundary problem is represented as a Taylor Series in $x$ coordinate for velocity and temperature which introduces functions of vertical coordinate (y), as coefficients of the expansion. The correspondent boundary problem formulation depends on parameters specific for the problem: Grashoff number, the plate height (L) and gravity constant. The main result of the paper is the set of equations for the coefficient functions for example choice of expansion terms number. The nonzero velocity at the starting point of a flow appears in such approach as a development of convecntional boundary layer theory formulation.

physics.flu-dyn↗
arXiv2013

A new Eulerian theory of turbulence constrained by random Galilean invariance

We propose a new Eulerian turbulence theory to obtain a closed set of equations for homogeneous, isotropic turbulent velocity field correlations and propagator functions by incorporating constraints of random Galilean invariance. This incorporation generates a few different equations for propagator and the present theory suggests a way to utilize them into the closure solutions of two-time and single-time velocity correlations' equations so as to properly account for random sweeping phenomena. The present theory yields exact solutions when applied to simple model problem of random oscillator.

math-ph↗
arXiv2013

Coupled Mesoscale-Large-Eddy Modeling of Realistic Stable Boundary Layer Turbulence

Site-specific flow and turbulence information are needed for various practical applications, ranging from aerodynamic/aeroelastic modeling for wind turbine design to optical diffraction calculations. Even though highly desirable, collecting on-site meteorological measurements can be an expensive, time-consuming, and sometimes a challenging task. In this work, we propose a coupled mesoscale-large-eddy modeling framework to synthetically generate site-specific flow and turbulence data. The workhorses behind our framework are a state-of-the-art, open-source atmospheric model called the Weather Research and Forecasting (WRF) model and a tuning-free large-eddy simulation (LES) model. Using this coupled framework, we simulate a nighttime stable boundary layer (SBL) case from the well-known CASES-99 field campaign. One of the unique aspects of this work is the usage of a diverse range of observations for characterization and validation. The coupled models reproduce certain characteristics of observed low-level jets. They also capture various scaling regimes of energy spectra, including the so-called spectral gap. However, the coupled models are unable to capture the intermittent nature of the observed surface fluxes. Lastly, we document and discuss: (i) the tremendous spatio-temporal variabilities of observed and modeled SBL flow fields, and (ii) the significant disagreements among different observational platforms. Based on these results, we strongly recommend that future SBL modeling studies consider rigorous validation exercises based on multi-sensor/multi-platform datasets. In summary, we believe that the numerical generation of realistic SBL is not an impossible task. Without any doubt, there remain several computational and fundamental challenges. The present work should be viewed as a first step to confront some of these challenges.

physics.ao-ph↗
arXiv2013

Mechanical equilibrium of two-component gas mixtures

Evaporation of liquid into a vapor-gas mixture is interesting and important process as for fundamental research and for different applications. In general, the rate at which a liquid evaporates is dependent on the transport of mass and energy occurring within both the liquid and vapor phases. This study is carried out on the base of continuum conservation equations for two-component medium. At the beginning the stability conditions for mechanical equilibrium are deduced. This paper is devoted to this theme.

physics.flu-dyn↗
arXiv2013

Modeling Statistical Properties of Solar Active Regions through DNS of 3D-MHD Turbulence

Statistical properties of the Sun's photospheric turbulent magnetic field, especially those of the Active Regions (ARs), have been studied using the line-of-sight data from magnetograms taken by SOHO and several other instruments (see e.g. Abramenko et al (2002, 2003),Abramenko and Yurchyshyn (2010)). This includes structure functions and their exponents, flatness curves and correlation functions. In these works, the dependence of structure function exponents ($ζ_p$) of the order of the structure functions ($\it{p}$) was modeled using a non-intermittent K41 model. It is now well known that the ARs are highly turbulent and are associated with strong intermittent events. In this paper we compare some of the observations from Abramenko et al (2003) with the log-Poisson model (Biskamp 2003) used for modeling intermittent MHD turbulent flows. Next, we analyze the structure function data obtained from the direct numerical simulations (DNS) of homogeneous, incompressible 3D-MHD turbulence in three cases: sustained by forcing, freely decaying and a flow initially driven and later allowed to decay (case 3). The respective DNS replicate the properties seen in the plots of $ζ_p$ against $\it{p}$ of ARs. We also reproduce the trends and changes observed in intermittency in flatness [Abramenko and Yurchyshyn (2010)] and correlation functions [Abramenko et al (2003)] of ARs. It is suggested from this analysis that an AR in the onset phase of a flare can be treated as a forced 3D-MHD turbulent system in its simplest form and that the flaring stage is representative of decaying 3D-MHD turbulence. It is also inferred that significant changes in intermittency from the initial onset phase of a flare to its final peak flaring phase, are related to the time taken by the system to reach the initial onset phase.

astro-ph.SR↗
arXiv2013

Analysis of the Taylor dissipation surrogate in forced isotropic turbulence

From the energy balance in wavenumber space expressed by the Lin equation, we derive a new form for the local Karman-Howarth equation for forced isotropic turbulence in real space. This equation is then cast into a dimensionless form, from which a combined analytical and numerical study leads us to deduce a new model for the scale-independent nondimensional dissipation rate $\Ceps$, which takes the form $\Ceps = \Cinf + C_L/R_L$, where the asymptotic value $\Cinf$ can be evaluated from the third-order structure function. This is found to fit the numerical data with $\Cinf = 0.47 \pm 0.01$ and $C_L= 18.5 \pm 1.3$. By considering $\Ceps - \Cinf$ on logarithmic scales, we show that $R_L^{-1}$ is indeed the correct Reynolds number behaviour. The model is compared to previous attempts in the literature, with encouraging agreement. The effects of the scale-dependence of the inertial and viscous terms due to finite forcing are then considered and shown to compensate one another, such that the model equation is applicable for systems subject to finite forcing. In addition, we also show that, contrary to the case of freely decaying turbulence, the characteristic decline in $\Ceps$ with increasing Reynolds number is due to the \emph{increase} in the surrogate expression $U^3/L$; the dissipation rate being maintained constant as a consequence of the fixed rate of forcing. A long-time non-turbulent stable state is found to exist for low Reynolds number numerical simulations which use negative damping as a means of energy injection.

physics.flu-dyn↗
arXiv2013

A new method of identifying self-similarity in isotropic turbulence

In order to analyse results for structure functions, $S_n(r)$, we propose plotting the ratio $|S_n(r)/S_3(r)|$ against the separation $r$. This method differs from the extended self-similarity (ESS) technique, which plots $S_n(r)$ against $S_3(r)$, where $S_3(r) \sim r$. Using this method in conjunction with pseudospectral evaluation of structure functions, for the particular case of $S_2(r)$ we obtain the new result that the exponent $ζ_2$ decreases as the Taylor-Reynolds number increases, with $ζ_2 \to 0.67 \pm 0.02$ as $R_λ\to \infty$. This supports the idea of finite-viscosity corrections to the K41 prediction for $S_2$, and is the opposite of the result obtained by ESS.

physics.flu-dyn↗
arXiv2013

Gravitational Drainage of Thin Films of Trisiloxane-(Poly)ethoxylate Superspreaders

Gravitational drainage of vertical films supported on a wire frame of superspreader SILWET L-77 and its cousin non-superspreader SILWET L-7607 revealed drastic differences. The superspreader films showed complicated dynamic turbulent-like interferometric patterns in distinction from the ordered color bands of the cousin non-superspreader which reminded those of the ordinary surfactants. Nevertheless the superspreader films stabilized themselves at the thickness below 50 nm and revealed an order of magnitude longer life time before bursting compared to the cousin non-superspreader. Notably, the superspreader revealed drastic differences from the non-superspreader in aqueous solutions with no contact with any solid Teflon surface. The theoretical part of the work attributed the self-stabilization of the superspreader films to significant disjoining pressure associated with the van der Waals repulsion of the fluffy surfaces of the film formed by long superspreader bilayers hanging from the free surfaces. The non-superspreaders do not possess any significant disjoining pressure in the film with thicknesses even in the range 30-50 nm. The results show that gravitational drainage of vertical films is a useful simple tool for measuring disjoining pressure.

physics.flu-dyn↗
arXiv2013

Note on the method of matched-asymptotic expansions for determining the force acting on a particle

This paper is an addendum to the article by Candelier, Mehaddi & Vauquelin (2013) where the motion of a particle in a stratified fluid is investigated theoretically, at small Reynolds and Péclet numbers. We review briefly the method of matched asymptotic expansions which is generally used in order to determine the force acting on a particle embedded in a given flow, in order to account for small, but finite, inertia effects. As part of this method, we present an alternative matching procedure, which is based on a series expansion of the far-field solution of the problem, performed in the sense of generalized functions. The way to perform such a series is presented succinctly and a simple example is provided.

physics.flu-dyn↗
arXiv2013

Vibration and Nonlinear Resonance in the Break-up of an Underwater Bubble

We use high-speed X-ray phase-contrast imaging, weakly nonlinear analysis and boundary integral simulations to characterize the final stage of underwater bubble break-up. The X-ray imaging study shows that an initial azimuthal perturbation to the shape of the bubble neck gives rise to oscillations that increasingly distort the cross-section shape. These oscillations terminate in a pinch-off where the bubble surface develops concave regions that contact similar to what occurs when two liquid drops coalesce. We also present a weakly nonlinear analysis that shows that this coalescence-like mode of pinch-off occurs when the initial shape oscillation interferes constructively with the higher harmonics it generates and thus reinforce each other's effects in bringing about bubble break-up. Finally we present numerical results that confirm the weakly nonlinear analysis scenario as well as provide insight into observed shape reversals. They demonstrate that when the oscillations interfere destructively, a qualitatively different mode of pinch-off results where the cross-section profile of the bubble neck develops sharply-curved regions.

physics.flu-dyn↗
arXiv2013

Energy transfer and dissipation in equilibrium and nonequilibrium turbulence

The nonequilibrium dissipation behaviour discovered for decaying fractal square grid-generated turbulence is experimentally investigated using hot-wire anemometry in a wind tunnel. The previous results are consolidated and benchmarked with turbulence generated by regular square-mesh grids, designed to retain certain geometrical parameters of the fractal square grid. This comparison shows that the nonequilibrium behaviour is manifested in both fractal square grid- and regular square-mesh grid-generated turbulence for a downstream region during the turbulence decay up to the first few multiples of the wake interaction distance. For one of the regular grids it is shown that beyond this region there is a transition to the classical dissipation behaviour if the local turbulent Reynolds number is sufficiently high. A sharp conclusion can thus be drawn that this behaviour is more general than initially thought and therefore of much greater scientific and engineering significance. The nonequilibrium dissipation phenomena is further investigated by experimentally measuring the terms of an inhomogeneous von Karman-Howarth-Monin equation. This equation is essentially a scale-by-scale energy transfer budget. From the data it is shown that the inhomogeneity of the turbulent flow does not tamper with the nonequilibrium phenomena and that the scaling of the nonlinear energy transfer, i.e. the transfer of energy to the small-scales, is out of balance with the dissipation. This imbalance leads to the growth of the small-scale advection to compensate for the increasing gap between the energy transferred and the energy dissipated. For the highest Reynolds number data it is also shown that the nonequilibrium dissipation scaling appears to be consistent with the expectation that it is asymptotically independent of the viscosity with a power-law spectra with the Kolmogorov-Obukhov exponent -5/3.

physics.flu-dyn↗
arXiv2013

Strong Ill-posedness of the incompressible Euler equation in borderline Sobolev spaces

For the $d$-dimensional incompressible Euler equation, the standard energy method gives local wellposedness for initial velocity in Sobolev space $H^s(\mathbb R^d)$, $s>s_c:=d/2+1$. The borderline case $s=s_c$ was a folklore open problem. In this paper we consider the physical dimensions $d=2,3$ and show that if we perturb any given smooth initial data in $H^{s_c}$ norm, then the corresponding solution can have infinite $H^{s_c}$ norm instantaneously at $t>0$. The constructed solutions are unique and even $C^{\infty}$-smooth in some cases. To prove these results we introduce a new strategy: large Lagrangian deformation induces critical norm inflation. As an application we also settle several closely related open problems.

math.AP↗
arXiv2013

The increased efficiency of fish swimming in a school

There is increasing evidence that fish gain energetic benefits when they swim in a school. The most recent indications of such benefits are a lower tail (or fin) beat at the back of a school and reduced oxygen consumption in schooling fish versus solitary ones. How such advantages may arise is poorly understood. Current hydrodynamic theories concern either fish swimming side by side or in a diamond configuration and they largely ignore effects of viscosity and interactions among wakes and individuals. In reality, however, hydrodynamic effects are complex and fish swim in many configurations. Since these hydrodynamic effects are difficult to study empirically, we investigate them in a computer model by incorporating viscosity and interactions among wakes and with individuals. We compare swimming efficiency of mullets of 12.6 cm travelling solitarily and in schools of four different configurations at several inter-individual distances. The resulting Reynolds number (based on fish length) is approximately 1150. We show that these fish always swim more efficiently in a school than alone (except in a dense phalanx). We indicate how this efficiency may emerge from several kinds of interactions among wakes and individuals. Since individuals in our simulations are not even intending to exploit the wake, gains in efficiency are obtained more easily than previously thought.

q-bio.QM↗
arXiv2013

How geometry determines the coalescence of low-viscosity drops

The coalescence of water drops on a substrate is studied experimentally. We focus on the rapid growth of the bridge connecting the two drops, which very quickly after contact ensues from a balance of surface tension and liquid inertia. For drops with contact angles below $90^\circ$, we find that the bridge grows with a self-similar dynamics that is characterized by a height $h\sim t^{2/3}$. By contrast, the geometry of coalescence changes dramatically for contact angles at $90^\circ$, for which we observe $h\sim t^{1/2}$, just as for freely suspended spherical drops in the inertial regime. We present a geometric model that quantitatively captures the transition from 2/3 to 1/2 exponent, and unifies the inertial coalescence of sessile drops and freely suspended drops.

physics.flu-dyn↗