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arXiv2014

Wave turbulence revisited: Where does the energy flow?

Turbulence in a system of nonlinearly interacting waves is referred to as wave turbulence. It has been known since seminal work by Kolmogorov, that turbulent dynamics is controlled by a directional energy flux through the wavelength scales. We demonstrate that an energy cascade in wave turbulence can be bi-directional, that is, can simultaneously flow towards large and small wavelength scales from the pumping scales at which it is injected. This observation is in sharp contrast to existing experiments and wave turbulence theory where the energy flux only flows in one direction. We demonstrate that the bi-directional energy cascade changes the energy budget in the system and leads to formation of large-scale, large-amplitude waves similar to oceanic rogue waves. To study surface wave turbulence, we took advantage of capillary waves on a free, weakly charged surface of superfluid helium He-II at temperature 1.7K. Although He-II demonstrates non-classical thermomechanical effects and quantized vorticity, waves on its surface are identical to those on a classical Newtonian fluid with extremely low viscosity. The possibility of directly driving a charged surface by an oscillating electric field and the low viscosity of He-II have allowed us to isolate the surface dynamics and study nonlinear surface waves in a range of frequencies much wider than in experiments with classical fluids.

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arXiv2014

Horizontal velocity field near the hot plate in turbulent natural convection

We study the velocity field in a horizontal (x-y) plane 1.5 mm above the hot plate in turbulent natural convection using PIV at a Rayleigh number Raw=106 and Prandtl number Pr=5.2. The plane of measurement is inside the velocity boundary layer estimated from the natural convection boundary layer equations[7] as well as inside the velocity boundary layer due to the large scale flow[2, 5].The boundary layer comprises of line plumes with sinking fluid between them. The instantaneous velocity variation from the center of the sinking fluid to the line plumes is found to deviate with the classical Prandtl-Blasius laminar boundary layer profile, which is assumed to be the nature of boundary layer by the GL theory [2, 5]. Our results agree well with the natural convection boundary layer profile. The time averaged mean velocity variation deviates from both natural convection and Blasius type profiles as expected as it depends on the orientation of the line plumes. Our measurement result is a proof to the theory of the presence of a natural convection boundary layer on both sides of a line plume [10].

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arXiv2014

Explicit Filtering in Large Eddy Simulation of Barotropic Turbulence in Spectral Space

Explicit filtering in large eddy simulation (LES) of a turbulent barotropic flow on the sphere in spectral space is studied and compared to implicit filtering. Here, a smooth filter is applied to the nondivergent barotropic vorticity equation (BVE) on the rotating sphere to divide the flow field into resolved scale (RS) and subfilter scale (SFS) motions. A portion of the SFS motions are reconstructed theoretically using the approximate deconvolution model (ADM). While the unreconstructed portion consists of the subgrid scale (SGS) motions and needs to be modeled separately. In order to investigate the effects of the explicit filtering alone no SGS model is used. It is shown that the explicit filtering accurately tracks the evolution of the coherent structures in two-dimensional turbulent flow on the rotating sphere, whereas the implicit filtering does not. It is also shown that explicit filtering improves the results of the temporal variation of the total kinetic energy and the total enstrophy and the variation of the energy spectrum with wavenumber compare to the implicit filtering. Although explicit filtering is more expensive than implicit filtering it increases the accuracy of the computations and improves the results, particularly where the location of coherent structures is concerned, a topic of particular importance in LES of atmospheric flows for climate and weather applications.

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arXiv2014

Energy spectrum of Buoyancy-driven Flows

Using high-resolution direct numerical simulation and arguments based on the kinetic energy flux $Π_u$, we demonstrate that for stably stratified flows, the kinetic energy spectrum $E_u(k) \sim k^{-11/5}$, the entropy spectrum $E_θ(k) \sim k^{-7/5}$, and $Π_u(k) \sim k^{-4/5}$ (Bolgiano-Obukhov scaling). This scaling is due to the depletion of kinetic energy because of buoyancy. For weaker buoyancy in stratified flows, $E_u(k)$ follows Kolmgorov's spectrum with a constant energy flux. We also argue that for Rayleigh Bénard convection, the Bolgiano-Obukhov scaling will not hold for the bulk flow due to the positive energy supply by buoyancy and non-decreasing $Π_u(k)$.

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arXiv2014

Exact solutions for a periodic assembly of bubbles in a Hele-Shaw channel

Exact solutions are reported for a periodic assembly of bubbles steadily co-travelling in a Hele-Shaw channel. The solutions are obtained as conformal mappings from a multiply connected circular domain in an auxiliary complex plane to the flow region in a period cell. The conformal mappings are constructed using the generalized Schwarz-Christoffel formula for multiply connected polygonal domains in terms of products of Schottky-Klein prime functions. It is shown that previous solutions for multiple steady bubbles in a Hele-Shaw cell are all particular cases of the solutions described herein. Examples of specific bubble configurations are discussed.

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arXiv2014

On the stabilizing mechanism of 2D absolute and global instabilities by 3D streaks

Global and local absolute instabilities of 2D wakes are known to be stabilized by spanwise periodic modulations of the wake profile. The present study shows that this stabilizing effect is of general nature and can be mimicked by enforcing spanwise periodic modulations of the wave advection velocity in the generalized complex Ginzburg-Landau equation. The first order sensitivity of the absolute and global growth rate to the enforced modulation is zero, exactly as in the Navier-Stokes case. We show that a second order sensitivity analysis is effective to quantify and interpret the observed stabilizing effect. The global growth rates predicted by the second order expansion closely match those issued from a direct computation of the eigenvalues. It is shown that, at leading order, the modulation of the wave advection velocity alters the effective wave diffusion coefficient in the dispersion relation and that this variation induces a reduction of the absolute growth rate and the stabilization of the global instability.

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arXiv2014

Universal asymptotic umbrella for hydraulic fracture modeling

The paper presents universal asymptotic solution needed for efficient modeling of hydraulic fractures. We show that when neglecting the lag, there is universal asymptotic equation for the near-front opening. It appears that apart from the mechanical properties of fluid and rock, the asymptotic opening depends merely on the local speed of fracture propagation. This implies that, on one hand, the global problem is ill-posed, when trying to solve it as a boundary value problem under a fixed position of the front. On the other hand, when properly used, the universal asymptotics drastically facilitates solving hydraulic fracture problems (both analytically and numerically). We derive simple universal asymptotics and comment on their employment for efficient numerical simulation of hydraulic fractures, in particular, by well-established Level Set and Fast Marching Methods.

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arXiv2014

Conical tip in frozen water drops

A theory is presented for the formation of a conical tip in water drops that are frozen on a flat surface below freezing temperature. For the known ice to water density ratio r = .917, the angle of aperture of this cone is found to be θ = 33.550, consistent with observations.

physics.flu-dyn↗
arXiv2014

Closed-Loop Turbulence Control Using Machine Learning

We propose a general model-free strategy for feedback control design of turbulent flows. This strategy called 'machine learning control' (MLC) is capable of exploiting nonlinear mechanisms in a systematic unsupervised manner. It relies on an evolutionary algorithm that is used to evolve an ensemble of feedback control laws until minimization of a targeted cost function. This methodology can be applied to any non-linear multiple-input multiple-output (MIMO) system to derive an optimal closed-loop control law. MLC is successfully applied to the stabilization of nonlinearly coupled oscillators exhibiting frequency cross-talk, to the maximization of the largest Lyapunov exponent of a forced Lorenz system, and to the mixing enhancement in an experimental mixing layer flow. We foresee numerous potential applications to most nonlinear MIMO control problems, particularly in experiments.

physics.flu-dyn↗
arXiv2014

Solution of hydraulic fracture problem accounting for lag

The paper presents a method for solving hydraulic fracture problems accounting for the lag. The method consists in matching the outer (basic) solution neglecting the lag, with the inner (auxiliary) solution of the derived 1D integral equation with conditions, accounting for the lag and asymptotic behavior of the opening and the net-pressure. The method refers to practically important cases, when the influence of the local perturbation, caused by the lag, becomes insignificant at a distance, where the leading plane-state asymptotics near the fracture front is still applicable. The universal asymptotics are used for finding the matching constants of the basic (outer) solution and for formulation of matching condition for the solution of inner (auxiliary) problem. The method is illustrated by the solution of the Spence and Sharp plane-strain problem for a fracture propagating symmetrically from the inlet, where a Newtonian fluid is pumped at a constant rate. It is stated that the method developed for deep fractures may also serve in the intermediate range between deep and shallow fractures.

physics.flu-dyn↗
arXiv2014

Comment on Magnetohydrodynamic non-Darcy mixed convection heat transfer from a vertical heated plate embedded in a porous medium with variable porosity, by Dulal Pal

In the above paper the author treats the boundary layer flow along a vertical flat plate, immersed in a Darcy Brinkman Forchheimer porous medium. The porosity and the permeability of the porous medium are variable across the boundary layer. In addition a magnetic field with constant strength is applied normal to the plate. The fluid temperature at the plate is constant and different from that of the ambient fluid. This temperature difference creates a buoyancy force and the flow is characterized as mixed convection. The partial differential equations of the boundary layer flow are transformed into ordinary differential equations and subsequently are solved with the Runge-Kutta Fehlberg method. The results are presented in two tables and 11 figures.

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arXiv2014

Compressive sampling for energy spectrum estimation of turbulent flows

Recent results from compressive sampling (CS) have demonstrated that accurate reconstruction of sparse signals often requires far fewer samples than suggested by the classical Nyquist--Shannon sampling theorem. Typically, signal reconstruction errors are measured in the $\ell^2$ norm and the signal is assumed to be sparse, compressible or having a prior distribution. Our spectrum estimation by sparse optimization (SpESO) method uses prior information about isotropic homogeneous turbulent flows with power law energy spectra and applies the methods of CS to 1-D and 2-D turbulence signals to estimate their energy spectra with small logarithmic errors. SpESO is distinct from existing energy spectrum estimation methods which are based on sparse support of the signal in Fourier space. SpESO approximates energy spectra with an order of magnitude fewer samples than needed with Shannon sampling. Our results demonstrate that SpESO performs much better than lumped orthogonal matching pursuit (LOMP), and as well or better than wavelet-based best M-term or M/2-term methods, even though these methods require complete sampling of the signal before compression.

physics.flu-dyn↗
arXiv2014

The effects of rotation on a double-diffusive layer in a rotating spherical shell

So far, numerical studies of double-diffusive layering in turbulent convective flows have neglected the effects of rotation. We undertake a first step into that direction by investigating how Coriolis forces affect a double-diffusive layer inside a rotating spherical shell. For this purpose we have run simulations in a parameter regime where these layers are expected to form and successively increased the rate of rotation with the result that fast rotation is found to have a similar stabilising effect on the overall convective flux as an increase of the stability ratio $R_ρ$ has in a non-rotating setup. We have also studied to what extent the regimes of rotational constraints suggested by King, Stellmach, and Buffett (2013) for rotation in the case of Rayleigh-Bénard convection are influenced by double-diffusive convection: their classification could also be applicable to the case of double-diffusive convection in a spherical shell if it is extended to be also a function of the stability ratio $R_ρ$. Furthermore, we examined the ratio of saline and thermal Nusselt numbers and compared our results with models of Spruit (2013), Rosenblum et al. (2011) and Wood, Garaud, and Stellmach (2013). We find our data to be fitted best by Spruit's model. Our result that fast rotation further decreases the convective transport, which is already lowered by double-diffusive convection, could play a major role for e.g. the modeling of the interior of some rapidly rotating giant planets, as gaseous giant planets have recently been proposed to be influenced by double-diffusive convection.

physics.flu-dyn↗
arXiv2014

Determination of the characteristics of a linear ducted sound source

Ducted flow devices for a range of purposes, such as air-moving fans, are routinely characterised experimentally to understand their acoustic performance as part of the continuing trend for quiet, high efficiency design. The International Organization for Standardization (ISO) method 5136 is widely used in industry and academia to determine the sound radiated into a duct. This involves placing the device at the centre of a long cylindrical duct with anechoic terminations at each end to eliminate reflections. A single off-axis microphone is used on the inlet and outlet sides that can theoretically capture the plane-wave mode amplitudes but this does not provide enough information to fully account for higher-order modes. In this study, the 'two-port' source model is formulated to include higher-order modes and applied for the first three modes as a proof of concept. This requires six independent surface pressure measurements on each side or 'port'. The resulting experimental set-up is much shorter than the ISO rig and does not require anechoic terminations. The relative importance of the higher-order modes has been considered and the inaccuracies when using the ISO method to find source sound power has been analysed.

physics.flu-dyn↗
arXiv2014

Comment on Y. Couder and E. Fort: "Single-Particle Diffraction and Interference at a Macroscopic Scale", Phys. Rev. Lett. (2006)

In a paper from 2006, Couder and Fort [1] describe a version of the famous double slit experiment performed with drops bouncing on a vibrated fluid surface, where interference in the particle statistics is found even though it is possible to determine unambiguously which slit the "walking" drop passes. It is one of the first papers in an impressive series, showing that such walking drops closely resemble de Broglie waves and can reproduce typical quantum phenomena like tunneling and quantized states [2-13]. The double slit experiment is, however, a more stringent test of quantum mechanics, because it relies upon superposition and phase coherence. In the present comment we first point out that the experimental data presented in [1] are not convincing, and secondly we argue that it is not possible in general to capture quantum mechanical results in a system, where the trajectory of the particle is well-defined.

physics.flu-dyn↗
arXiv2014

Boundary Layer Adaptivity For Incompressible Turbulent Flows

Boundary layers in turbulent flows require fine grid spacings near the walls which depend on the choice of turbulence model. To satisfy these requirements a semi-structured mesh is generally used in this area with orthogonal and layered elements. Adaptation of such a mesh needs to take into account the flow physics along with the standard error indicator approach. In this paper a novel methodology which combines Hessian based error indicators with flow physics to drive mesh adaptation is illustrated. Particular focus is on the thickness adaptation of the layered mesh. The technique is applied to two turbulent incompressible flow cases and its effectiveness is studied.

physics.flu-dyn↗
arXiv2014

Flagella-induced transitions in the collective behavior of confined microswimmers

Bacteria exist in a free-swimming state or in a sessile biofilm state. The transition from free-swimming to sessile mode is characterized by changes in gene expression which alter, among others,the mechanics of flagellar motility. In this paper, we propose an idealized physical model to investigate the effects of flagellar activity on the hydrodynamic interactions among a population of microswimmers. We show that decreasing flagellar activity induces a hydrodynamically-triggered transition in confined microswimmers from turbulent-like swimming to aggregation and clustering. These results suggest that the interplay between flagellar activity and hydrodynamic interactions provides a physical mechanism for coordinating collective behaviors in confined bacteria, with potentially profound implications on biofilm initiation.

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