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arXiv2021

On the Origins of the Oceanic Ultraviolet Catastrophe

We provide a first-principles analysis of the energy fluxes in the oceanic internal wavefield. The resulting formula is remarkably similar to the renowned phenomenological formula for the turbulent dissipation rate in the ocean which is known as the Finescale Parameterization. The prediction is based on the wave turbulence theory of internal gravity waves and on a new methodology devised for the computation of the associated energy fluxes. In the standard spectral representation of the wave energy density, in the two-dimensional vertical wavenumber - frequency domain, the energy fluxes associated with the steady state are found to be directed downscale in both coordinates, closely matching the Finescale-Parameterization formula in functional form and in magnitude. These energy transfers are composed of a `local' and a `scale-separated' contributions; while the former is quantified numerically, the latter is dominated by the Induced Diffusion process and is amenable to analytical treatment. Contrary to previous results indicating an inverse energy cascade from high frequency to low, at odds with observations, our analysis of all non-zero coefficients of the diffusion tensor predicts a direct energy cascade. Moreover, by the same analysis fundamental spectra that had been deemed `no-flux' solutions are reinstated to the status of `constant-downscale-flux' solutions. This is consequential for an understanding of energy fluxes, sources and sinks that fits in the observational paradigm of the Finescale Parameterization, solving at once two long-standing paradoxes that had earned the name of `Oceanic Ultraviolet Catastrophe'.

physics.flu-dyn↗

arXiv2013

Effective viscosity of non-gravitactic Chlamydomonas Reinhardtii microswimmer suspensions

Active microswimmers are known to affect the macroscopic viscosity of suspensions in a more complex manner than passive particles. For puller-like microswimmers an increase in the viscosity has been observed. It has been suggested that the persistence of the orientation of the microswimmers hinders the rotation that is normally caused by the vorticity. It was previously shown that some sorts of algaes are bottom-heavy swimmers, i.e. their centre of mass is not located in the centre of the body. In this way, the algae affects the vorticity of the flow when it is perpendicular oriented to the axis of gravity. This orientation of gravity to vorticity is given in a rheometer that is equipped with a cone-plate geometry. Here we present measurements of the viscosity both in a cone-plate and a Taylor-Couette cell. The two set-ups yielded the same increase in viscosity although the axis of gravitation in the Taylor-Couette cell is parallel to the direction of vorticity. In a complementary experiment we tested the orientation of the direction of swimming through microscopic observation of single \textit{Chlamydomonas reinhardtii} and could not identify a preferred orientation, i. e. our specific strain of \textit{Chlamydomonas reinhardtii} are not bottom-heavy swimmers. We thus conclude that bottom heaviness is not a prerequisite for the increase of viscosity and that the effect of gravity on the rheology of our strain of \textit{Chlamydomonas reinhardtii} is negligible. This finding reopens the question of whether origin of persistence in the orientation of cells is actually responsible for the increased viscosity of the suspension.

physics.bio-ph↗

arXiv2014

Energy transfers and magnetic energy growth in small-scale dynamo

In this letter we investigate the dynamics of magnetic energy growth in small-scale dynamo by studying energy transfers, mainly energy fluxes and shell-to-shell energy transfers. We perform dynamo simulations for magnetic Prandtl number $\mathrm{Pm}=20$ on $1024^3$ grid using pseudospectral method. We demonstrate that the magnetic energy growth is caused by nonlocal energy transfers from the large-scale or forcing-scale velocity field to small-scale magnetic field. The peak of these energy transfers move towards lower wavenumbers as dynamo evolves, which is the reason why the integral scale of the magnetic field increases with time. The energy transfers $U2U$ (velocity to velocity) and $B2B$ (magnetic to magnetic) are forward and local.

physics.flu-dyn↗

arXiv2014

Lattice Boltzmann Model for The Volume-Averaged Navier-Stokes Equations

A numerical method, based on the discrete lattice Boltzmann equation, is presented for solving the volume-averaged Navier-Stokes equations. With a modified equilibrium distribution and an additional forcing term, the volume-averaged Navier-Stokes equations can be recovered from the lattice Boltzmann equation in the limit of small Mach number by the Chapman-Enskog analysis and Taylor expansion. Due to its advantages such as explicit solver and inherent parallelism, the method appears to be more competitive with traditional numerical techniques. Numerical simulations show that the proposed model can accurately reproduce both the linear and nonlinear drag effects of porosity in the fluid flow through porous media.

physics.flu-dyn↗

arXiv2014

Wrinkling instability of vesicles in steady linear flow

We present experimental observations and numerical simulations of a wrinkling instability that occurs at sufficiently high strain rates in the trembling regime of vesicle dynamics in steady linear flow. Spectral and statistical analysis of the data shows similarities and differences with the wrinkling instability observed earlier for vesicles in transient elongation flow. The critical relevance of thermal fluctuations for this phenomenon is revealed by a simple model using coupled Langevin equations that reproduces the experimental observations quite well.

cond-mat.soft↗

arXiv2014

An algorithm to estimate unsteady and quasi-steady pressure fields from velocity field measurements

We describe and characterize a method for estimating the pressure field corresponding to velocity field measurements, such as those obtained by using particle image velocimetry. The pressure gradient is estimated from a time series of velocity fields for unsteady calculations or from a single velocity field for quasi-steady calculations. The corresponding pressure field is determined based on median polling of several integration paths through the pressure gradient field in order to reduce the effect of measurement errors that accumulate along individual integration paths. Integration paths are restricted to the nodes of the measured velocity field, thereby eliminating the need for measurement interpolation during this step and significantly reducing the computational cost of the algorithm relative to previous approaches. The method is validated by using numerically-simulated flow past a stationary, two-dimensional bluff body and a computational model of a three-dimensional, self-propelled anguilliform swimmer to study the effects of spatial and temporal resolution, domain size, signal-to-noise ratio, and out-of-plane effects. Particle image velocimetry measurements of a freely-swimming jellyfish medusa and a freely-swimming lamprey are analyzed using the method to demonstrate the efficacy of the approach when applied to empirical data.

physics.flu-dyn↗

arXiv2014

Pressure pulsations in reciprocating pump piping systems Part 1: Modelling

A distributed parameter model of pipeline transmission line behaviour is presented, based on a Galerkin method incorporating frequency-dependent friction. This is readily interfaced to an existing model of the pumping dynamics of a plunger pump to allow time-domain simulations of pipeline pressure pulsations in both suction and delivery lines. A new model for the pump inlet manifold is also proposed.

physics.flu-dyn↗

arXiv2014

The available-enthalpy (flow-exergy) cycle. Part-I: introduction and basic equations

A diagnostic package is derived from the concept of specific available enthalpy, leading to the definition of a local and complete energy cycle. It is useful to understand the transformations of energy occurring at any particular pressure level or pressure layer of a limited area domain. The global version of this diagnostic tool is very similar to the cycle of Lorenz, but the local counterpart contains several additional terms, with zonal, eddy and static-stability components close to definitions already given by Pearce. The new cycle takes into account the flow of energy components across the vertical and horizontal boundaries, with additional conversion terms involving potential energy, leading to accurate computations of dissipation and generation terms obtained as residuals. A new accurate temporal scheme is proposed in order to allow use of a large time interval in future numerical applications. Finally, comments are made on the arbitrary choice for two constant reference values for pressure and temperature.

physics.ao-ph↗

arXiv2014

The available-enthalpy (flow-exergy) cycle. Part-II: applications to idealized baroclinic waves

The local available-enthalpy cycle proposed in Part I of this paper is applied to document energetics of three numerical simulations, representing life cycles of idealized baroclinic waves. An improved temporal numerical scheme defined in Part I is used in this study, together with the Arpege-IFS model using a T42 triangular truncation. A 45°N and 200 hPa dry unstable jet is constructed with the most unstable mode at zonal wave number 8. Energetic impacts of both horizontal and vertical diffusion schemes are determined separately. The role of ageostrophic winds within the Ekman layer is investigated, leading to an explanation for large observed values for the dissipation terms and to a new formulation of the potential-energy conversions. The magnitudes of these new conversion terms are compared with those of the usual barotropic and baroclinic conversions. A new version for the available-enthalpy cycle is proposed. It is suitable for open systems and it includes explicitly the potential-energy component as a transitional reservoir. Finally, some results from Intensive Observing Period 15 of the Fronts and Atlantic Storm-Track EXperiment (FASTEX) are compared with those from the idealized diabatic experiment.

physics.ao-ph↗

arXiv2013

Estimation of unsteady aerodynamics in the wake of a freely flying European starling

Wing flapping is one of the most widespread propulsion methods found in nature; however, the current understanding of the aerodynamics in bird wakes is incomplete. The role of the unsteady motion in the flow and its contribution to the aerodynamics is still an open question. In the current study, the wake of a freely flying European starling has been investigated using long-duration high-speed Particle Image Velocimetry (PIV) in the near wake. Kinematic analysis of the wings and body of the bird has been performed using additional high-speed cameras that recorded the bird movement simultaneously with the PIV measurements. The wake evolution of four complete wingbeats has been characterized through reconstruction of the time resolved data, and the aerodynamics in the wake have been analyzed in terms of the streamwise forces acting on the bird. The profile drag from classical aerodynamics was found to be positive during most of the wingbeat cycle, yet kinematic images show that the bird does not decelerate. It is shown that unsteady aerodynamics are necessary to satisfy the drag/thrust balance by approximating the unsteady drag term. These findings may shed light on the flight efficiency of birds by providing a partial answer to how they minimize drag during flapping flight.

physics.flu-dyn↗

arXiv2013

Beating the jetting regime

We study numerically the dynamics of jets and drops in a microcapillary co-flow device. The co-flow stream encounters different flow regimes, including dripping, jetting. Using a level-set/finite element axysimmetric numerical simulation, we study the dynamics of breakup of a jet subject to flow rate perturbations. A scaling law for the width of the unperturbed jet is presented and compared to existing experimental results as well as numerical measurements. Then, we show that the introduction of a sinusoidal perturbation of the inner fluid flow rate can facilitate breakup of the fluid in regimes where a jet is usually observed. Moreover, the flow rate perturbation leads to a good control over the size and the frequency of the resulting droplets. Using theoretical modelling, we provide a criterion to determine the optimal frequency to break up the jet. We also derive scaling laws to determine the volume of inner fluid encapsulated in the emulsion droplets as a function of the frequency and to estimate the distance for the jet to break up as a function of the amplitude of perturbation. These scaling laws are in good agreement with results of numerical simulations. Our work suggests a novel approach and offers guiding principles to break up liquid jets in cases where dripping is difficult to achieve.

physics.flu-dyn↗

arXiv2013

An Efficient Coarse Grid Projection Method for Quasigeostrophic Models of Large-Scale Ocean Circulation

This paper puts forth a coarse grid projection (CGP) multiscale method to accelerate computations of quasigeostrophic (QG) models for large scale ocean circulation. These models require solving an elliptic sub-problem at each time step, which takes the bulk of the computational time. The method we propose here is a modular approach that facilitates data transfer with simple interpolations and uses black-box solvers for solving the elliptic sub-problem and potential vorticity equations in the QG flow solvers. After solving the elliptic sub-problem on a coarsened grid, an interpolation scheme is used to obtain the fine data for subsequent time stepping on the full grid. The potential vorticity field is then updated on the fine grid with savings in computational time due to the reduced number of grid points for the elliptic solver. The method is applied to both single layer barotropic and two-layer stratified QG ocean models for mid-latitude oceanic basins in the beta plane, which are standard prototypes of more realistic ocean dynamics. The method is found to accelerate these computations while retaining the same level of accuracy in the fine-resolution field. A linear acceleration rate is obtained for all the cases we consider due to the efficient linear-cost fast Fourier transform based elliptic solver used. We expect the speed-up of the CGP method to increase dramatically for versions of the method that use other, suboptimal, elliptic solvers, which are generally quadratic cost. It is also demonstrated that numerical oscillations due to lower grid resolutions, in which the Munk scales are not resolved adequately, are effectively eliminated with CGP method.

physics.flu-dyn↗

arXiv2022

A removable temperature sensors holder for cryogenic Rayleigh-Bénard convection cell

A removable holder carrying a set of miniature temperature sensors inside our Rayleigh-Bénard convection cylindrical cell has been developed. The sensors should not disturb the temperature and velocity fields of the buoyancy-driven turbulent flow of our working fluid - cryogenic helium gas (~ 5 K). The cell, 300 mm both in diameter and height, must withstand the overpressure up to 2.5 bar, which is why all its parts are welded together. The holder consists of a pair of identical feedthroughs (each with 6 glass-sealed pins), constantan wires (0.1 mm), Be bronze springs and insulating elements and enables installing up to 6 sensors simultaneously, with the option to replace the damaged ones. We already used two such holders and obtained a map of local temperature and its fluctuations in 12 positions inside the cell.

physics.flu-dyn↗

arXiv2017

Skating on slippery ice

The friction of a stationary moving skate on smooth ice is investigated, in particular in relation to the formation of a thin layer of water between skate and ice. It is found that the combination of ploughing and sliding gives a friction force that is rather insensitive for parameters such as velocity and temperature. The weak dependence originates from the pressure adjustment inside the water layer. For instance, high velocities, which would give rise to high friction, also lead to large pressures, which, in turn, decrease the contact zone and so lower the friction. The theory is a combination and completion of two existing but conflicting theories on the formation of the water layer.

cond-mat.other↗

arXiv2018

Perfect Fluids

We develop a new theory of perfect fluids with translation and rotation symmetry, which is also applicable in the absence of any type of boost symmetry. It involves introducing a new fluid variable, the kinetic mass density, which is needed to define the most general energy-momentum tensor for perfect fluids. Our theory leads to corrections to the Euler equations for perfect fluids that might be observable in hydrodynamic fluid experiments. We also derive new expressions for the speed of sound in perfect fluids. Our theory reduces to the known perfect fluid models when boost symmetry is present. It can also be adapted to (non-relativistic) scale invariant fluids with critical exponent $z$. We show that perfect fluids cannot have Schrödinger symmetry unless $z=2$. For generic values of $z$ there can be fluids with Lifshitz symmetry, and as a concrete example, we work out in detail the thermodynamics and fluid description of an ideal gas of Lifshitz particles and compute the speed of sound for the classical and quantum Lifshitz gasses.

hep-th↗

arXiv2018

Odd surface waves in two-dimensional incompressible fluids

We consider free surface dynamics of a two-dimensional incompressible fluid with odd viscosity. The odd viscosity is a peculiar part of the viscosity tensor which does not result in dissipation and is allowed when parity symmetry is broken. For the case of incompressible fluids, the odd viscosity manifests itself through the free surface (no stress) boundary conditions. We first find the free surface wave solutions of hydrodynamics in the linear approximation and study the dispersion of such waves. As expected, the surface waves are chiral and even exist in the absence of gravity and vanishing shear viscosity. In this limit, we derive effective nonlinear Hamiltonian equations for the surface dynamics, generalizing the linear solutions to the weakly nonlinear case. Within the small surface angle approximation, the equation of motion leads to a new class of non-linear chiral dynamics governed by what we dub the {\it chiral} Burgers equation. The chiral Burgers equation is identical to the complex Burgers equation with imaginary viscosity and an additional analyticity requirement that enforces chirality. We present several exact solutions of the chiral Burgers equation. For generic multiple pole initial conditions, the system evolves to the formation of singularities in a finite time similar to the case of an ideal fluid without odd viscosity. We also obtain a periodic solution to the chiral Burgers corresponding to the non-linear generalization of small amplitude linear waves.

physics.flu-dyn↗

arXiv2012

Free-surface flow simulations for discharge-based operation of hydraulic structure gates

We combine non-hydrostatic flow simulations of the free surface with a discharge model based on elementary gate flow equations for decision support in operation of hydraulic structure gates. A water level-based gate control used in most of today's general practice does not take into account the fact that gate operation scenarios producing similar total discharged volumes and similar water levels may have different local flow characteristics. Accurate and timely prediction of local flow conditions around hydraulic gates is important for several aspects of structure management: ecology, scour, flow-induced gate vibrations and waterway navigation. The modelling approach is described and tested for a multi-gate sluice structure regulating discharge from a river to the sea. The number of opened gates is varied and the discharge is stabilized with automated control by varying gate openings. The free-surface model was validated for discharge showing a correlation coefficient of 0.994 compared to experimental data. Additionally, we show the analysis of CFD results for evaluating bed stability and gate vibrations.

cs.CE↗

arXiv2014

The mean-field dynamo model

The 2D Parker's mean-field dynamo equations with a various distributions of the $α$- and $ω$-effects are considered. We show that smooth profiles of $α$ and $ω$ can produce dipole configuration of the magnetic field with the realistic magnetic energy spectrum. We emphasize that fluctuating $α$-effect leads to increase of the magnetic energy at the small scales, breaking the dipole configuration of the field. The considered geostrophic profiles of $α$ and $ω$ correspond to the small-scale polarwards/equatorwards travelling waves with the small dipole field contribution. The same result is observed for the dynamic form of the $α$-quenching, where two branches of the weak and strong solution coexist.

physics.flu-dyn↗