# Physics - Fluid Dynamics Publications (50)

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## Physics - Fluid Dynamics Publications

The approaches taken to describe and develop spatial discretisations of the domains required for geophysical simulation models are commonly ad hoc, model or application specific and under-documented. This is particularly acute for simulation models that are flexible in their use of multi-scale, anisotropic, fully unstructured meshes where a relatively large number of heterogeneous parameters are required to constrain their full description. As a consequence, it can be difficult to reproduce simulations, ensure a provenance in model data handling and initialisation, and a challenge to conduct model intercomparisons rigorously. Read More

Geophysical model domains typically contain irregular, complex fractal-like boundaries and physical processes that act over a wide range of scales. Constructing geographically constrained boundary-conforming spatial discretizations of these domains with flexible use of anisotropically, fully unstructured meshes is a challenge. The problem contains a wide range of scales and a relatively large, heterogeneous constraint parameter space. Read More

An unsteady three-dimensional boundary element method is developed to provide fast calculations of biological and bio-inspired self-propelled locomotion. The approach uniquely combines an unsteady three-dimensional boundary element method, a boundary layer solver and self-propelled equations of motion. This novel implementation allows for the self-propelled speed, power, efficiency and economy to be accurately calculated. Read More

Inviscid computational results are presented on a self-propelled virtual body combined with an airfoil undergoing pitch oscillations about its leading-edge. The scaling trends of the time-averaged thrust forces are shown to be predicted accurately by Garrick's theory. However, the scaling of the time-averaged power for finite amplitude motions is shown to deviate from the theory. Read More

This paper reports the phenomenon of resonance weakening and streaming onset in two phase acoustofluidics by performing numerical simulations of a capillary droplet suspended in a microfluidic chamber. The simulations show that depending on the relative acoustic properties of the two phases, it is possible to observe (i)~the decrease in the total acoustic energy as the oscillation amplitude at the wall increases, and (ii)~the onset of acoustic streaming. The impact of these findings in terms of acoustic focusing inside droplets is also discussed. Read More

Spherical shell dynamo models based on rotating convection show that the flow within the tangent cylinder is dominated by an off-axis plume that extends from the inner core boundary to high latitudes and drifts westward. Earlier studies explained the formation of such a plume in terms of the effect of a uniform axial magnetic field that significantly increases the lengthscale of convection in a rotating plane layer. However, rapidly rotating dynamo simulations show that the magnetic field within the tangent cylinder has severe lateral inhomogeneities that may influence the onset of an isolated plume. Read More

Long waves in shallow water propagating over a background shear flow towards a sloping beach are being investigated. The classical shallow-water equations are extended to incorporate both a background shear flow and a linear beach profile, resulting in a non-reducible hyperbolic system. Nevertheless, it is shown how several changes of variables based on the hodograph transform may be used to transform the system into a linear equation which may be solved exactly using the method of separation of variables. Read More

I discuss two related nonlinear mechanisms of tidal dissipation that require finite tidal deformations for their operation: the elliptical instability and the precessional instability. Both are likely to be important for the tidal evolution of short-period extrasolar planets. The elliptical instability is a fluid instability of elliptical streamlines, such as in tidally deformed non-synchronously rotating or non-circularly orbiting planets. Read More

Using a (1+2)-dimensional boson-vortex duality between non-linear electrodynamics and a two-component compressible Bose-Einstein condensate (BEC) with spin-orbit (SO) coupling, we obtain generalised versions of the hydrodynamic continuity and Euler equations where the phase defect and non-defect degrees of freedom enter separately. We obtain the generalised Magnus force on vortices under SO coupling, and associate the linear confinement of vortices due to SO coupling with instanton fluctuations of the dual theory. Read More

This paper concerns feedback stabilization of point vortex equilibria above an inclined thin plate and a three-plate configuration known as the Kasper Wing in the presence of an oncoming uniform flow. The flow is assumed to be potential and is modeled by the 2D incompressible Euler equations. Actuation has the form of blowing and suction localized on the main plate and is represented in terms of a sink-source singularity, whereas measurement of pressure across the plate serves as system output. Read More

We present a numerical spectral method to solve systems of differential equations on an infinite interval $y\in (-\infty, \infty)$ in presence of linear differential operators of the form $Q(y) \left(\partial/\partial_y\right)^b$ (where $Q(y)$ is a rational fraction and $b$ a positive integer). Even when these operators are not parity-preserving, we demonstrate how a mixed expansion in interleaved Chebyshev rational functions $TB_n(y)$ and $SB_n(y)$ preserves the sparsity of their discretization. This paves the way for fast $O(N\ln N)$ and spectrally accurate mixed implicit-explicit time-marching of sets of linear and nonlinear equations in unbounded geometries. Read More

The dynamics of a three-dimensional axisymmetric bluff-body wake are examined at low Reynolds regimes where transitions take place through spatio-temporal symmetry breaking. A linear stability analysis is employed to identify the critical Reynolds number associated with symmetry breaking, and the associated eigenmodes, known as global modes. The analysis shows that the axisymmetric stable base flow breaks the rotational symmetry through a pitchfork $m=1$ bifurcation, in agreement with previously reported results for axisymmetric wakes. Read More

The exact analytic solution of the Cauchy problem in unbounded space is obtained for the three-dimensional Euler-Helmholtz (EH) equation in the case of a nonzero-divergence velocity field. The solution obtained describes the inertial vortex motion of an ideal compressible medium and coincides with the exact solution to the three-dimensional Riemann-Hopf (RH) equation which simulates turbulence without pressure [Chefranov, 1991]. A necessary and sufficient condition of the onset of a singularity in the evolution of the enstrophy in finite time t=t_0 is obtained for this solution when its continuation is possible in times t>=t_0 in the Sobolev space H^0(R^3) but cannot be made in H^1(R^3). Read More

Variational principles for magnetohydrodynamics (MHD) were introduced by previous authors both in Lagrangian and Eulerian form. In this paper we introduce simpler Eulerian variational principles from which all the relevant equations of non-barotropic MHD can be derived for certain field topologies. The variational principle is given in terms of five independent functions for non-stationary non-barotropic flows. Read More

We investigate the transition to a Landau-Levich-Derjaguin film in forced dewetting using a quadtree adaptive solution to the Navier-Stokes equations with surface tension. A discretization of the capillary forces near the receding contact line is used that yields an equilibrium for a specified contact angle $\theta_\Delta$ called the numerical contact angle. Despite the well-known contact line singularity, dynamic simulations can proceed without any explicit additional numerical procedure, yielding an implicitly dynamic contact angle model. Read More

We show that some statistical properties of forced two-dimensional turbulence have an important sensitivity to the form of large-scale dissipation which is required to damp the inverse cascade. We consider three models of large-scale dissipation: linear "Ekman" drag, non-linear quadratic drag, and scale selective hypo-drag that damps only low-wavenumber modes. In all cases, the statistically steady vorticity field is dominated by almost axisymmetric vortices, and the probability density function of vorticity is non-Gaussian. Read More

Drag laws for particles in fluids are often expressed in terms of the undisturbed fluid velocity, defined as the fluid velocity a particle sees before the disturbance develops in the fluid. In two-way coupled point-particle simulations the information from the undisturbed state is not available and must be approximated using the disturbed velocity field. Horwitz and Mani (2016) recently developed a procedure to estimate the undisturbed velocity for particles moving at low Reynolds number and obeying the Stokes drag law. Read More

The interaction of an elastic sheet with a thin viscous film appears in a wide range of natural phenomena and can be utilized as an actuation mechanism for surface deformations, applicable to microfluidics, optics, and soft robotics. Implementation of such configurations inherently takes place over finite domains and often requires pre-stretching of the sheet. Under the assumptions of strong pre-stretching and small deformations of the lubricated elastic sheet, we derive Green's functions describing the deformation in a finite domain due to external forces acting either directly on the sheet or through the fluid, accounting for both bending and stretching effects. Read More

Two-dimensional turbulent flows, and to some extent, geophysical flows, are systems with a large number of degrees of freedom, which, albeit fluctuating, exhibit some degree of organization: coherent structures emerge spontaneously at large scales. In this short course, we show how the principles of equilibrium statistical mechanics apply to this problem and predict the condensation of energy at large scales and allow for computing the resulting coherent structures. We focus on the structure of the theory using the language of large deviation theory. Read More

We show that an electric field parallel to an electrically neutral surface can generate flow of electrolytic mixtures in small channels. We term this solvo-osmotic flow, since the flow is induced by the asymmetric preferential solvation of ions at the liquid-solid interface. The generated flow is comparable in magnitude to the ubiquitous electro-osmotic flow at charged surfaces, but for a fixed surface charge density, it differs qualitatively in its dependence on ionic strength. Read More

Understanding the mixing capability of mixing devices based on their geometric shape is an important issue both for predicting mixing processes and for designing new mixers. The flow patterns in mixers are directly connected with the modes of the local strain rate, which is generally a combination of elongational flow and planar shear flow. We develop a measure to characterize the modes of the strain rate for general flow occurring in mixers. Read More

While a theoretical limit has long been established for the performance of a single turbine, no corresponding upper bound exists for the power output from a large wind farm, making it difficult to evaluate the available potential for further performance gains. Here we build a model describing the essential features of a large array of turbines with arbitrary design and layout, by considering a fully-developed wind farm whose upper edge is bounded by a self-similar boundary layer. The exchanges between the wind farm, the overlaying boundary layer, and the outer flow are parameterized by means of the classical entrainment hypothesis. Read More

Many species of millimetric fungus-harvesting termites collectively build uninhabited, massive mound structures enclosing a network of broad tunnels which protrude from the ground meters above their subterranean nests. It is widely accepted that the purpose of these mounds is to give the colony a controlled micro-climate in which to raise fungus and brood by managing heat, humidity, and respiratory gas exchange. While different hypotheses such as steady and fluctuating external wind and internal metabolic heating have been proposed for ventilating the mound, the absence of direct in-situ measurement of internal air flows has precluded a definitive mechanism for this critical physiological function. Read More

This study focuses on a parametric study of the laminar fast transient flow of non-Newtonian fluids through helical pipes. Classical simulations of fluid hammer do not deal with the pipeline helicity and non-Newtonian characteristics of the fluid, while the present work addresses those features. To this end, the power-law model is employed to accommodate the non-Newtonian behavior of the fluid. Read More

A new highly efficient method is developed for computation of traveling periodic waves (Stokes waves) on the free surface of deep water. A convergence of numerical approximation is determined by the complex singularites above the free surface for the analytical continuation of the travelling wave into the complex plane. An auxiliary conformal mapping is introduced which moves singularities away from the free surface thus dramatically speeding up numerical convergence by adapting the numerical grid for resolving singularities while being consistent with the fluid dynamics. Read More

Atmospheric water vapour is an essential ingredient of weather and climate. Key features of its distribution can be represented by kinematic models which treat it as a passive scalar advected by a prescribed flow and reacting through condensation. Condensation acts as a sink that maintains specific humidity below a prescribed, space-dependent saturation value. Read More

The drag of turbulent flows can be drastically decreased by addition of small amounts of high molecular weight polymers. While drag reduction initially increases with polymer concentration, it eventually saturates to what is known as the maximum drag reduction (MDR) asymptote; this asymptote is generally attributed to the dynamics being reduced to a marginal yet persistent state of subdued turbulent motion. Contrary to this accepted view we will show in the following that for an appropriate choice of parameters polymers can reduce the drag beyond the suggested asymptotic limit, eliminating turbulence and giving way to laminar flow. Read More

Computational results are presented on comparison of intermittently and continuously pitching two dimensional airfoils. In literature, a viscous mechanism proposed by Lighthill (1971) where skin friction of an undulating body can be around 3 - 5 times greater than a rigidly-held coasting body, has been the well adopted explanation of energetic advantage of the intermittent gait over continuous gait. We find that in an inviscid environment, with only involvement of pressure forces, up to 60% of energy is saved by using intermittent swimming. Read More

We use interface-resolved numerical simulations to study finite-size effects in turbulent channel flow of neutrally-buoyant spheres. Two cases with particle sizes differing by a factor of 2, and same solid volume fraction of 20% and bulk Reynolds number are considered. These are complemented with two reference single-phase flows: the unladen case, and the flow of a Newtonian fluid with the effective suspension viscosity of the same mixture in laminar regime. Read More

The vortices that appear repeatedly and suggest turbulent dynamics are crucial to the understanding of sheared turbulence. These vortices produce order out of chaos, benefiting the turbulence modelling that focuses only on statistically stable quantities. In three dimensions, the hairpin vortices play such a fundamental role in the transport of momentum and energy for wall bounded sheared turbulence. Read More

Droplet evaporation in turbulent sprays involves unsteady, multiscale and multiphase processes which make its comprehension and model capabilities still limited. The present work aims to investigate droplet vaporization dynamics within a turbulent spatial developing jet in dilute, non-reacting conditions. We address the problem using a Direct Numerical Simulation of jet laden with acetone droplets using an hybrid Eulerian/Lagrangian approach based on the point droplet approximation. Read More

A novel derivation of lattice Boltzmann method (LBM) based on Method of Characteristics is presented in this paper. It is shown that LBM is literally a characteristic-line integral of BGK-Boltzmann equation, and the integrals in velocity space and time space, twisted in traditional LBM theory due to relaxation time solving, are independent. Referring to the classical LBM theory, the derivations of LBM evolution equation, macroscopic equation and discrete equilibrium distribution are demonstrated detailly in this paper. Read More

Turbulent flows preferentially concentrate inertial particles depending on their stopping time or Stokes number, which can lead to significant spatial variations in the particle concentration. Cascade models are one way to describe this process in statistical terms. Here, we use a direct numerical simulation (DNS) dataset of homogeneous, isotropic turbulence to determine probability distribution functions (PDFs) for cascade multipliers, which determine the ratio by which a property is partitioned into sub-volumes as an eddy is envisioned to decay into smaller eddies. Read More

Metal mixing plays critical roles in the enrichment of metals in galaxies. The abundance of elements such as Mg, Fe, and Ba in metal-poor stars help us understand the metal mixing in galaxies. However, the efficiency of metal mixing in galaxies is not yet understood. Read More

We study numerically the inertial migration of a single rigid sphere and an oblate spheroid in straight square and rectangular ducts. A highly accurate interface-resolved numerical algorithm is employed to analyse the entire migration dynamics of the oblate particle and compare it with that of the sphere. Similarly to the inertial focusing of spheres, the oblate particle reaches one of the four face-centred equilibrium positions, however they are vertically aligned with the axis of symmetry in the spanwise direction. Read More

A method for inverse design of horizontal axis wind turbines (HAWTs) is presented in this paper. The direct solver for aerodynamic analysis solves the Reynolds Averaged Navier Stokes (RANS) equations, where the effect of the turbine rotor is modeled as momentum sources using the actuator disk model (ADM); this approach is referred to as RANS/ADM. The inverse problem is posed as follows: for a given selection of airfoils, the objective is to find the blade geometry (described as blade twist and chord distributions) which realizes the desired turbine aerodynamic performance at the design point; the desired performance is prescribed as angle of attack ($\alpha$) and axial induction factor ($a$) distributions along the blade. Read More

The paper contains an extension of the Khristianovich-Geertsma-de Klerk (KGD) model to the case when the confining rock pressure, which closes a hydraulic fracture, varies in the direction of its propagation. The extension is impelled by the need to simulate fracture hampering (acceleration) when it penetrates into a layer with increased (decreased) rock pressure. The paper presents the problem formulation, an efficient numerical method for its solving, examples of fractures propagating through layers with various stresses and general conclusions. Read More

Instabilities in rotating detonation are concerned because of their potential influence on the stability of operation. Previous studies on instability of 2-D rotating detonation mainly cared about the one of the contact discontinuity originated from the conjunction of the detonation and oblique shock. Hishida et al. Read More

The generation of droplets at low Reynolds numbers is driven by non-linear dynamics that give rise to complex patterns concerning both the droplet-to-droplet spacing and the individual droplet sizes. Here we demonstrate an experimental system in which a time-varying energy landscape provides a periodic magnetic force that generates an array of droplets from an immiscible mixture of ferrofluid and silicone oil. The resulting droplet patterns are periodic, owing to the nature of the magnetic force, yet the droplet spacing and size can vary greatly by tuning a single bias pressure applied on the ferrofluid phase; for a given cycle period of the magnetic force, droplets can be generated either at integer multiples (1, 2, etc. Read More

In chaotic deterministic systems, seemingly stochastic behavior is generated by relatively simple, though hidden, organizing rules and structures. Prominent among the tools used to characterize this complexity in 1D and 2D systems are techniques which exploit the topology of dynamically invariant structures. However, the path to extending many such topological techniques to three dimensions is filled with roadblocks that prevent their application to a wider variety of physical systems. Read More

We formulate a model for the mass exchange between oil at and below the sea surface. This is a particularly important aspect of modeling oil spills. Surface and subsurface oil have different chemical and transport characteristics and lumping them together would compromise the accuracy of the resulting model. Read More

Linear waves are investigated in a rotating gas under the condition of strong centrifugal acceleration of the order $10^6 g$ realized in gas centrifuges for separation of uranium isotopes. Sound waves splits into three families of the waves under these conditions. Dispersion equations are obtained. Read More

We study the hydrodynamic mechanisms involved in the motion of the contact line formed at the end region of a liquid filament laying on a planar and horizontal substrate. Since the flow develops under partially wetting conditions, the tip of the filament recedes and forms a bulged region (head), that subsequently develops a neck region behind it. Later on, the neck breaks up leading to a separated drop, while the rest of the filament restarts the sequence. Read More

We study theoretically the edge fracture instability in sheared complex fluids, by means of linear stability analysis and direct nonlinear simulations. We derive an exact analytical expression for the onset of edge fracture in terms of the shear-rate derivative of the fluid's second normal stress difference, the shear-rate derivative of the shear stress, the jump in shear stress across the interface between the fluid and the outside medium (usually air), the surface tension of that interface, and the rheometer gap size. We provide a full mechanistic understanding of the edge fracture instability, carefully validated against our simulations. Read More

A rarefied gas is considered in a channel consisting of two infinite parallel plates between which an evenly spaced array of smaller plates is arranged normal to the channel direction. Each of these smaller plates is assumed to possess one ideally specularly reflective and one ideally diffusively reflective side. When the temperature of the small plates differs from the temperature of the sidewalls of the channel, these boundary conditions result in a temperature profile around the edges of each small plate which breaks the reflection symmetry along the channel direction. Read More

The modulation instability (MI) is a universal mechanism that is responsible for the disintegration of weakly nonlinear narrow-banded wave fields and the emergence of localized extreme events in dispersive media. The instability dynamics is naturally triggered, when unstable energy side-bands located around the main energy peak are excited and then follow an exponential growth law. As a consequence of four wave mixing effect, these primary side-bands generate an infinite number of additional side-bands, forming a triangular side-band cascade. Read More

The development of needle-free injection systems utilizing high-speed microjets is of great importance to world healthcare. It is thus crucial to control the microjets, which are often induced by underwater shock waves. In this contribution from fluid-mechanics point of view, we experimentally investigate the effect of a shock wave on the velocity of a free surface (microjet) and underwater cavitation onset in a microchannel, focusing on the pressure impulse and peak pressure of the shock wave. Read More

In this work, we report the phenomenon of formation of particle aggregates in the form of thin slender strings when a polyacrylamide (PAM) solution, laden with polystyrene (PS) particles is introduced into a microfluidic device containing an array of micropillars. PAM and dilute solution of PS beads is introduced into the microfluidic channel through two separate inlets and localized particle aggregation is found to occur under certain conditions. The particle aggregates initially have a string-like morphology that remain tethered at their ends to the micropillar walls, while the rest of the structure remains suspended in the fluid medium. Read More

The settling of cohesive sediment is ubiquitous in aquatic environments. In the settling process, the silt particles show behaviors that are different from non-cohesive particles due to the influence of inter-particle cohesive force. While it is a consensus that cohesive behaviors depend on the characteristics of sediment particles (e. Read More

A weakly-nonlinear potential theory is developed for the description of deep penetrating pressure fields caused by single and colliding wave groups of collinear waves due to the second-order nonlinear interactions. The result is applied to the representative case of groups with the sech-shape of envelope solitons in deep water. When solitary groups experience a head-on collision, the induced due to nonlinearity dynamic pressure may have magnitude comparable with the magnitude of the linear solution. Read More