The interaction between planetary waves and an arbitrary zonal flow is studied from a phase-space viewpoint. Using the Wigner distribution, a planetary wave Vlasov equation is derived that includes the contribution of the mean flow to the zonal potential vorticity gradient. This equation is applied to the problem of planetary wave modulational instability, where it is used to predict a fastest growing mode of finite wavenumber. A wave-mean flow numerical model is used to test the analytical predictions, and an intuitive explanation of modulational instability and jet asymmetry is given via the motion of planetary wavepackets in phase space.
The connection between transport barriers and potential vorticity (PV) barriers in PV-conserving flows is investigated with a focus on zonal jets in planetary atmospheres. A perturbed PV-staircase model is used to illustrate important concepts. This flow consists of a sequence of narrow eastward and broad westward zonal jets with a staircase PV structure; the PV-steps are at the latitudes of the cores of the eastward jets. Numerically simulated solutions to the quasigeostrophic PV conservation equation in a perturbed PV-staircase flow are presented. These simulations reveal that both eastward …
Recent studies found that atmospheric superrotation (i.e., west-to-east winds over the equator) on tidally locked planets can modify the phase of planetary waves. But, a clear relationship between the superrotation and the magnitude of the phase shift was not examined. In this study, we re-investigate this problem using a two-dimensional (2D) linear shallow water model with a specified uniform zonal flow. We find that the degree of the phase shift is a monotonic but nonlinear function of the strength of the mean flow, and the phase shift has two limits of -$π$ and +$π$. The existence of these …
Jets coexist with planetary scale waves in the turbulence of planetary atmospheres. The coherent component of these structures arises from cooperative interaction between the coherent structures and the incoherent small-scale turbulence in which they are embedded. It follows that theoretical understanding of the dynamics of jets and planetary scale waves requires adopting the perspective of statistical state dynamics (SSD) which comprises the dynamics of the interaction between coherent and incoherent components in the turbulent state. In this work the S3T implementation of SSD for barotropic …
The meridional temperature profile of the upper layers of planetary atmospheres is set through a balance between differential radiative heating by a nearby star, or by intrinsic heat fluxes emanating from the deep interior, and the redistribution of that heat across latitudes by turbulent flows. These flows spontaneously arise through baroclinic instability of the meridional temperature gradients maintained by the forcing. When planetary curvature is neglected, this turbulence takes the form of coherent vortices that mix the meridional temperature profiles. However, the curvature of the planet…
Understanding the atmospheric low-frequency variability is of crucial importance in fields such as climate studies, climate change detection, and extended-range weather forecast. The Northern Hemisphere climate features the planetary waves as a relevant ingredient of the atmospheric variability. Several observations and theoretical arguments seem to support the idea that winter planetary waves indicator obey a non-Gaussian statistics and may present a multimodal probability density function, thus characterizing the low-frequency portion of the climate system. We show that the upper tropospheri…
Strong eastward jets at the equator have been observed in many planetary atmospheres and simulated in numerical models of varying complexity. However, the nature of the transition from a conventional state of the general circulation, with easterlies or weak westerlies in the tropics, to such a superrotating state remains unclear. Is it abrupt or continuous? This question may have far-reaching consequences, as it may provide a mechanism for abrupt climate change in a planetary atmosphere, both through the loss of stability of the conventional circulation and through potential noise-induced tran…
This fluid dynamic video entry to the 2011 APS-DFD Gallery of Fluid Motion details the transient evolution of the free surface surrounding the impact region of a low-viscosity laminar liquid jet as it enters a quiescent pool. The close-up images depict the destabilization and breakup of the annular air gap and the subsequent entrainment of bubbles into the bulk liquid.
Solution of a problem on the interaction mechanics of a free liquid jet with a flat plate, body and with other jet has been achieved by means of a graphic-analytical method, developed by author of the given article. This method has allowed physically adequately and visually to describe the flow field near the streamlined surface and to give expressions for quantitative evaluation of the jet pressure profile onto this surface. This method is equally correct for both a flat jet and a jet with a round cross-section. Analysis of the flow field has allowed to detect a jet component, induced by the …
We study rapidly-rotating Boussinesq convection driven by internal heating in a full sphere. We use a numerical model based on the quasi-geostrophic approximation for the velocity field, whereas the temperature field is three-dimensional. This approximation allows us to perform simulations for Ekman numbers down to 1e-8, Prandtl numbers relevant for liquid metals (~0.1) and Reynolds numbers up to 3e4. Persistent zonal flows composed of multiple jets form as a result of the mixing of potential vorticity. For the largest Rayleigh numbers computed, the zonal velocity is larger than the convective…
Experiments on the impact of a densely-packed jet of non-cohesive grains onto a fixed target show that the impact produces an ejecta sheet comprised of particles in collimated motion. The ejecta sheet leaves the target at a well-defined angle whose value agrees quantitatively with the sheet angle produced by water jet impact. Motivated by these experiments, we examine the idealized problem of dense granular jet impact onto a frictionless target in two dimensions. Numerical results for the velocity and pressure fields within the granular jet agree quantitatively with predictions from an exact s…
Over the last two decades, since explosive boiling has been widely used in industry, research on it has been increased. Thermal bubble jet printer, micro injectors and using in micro medicine for injection are some possible applications. The operation of thermal bubble jets consist of three stages: 1- Heat transfer process, 2- Bubble formation and growth in the microchannel, and 3-Drop ejection. The effect of fluid properties on the operation of thermal bubble jet is investigated in this paper. Thus the effect of fluid properties is investigated in each above mentioned processes. Eventually, c…
The breakup of a fluid jet into droplets has long fascinated natural scientists, with early research dating back to the 19th century. Infinitesimal perturbations to a jet grow because of surface tension, which eventually leads to breakup of the jet into droplets (Rayleigh-Plateau instability). Although this classical phenomenon has long been studied, it is not clear how it is modified when the fluid is replaced by an active fluid. In this study, we investigate instabilities of a jet of an active fluid. The active fluid is modelled by a suspension of microswimmers that propel themselves by gene…
We present a lattice Boltzmann model for charged leaky dielectric multiphase fluids in the context of electrified jet simulations, which are of interest for a number of production technologies including electrospinning. The role of non-linear rheology on the dynamics of electrified jets is considered by exploiting the Carreau model for pseudoplastic fluids. We report exploratory simulations of charged droplets at rest and under a constant electric field, and we provide results for charged jet formation under electrospinning conditions.
In the present work we formulated the boundary-value-problem, comprising partial differential equations (PDEs) of steady flow for laminar/turbulent circular jet of a micropolar fluid. A new boundary layer-similarity transformation/solution was derived which is valid not only for the Newtonian fluids but also for the micropolar fluids. Through this transformation PDEs are transformed into the ordinary differential equations (ODEs). These ODEs were solved numerically by the finite-difference method. The obtained results were compared with existing results [9] for the Newtonian fluids. The compar…
Mixing characteristics of a supersonic jet influenced by a Downstream Microjet Fluidic Injection (DMFI) system are numerically investigated. The DMFI system is built on the observation of a previous experimental study that utilized transverse fluidic injection from four equally spaced injection ports placed on an injection tube at a distance downstream of a 1.5 Mach number nozzle. The measurements from these previous experiments demonstrated thickening and mixing enhancement of the jet shear layer as a result of fluidic injection. The current numerical study examines the underlying physics of …
Planetary atmospheres are commonly thought to result from the efficient outgassing of cooling magma oceans. During this stage, vigorous convective motions in the molten interior are believed to rapidly transport the dissolved volatiles to shallow depths where they exsolve and burst at the surface. This assumption of efficient degassing and atmosphere formation has important implications for planetary evolution, but has never been tested against fluid dynamics considerations. Yet, during a convective cycle, only a finite fraction of the magma ocean can reach the shallow depths where volatiles e…
A jet of heavy fluid is injected upwards, at time $t=0$, into a lighter fluid and reaches a maximum height at time $t=t_i$ and then flows back around the upward flow. A similar flow situation occurs for a light fluid injected downward into a heavy one. In this paper an exact analytical expression for $t_i$ is derived. The expression remains valid for laminar and turbulent buoyant jets with or without swirl.
Tidal dissipation in planets and stars is one of the key physical mechanisms driving the evolution of star-planet and planet-moon systems. Several signatures of its action are observed in planetary systems thanks to their orbital architecture and the rotational state of their components. Tidal dissipation inside the fluid layers of celestial bodies are intrinsically linked to the dynamics and the physical properties of the latter. This complex dependence must be characterized. We compute the tidal kinetic energy dissipated by viscous friction and thermal diffusion in a rotating local fluid Car…
We perform three-dimensional simulations of a granular jet impact for both frictional and frictionless grains. Small shear stress observed in the experiment[X. Cheng et al., Phys. Rev. Lett. 99, 188001 (2007) ] is reproduced through our simulation. However, the fluid state after the impact is far from a perfect fluid, and thus, similarity between granular jets and quark gluon plasma is superficial, because the observed viscosity is finite and its value is consistent with the prediction of the kinetic theory.
This paper describes work done in investigating cratering processes by impinging jets. It accompanies a video made for the fluid dynamics video presentations at the Division of Fluid Dynamics meeting, November 22-24, 2009.
In this paper, we carry out a semi-analytic general relativistic study of a Gamma-Ray Bursts (GRB) jet that is breaking out of a cocoon or stellar envelope. We solve hydrodynamic equations with the relativistic equation of state that takes care of fluid composition. In short GRBs, a general relativistic approach is required to account for curved spacetime in strong gravity. The piercing of the jet through the cocoon resembles a de Laval nozzle and the jet may go through recollimation shock transitions. We show that the possibility of shock transition and the shock properties are sensitive to t…
Penetration process and an instability on a liquid jet impinging to a stream of the same fluid in a channel is focused. The jet penetrated into the stream is wrapped by entrained air, and coalesces with the stream when the air sheath around the jet collapses. We introduce instability arisen on the jet and the vigorous effect of the entrained-air sheath on the dynamic behavior of the jet in this fluid dynamics video.
The bounded oscillations of rotating fluid-filled ellipsoids can provide physical insight into the flow dynamics of deformed planetary interiors. The inertial modes, sustained by the Coriolis force, are ubiquitous in rapidly rotating fluids and Vantieghem (2014, Proc. R. Soc. A, 470, 20140093, doi:10.1098/rspa.2014.0093) pioneered a method to compute them n incompressible fluid ellipsoids. Yet, taking density (and pressure) variations into account is required for accurate planetary applications, which has hitherto been largely overlooked in ellipsoidal models. To go beyond the incompressible t…
In industrial applications, developing predictive tools relying on numerical simulations using reduced-order models nourish the need of building a validation strategy. In the context of cryogenic atomization, we propose to build a hierarchy of direct numerical simulation test cases to assess qualitatively and quantitatively diffuse interface models. The present work proposes an initiation of the validation strategy with an air-assisted water atomization using a coaxial injector.
The problem of buckling and coiling of jets of viscous, Newtonian liquids has received a substantial level of attention over the past two decades, both from experimental and theoretical points of view. Nevertheless, many industrial fluids and consumer products are non-Newtonian, and their rheological properties affect their flow behavior. The present work aims at studying the dynamics of cylindrical jets of a viscoelastic, shear-thinning solution of cetylpyridinium salt (CPyCl). In concentrated solutions, CPyCl surfactant molecules have been shown to assemble in long wormlike micellar structur…
Fluid flow and convective heat transfer in rotor-stator configurations, which are of great importance in different engineering applications, are treated in details in this review. The review focuses on convective heat transfer in predominantly outward air flow in the rotor-stator geometries with and without impinging jets and incorporates two main parts, namely, experimental/theoretical methodologies and geometries/results. Experimental methodologies include naphthalene sublimation techniques, steady state (thin layer) and transient (thermochromic liquid crystals) thermal measurements, thermoc…
We study the shear-driven instability, of Kelvin-Helmholtz type, that forms at the interface between a cylindrical jet of flowing fluid and its surroundings. The results of an infinitesimal-amplitude theory based on linearising the system about the undisturbed jet are given. A novel numerical model based on the Galerkin spectral method is developed and employed to simulate the non-linear development of the jet in the weakly-compressible Boussinesq regime. Representative results demonstrating the viability of this model are given, and are shown to agree with the linear analysis for small distur…
The precise mechanism that forms jets and large-scale vortices on the giant planets is unknown. An inverse cascade has been suggested. Alternatively, energy may be directly injected by small-scale convection. Our aim is to clarify whether an inverse cascade feeds zonal jets and large-scale eddies in a system of rapidly rotating, deep, geostrophic spherical-shell convection. We analyze the nonlinear scale-to-scale transfer of kinetic energy in such simulations as a function of the azimuthal wave number, m. We find that the main driving of the jets is associated with upscale transfer directly fr…
Truncated Taylor expansions of smooth flow maps are used in Hamilton's principle to derive a multiscale Lagrangian particle representation of ideal fluid dynamics. Numerical simulations for scattering of solutions at one level of truncation are found to produce solutions at higher levels. These scattering events to higher levels in the Taylor expansion are interpreted as modeling a cascade to smaller scales.
In this study, it was formulated the boundary-value-problem (BVP), comprising partial differential equations (PDEs), of steady flow for plane, laminar jet of a micropolar fluid. A new similarity transformation/solution was derived which is valid not only for the Newtonian fluids but also for the micropolar fluids. Obviously, this transformation will be transformed the PDEs into the ordinary differential equations (ODEs). These ODEs were solved numerically by the finite difference method. The obtained results were compared with existing results [1, 12] for the Newtonian fluids. The comparison w…
This fluid dynamics video is an entry for the Gallery of Fluid Motion of the 66th Annual Meeting of the APS-DFD. In this video, the scalar transfer across the turbulent/non-turbulent (T/NT) interface in a planar jet is investigated by using a direct numerical simulation. Visualization of the scalar flux across the T/NT interface shows that the diffusive species premixed in the ambient flow is transferred into the turbulent region mainly across the leading edge (Here, the leading edge is the T/NT interface across which the turbulent fluid turns into the non-turbulent fluid in the streamwise dir…
This paper is associated with a poster winner of a 2019 American Physical Society Division of Fluid Dynamics (DFD) Milton van Dyke Award for work presented at the DFD Gallery of Fluid Motion. The original poster is available online at the Gallery of Fluid Motion, https://doi.org/10.1103/APS.DFD.2019.GFM.P0015.
An attractive technique for forming and collecting aggregates of magnetic material at a liquid--air interface by an applied magnetic field gradient was recently addressed theoretically and experimentally [Soft Matter, (9) 2013, 8600-8608]: when the magnetic field is weak, the deflection of the liquid--air interface has a steady shape, while for sufficiently strong fields, the interface destabilizes and forms a jet that extracts magnetic material. Motivated by this work, we develop a numerical model for the closely related problem of solving two-phase Navier--Stokes equations coupled with the s…
Planetary and magnetohydrodynamic drift-wave turbulence is observed to self-organize into large scale structures such as zonal jets and coherent vortices. In this Letter we present a non-equilibrium statistical theory, the Stochastic Structural Stability theory (SSST), that can make predictions for the formation and finite amplitude equilibration of non-zonal and zonal structures (lattice and stripe patterns) in homogeneous turbulence. This theory reveals that the emergence of large scale structure is the result of an instability of the interaction between the coherent flow and the associated …
We experimentally studied the effect of flexibility on the flow produced by sinusoidally pitching foil in quiescent fluid. The rigid foil produces a weak, divergent and meandering jet. On the contrary, the foil with a flexible flap produces an orderly, narrow, coherent jet. It has been observed that such orderly jet is produced when the flap has appropriate flexibility. The jet produced in quiescent fluid by the flexible foil is accompanied by a corresponding thrust. In that sense, this is simple and different type of hovering.
This fluid dynamics video is an entry for the Gallery of Fluid Motion for the 66th Annual Meeting of the Fluid Dynamics Division of the American Physical Society. We show the curious behaviour of a light ball interacting with a liquid jet. For certain conditions, a ball can be suspended into a slightly inclined liquid jet. We studied this phenomenon using a high speed camera. The visualizations show that the object can be `juggled' for a variety of flow conditions. A simple calculation showed that the ball remains at a stable position due to a Bernoulli-like effect. The phenomenon is very stab…
We propose a family of two-phase-fluid models for a full-cone turbulent round jet that describe its dynamics in a simple but comprehensive manner with the apex angle of the cone being the main disposable parameter. The basic assumptions are that (i) the jet is statistically stationary and that (ii) it can be approximated by a mixture of two fluids with their phases in dynamic equilibrium (so-called Locally Homogeneous Flow). To derive the model, we impose either full or partial conservation of the initial mass and total power fluxes, introducing mass and power loss factors as disposable parame…
We propose a two-phase-fluid model for a full-cone turbulent round jet that describes its dynamics in a simple but comprehensive manner with only the apex angle of the cone being a disposable parameter. The basic assumptions are that (i) the jet is statistically stationary and that (ii) it can be approximated by a mixture of two fluids with their phases in dynamic equilibrium. To derive the model, we impose conservation of the initial volume and total momentum fluxes. Our model equations admit analytical solutions for the composite density and velocity of the two-phase fluid, both as functions…
In this fluid dynamics video, results from high fidelity numerical simulations are presented, which have been carried out to study the flow and droplet dynamics of liquid sheets formed by two impinging jets. A three-dimensional Volume-of-Fluid (VOF) method with adaptive mesh refinement (AMR) based on octree meshes [1] is used to simulate the various flow patterns associated with impinging jets, secondary breakup and binary collision of droplets. In addition to AMR, a thickness based refinement algorithm is also developed and implemented to efficiently resolve the various scales of surface tens…
In this fluid dynamics video prepared for the APS-DFD Gallery of Fluid Motion we study the Kelvin-Helmholtz instability for both Newtonian and viscoelastic jets. The nonlinear dynamics of the jet motion are slowed down by orders of magnitude using a synchronized strobe effect coupled with precise timing control of perturbation frequencies. Our results show that at high wave-numbers the imposed perturbations initially grow linearly with time and the jet axis remains straight while the Kelvin-Helmholtz wave amplitude grows and rolls up into bags that encapsulate the central jet within themselves…
We investigate ambient fluid entrainment and near-field flow characteristics of a free surface plunging jet for five Reynolds numbers ranging from 3000 to 10000 using time-resolved stereo particle image velocimetry (SPIV). We present time-averaged velocities, RMS velocity fluctuations, mean entrainment and unsteady flow features and compare them with previous studies on free jets. We find that plunging jets have a smaller potential core length, and earlier decay of the mean centerline velocity. The peak RMS velocity fluctuations occur at a location significantly upstream compared to the free j…
In this paper, we present an interesting method to microfabricate a tilted micro air jet generator. We used the well-know deep reactive ion etching (DRIE) technique in order to realize in a silicon substrate a double side etching. For aircraft and cars, micro air jets will take an important place for fluid control. Micro air jets are characterized by their speed, frequency and tilt. Usually, this micro air jets are produced by fluidic microsystems. We presented experimental results about micro tilted air jets. A comparison between finite element method simulation, theory and experimental resul…
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 regim…
We study experimentally and theoretically mixing at the external boundary of a submerged turbulent jet. In the experimental study we use Particle Image Velocimetry and an Image Processing Technique based on the analysis of the intensity of the Mie scattering to determine the spatial distribution of tracer particles. An air jet is seeded with the incense smoke particles which are characterized by large Schmidt number and small Stokes number. We determine the spatial distributions of the jet fluid characterized by a high concentration of the particles and of the ambient fluid characterized by a …
