We investigate exact nonlinear waves on surfaces locally approximating the rotating sphere for two-dimensional inviscid incompressible flow. Our first system corresponds to a beta-plane approximation at the equator and the second to a gamma approximation, with the latter describing flow near the poles. We find exact wave solutions in the Lagrangian reference frame that cannot be written down in closed form in the Eulerian reference frame. The wave particle trajectories, contours of potential vorticity and Lagrangian mean velocity take relatively simple forms. The waves possess a non-trivial Lagrangian mean flow that depends on the amplitude of the waves and on a particle label that characterizes values of constant potential vorticity. The mean flow arises due to potential vorticity conservation on fluid particles. Solutions over the entire space are generated by assuming that the flow far from the origin is zonal and there is a region of constant potential vorticity between this zonal flow and the waves. In the gamma approximation a class of waves are found which, based on analogous solutions on the plane, we call Ptolemaic vortex waves. The mean flow of some of these waves resemble polar jet streams. Several illustrative solutions are used as initial conditions in the fully spherical rotating Navier-Stokes equations, where integration is performed via the numerical scheme presented in Salmon and Pizzo (2023). The potential vorticity contours found from these numerical experiments vary between stable permanent progressive form and fully turbulent flows generated by wave breaking.
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.
We investigate the collision of a continuous liquid jet with a regular stream of immiscible droplets. The immiscible liquids, namely silicon oil for the continuous jet and an aqueous glycerol solution for the drop stream, are selected to enable the total wetting of the drops by the jet liquid. Four different regimes are experimentally identified: drops in jet, encapsulation without satellites, encapsulation with satellites from the jet liquid and mixed fragmentation. The drops in jet regime, potentially of great interest for new applications, corresponds to a regular stream of drops embedded i…
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…
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 …
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 …
Vortex-sheet models of jets are widely used to describe the dynamics of modes, such as the Kelvin-Helmholtz instability and guided acoustic waves. However, it is seldom pointed out in the literature the absence of the free-stream acoustic modes in the vortex-sheet spectrum. This indicates that free-stream sound waves are not eigensolutions of the parallel jet. This family of modes is important if, for example, one is interested in problems of sound emission or flow-acoustic interactions. In this work we show how a distantly-confined jet may be used as a surrogate problem for the free jet, in w…
To investigate the influence of the orifice geometry on near-field coherent structures in a jet, Fourier-POD is applied. Velocity and vorticity snapshots obtained from tomographic particle image velocimetry at the downstream distance of two equivalent orifice diameters are analysed. Jets issuing from a circular orifice and from a fractal orifice are examined, where the fractal geometry is obtained from a repeating fractal pattern applied to a base square shape. While in the round jet energy is mostly contained at wavenumber m=0, associated to the characteristic Kelvin-Helmholtz vortex rings, i…
The lift-off characteristics of supersonic streamwise vortex in oblique shock-wave/jet interaction (OS/JI for short), extracted from a wall-mount ramp injector in scramjet, is studied through Large-eddy simulation method. Shocked helium jet is deformed into a pair of streamwise vortex with a co-rotating companion vortex showing the lift-off characteristic immediately after shock. Based on the objective coordinate system in frame of oblique shock structure, it is found that the nature of three-dimensional lift-off structure of a shockinduced streamwise vortex is inherently and precisely control…
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…
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 …
In this paper we reveal the physics underlying the conditions needed for the generation of emulsions composed of uniformly sized drops of micrometric or submicrometric diameters when two immiscible streams flow in parallel under the so-called tip streaming regime after Suryo & Basaran (2006). Indeed, when inertial effects in both liquid streams are negligible, the inner to outer flow-rate and viscosity ratios are small enough and the capillary number is above an experimentally determined threshold which is predicted by our theoretical results with small relative errors, a steady micron-sized j…
We study the self-similarity and dissipation scalings of a turbulent planar jet and the theoretically implied mean flow scalings. Unlike turbulent wakes where such studies have already been carried out (Dairay et al. 2015; Obligado et al. 2016), this is a boundary- free turbulent shear flow where the local Reynolds number increases with distance from inlet. The Townsend-George theory revised by Dairay et al. (2015) is applied to turbulent planar jets. Only a few profiles need to be self-similar in this theory. The self- similarity of mean flow, turbulence dissipation, turbulent kinetic energy …
In this paper, Jupiter's Great Red Spot (GRS) is used to determine properties of the Jovian atmosphere that cannot otherwise be found. These properties include the potential vorticity of the GRS and its neighboring jet streams, the shear imposed on the GRS by the jet streams, and the vertical entropy gradient (i.e., Rossby deformation radius). The cloud cover of the GRS, which is often used to define the GRS's area and aspect ratio, is found to differ significantly from the region of the GRS's potential vorticity anomaly. The westward-going jet stream to the north of the GRS and the eastward-g…
The planar laminar flow resulting from the impingement of two gaseous jets of different density issuing into an open space from aligned steadily fed slot nozzles of semi-width $R$ separated a distance $2H$ is investigated by numerical and analytical methods, with specific consideration given to the high-Reynolds and low-Mach number conditions typically present in counterflow-flame experiments, for which the flow is nearly inviscid and incompressible. It is shown that introduction of a density-weighted vorticity-stream function formulation effectively reduces the problem to one involving two je…
We develop a methodology to identify finite-time Lagrangian structures from data and models using an extension of the Koopman operator-theoretic methods developed for velocity fields with simple (periodic, quasi-periodic) time-dependence. To achieve this, the notion of the Finite Time Ergodic (FiTER) partition is developed and rigorously justified. In combination with a clustering-based approach, the methodology enables identification of the temporal evolution of Lagrangian structures in a classic, benchmark, oceanographic transport problem, namely the cross-stream flux induced by the interact…
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…
In this paper, the size of bubbles formed through the breakup of a gaseous jet in a co-axial microfluidic device is derived. The gaseous jet surrounded by a co-flowing liquid stream breaks up into monodisperse microbubbles and the size of the bubbles is determined by the radius of the inner gas jet and the bubble formation frequency. We obtain the radius of the gas jet by solving the Navier-Stokes equations for low Reynolds number flows and by minimization of the dissipation energy. The prediction of the bubble size is based on the system's control parameters only, i.e. the inner gas flow rate…
The current work presents a tensor formulation of the Lumley Decomposition (LD), introduced in its original form by Lumley (1967b), allowing decompositions of turbulent flow fields in curvilinear coordinates. The LD in his form is shown to enable semi-analytical decompositions of self-similar turbulent flows in general coordinate systems. The decomposition is applied to the far-field region of the fully developed turbulent axi-symmetric jet, which is expressed in stretched spherical coordinates in order to exploit the self-similar nature of the flow while ensuring the self-adjointness of the L…
The overcoming of a mechanics problem on origin of secondary jet flows, on dynamics of its development and interaction with the main stream of the viscous fluid is reached by means of elucidation of the energy distribution in the stream at its interaction with the flow system walls and a body surface. In contrast to a traditional conception on a total head of a fluid stream in a pipe as a sum of a velocity head and a static pressure, it is ascertained that this sum is only longitudinal component of the stream total head vector. It is stated a new conception and it is produced the expressions f…
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…
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…
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…
As shown by Ganan-Calvo and co-workers, a free liquid jet can be compressed in iameter through gas-dynamic forces exerted by a co-flowing gas, obviating the need for a solid nozzle to form a microscopic liquid jet and thereby alleviating the clogging problems that plague conventional droplet sources of small diameter. We describe in this paper a novel form of droplet beam source based on this principle. The source is miniature, robust, dependable, easily fabricated, and eminently suitable for delivery of microscopic liquid droplets, including hydrated biological samples, into vacuum for analys…
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 …
