Transverse Velocity Fluctuations Research Articles

Characterization of Turbulent Fluctuations in the Sub-Alfvénic Solar Wind

Parker Solar Probe (PSP) observed sub-Alfvénic solar wind intervals during encounters 8–14, and low-frequency magnetohydrodynamic (MHD) turbulence in these regions may differ from that in super-Alfvénic wind. We apply a new mode decomposition analysis to the sub-Alfvénic flow observed by PSP on 2021 April 28, identifying and characterizing entropy, magnetic islands, forward and backward Alfvén waves, including weakly/nonpropagating Alfvén vortices, forward and backward fast and slow magnetosonic (MS) modes. Density fluctuations are primarily and almost equally entropy- and backward-propagating slow MS modes. The mode decomposition provides phase information (frequency and wavenumber k) for each mode. Entropy density fluctuations have a wavenumber anisotropy of k ∥ ≫ k ⊥, whereas slow-mode density fluctuations have k ⊥ > k ∥. Magnetic field fluctuations are primarily magnetic island modes (δ B i ) with an O(1) smaller contribution from unidirectionally propagating Alfvén waves (δ B A+) giving a variance anisotropy of 〈δBi2〉/〈δBA2〉=4.1 . Incompressible magnetic fluctuations dominate compressible contributions from fast and slow MS modes. The magnetic island spectrum is Kolmogorov-like k⊥−1.6 in perpendicular wavenumber, and the unidirectional Alfvén wave spectra are k∥−1.6 and k⊥−1.5 . Fast MS modes propagate at essentially the Alfvén speed with anticorrelated transverse velocity and magnetic field fluctuations and are almost exclusively magnetic due to β p ≪ 1. Transverse velocity fluctuations are the dominant velocity component in fast MS modes, and longitudinal fluctuations dominate in slow modes. Mode decomposition is an effective tool in identifying the basic building blocks of MHD turbulence and provides detailed phase information about each of the modes.

Comparative predictions of turbulent non-isothermal flow of a viscoplastic fluid with yield stress

RANS simulation of turbulent non-isothermal flow in a pipe by transition of Newtonian fluid into a viscoplastic non-Newtonian fluid is carried out. Carrier phase turbulence was modeled using two-equation isotropic k‒ε˜ – model and Reynolds stress transport model. Results of calculations of Newtonian and non-Newtonian power-law fluids were compared with data of DNS calculations of other authors. Comparisons with data from other works for isothermal Schwedoff-Bingham fluid were performed in this work using k‒ε˜ – model. Satisfactory agreement was obtained with data from other studies for the axial averaged velocity and turbulent kinetic energy radial profiles (the difference is up to 15 %). Reynolds stress transport model showed significant anisotropy between streamwise and transverse velocity fluctuations (up to several times) and good agreement with DNS results of other authors. Averaged and pulsation profiles express the indicated transformation of the non-isothermal turbulent flow.

Impact of compliant coating on Mack-mode evolution in hypersonic boundary layers

This paper focuses on the linear evolution of Mack instability modes in a hypersonic boundary layer over a flat plate that is partially coated by a compliant section. The compliant section is a thin, flexible membrane covering on a porous wall consisting of micro holes. The instability pressure could induce a vibration of the membrane, leading to a feedback to the boundary-layer fluids through the transverse velocity fluctuation. Such a process is formulated by an admittance boundary condition for the boundary-layer perturbation, which is dependent on the thickness and tension of the membrane, the properties of the porous wall, and the frequency of the Mack-mode perturbation. Using this admittance condition, the impact of the compliant coating on the Mack growth rate is studied systematically by solving the compressible Orr–Sommerfeld equations. It is found that the compliant coating could suppress the Mack instability with a frequency band in the neighbourhood of the most unstable frequency, and the stabilising frequency band widens as the membrane thickness and tension decrease, indicating a more favourable effect of a softer membrane. For a Mack mode with a specified dimensional frequency – since its dimensionless frequency, normalised by the local boundary-layer thickness and oncoming velocity, increases as it propagates downstream – the second-mode frequency band usually appears in downstream locations, and so does the stabilising effect of the membrane. Thus it is favourable to apply a compliant panel at a downstream region. In this situation, the solid–compliant junction could produce an additional scattering effect on the evolution of the Mack mode due to the sudden change of its boundary condition. The scattering effect is quantified by a transmission coefficient defined by the equivalent amplitude of the compliant-wall perturbation to the solid-wall perturbation, which can be obtained by the harmonic linearised Navier–Stokes (HLNS) approach. If the admittance is weak, then the transmission coefficient can also be predicted by an analytical solution based on the residue theorem. It is found that most of the second modes are suppressed by the scattering effect as long as the argument of the admittance is in the interval $[150^\circ, 210^\circ ]$ , agreeing with most of the physical situation. The analytical predictions agree well with the HLNS calculations when the modulus of the admittance is less than $O(0.1)$ .

Wall friction and heat transfer in turbulent pulsating flow in a square duct

For the first time, a DNS study of pulsating turbulent flows and heat transfer in a square duct is performed. Calculations were carried out at Re=2200 in the current-dominance mode for eight values of the oscillation period and three values of the Prandtl number. It was found that the time-mean friction coefficient in the studied pulsating flows has a lower value than in the stationary flow. The difference reaches −14.7%. The values of the Nusselt numbers are also decreasing, albeit by a smaller amount. The features of secondary flows of Prandtl’s 2nd kind at different phases of the flow oscillations are studied. The profiles of the wall friction stress and heat transfer coefficients and their evolution over time are determined. The time-oscillations of the wall friction are entirely determined by the oscillations of the main flow, being ahead of it in phase by π/4, which coincides with the behavior of laminar pulsating flows at high frequencies. The oscillations in heat transfer on the wall are determined by oscillations in the intensity of turbulent heat exchange, and the change in the latter occurs almost in phase with a change in the volume-average intensity of the transverse velocity fluctuations.

Altering the wake dynamics of a circular cylinder with harmonic forcing

The time-averaged velocity profile in the wake of a circular cylinder resembles a “U” type or a “V” type profile due to a velocity defect. Bhattacharya and J. W. Gregory [“The effect of spatially and temporally modulated plasma actuation on cylinder wake,” AIAA J. 58, 3808–3818 (2020)] showed experimentally that the wake dynamics could be altered with harmonic forcing in such a way that instead of a velocity defect, a “jet-like” profile emerged with a characteristic “W” profile. The harmonic forcing was created by modulating the waveform of a dielectric barrier discharge plasma actuators' supply signal with a frequency twice that of the shedding frequency. However, the reason for the appearance of the “W” profile was not clear in S. Bhattacharya and J. W. Gregory [“The effect of spatially and temporally modulated plasma actuation on cylinder wake,” AIAA J. 58, 3808–3818 (2020).] In this paper, we use numerical simulation to recreate the test conditions implemented by Bhattacharya and J. W. Gregory [“The effect of spatially and temporally modulated plasma actuation on cylinder wake,” AIAA J. 58, 3808–3818 (2020).] We apply large-eddy simulation to study the impact of the pulsed, harmonic forcing on the wake of a circular cylinder at a subcritical Reynolds number of 4700. The plasma actuators are modeled with a body-force approach. The frequency of the driving signal of the plasma actuator is modulated at twice the shedding frequency. The amplitude of the signal is set at 6 kV peak to peak to create a blowing ratio of 0.8. The goal is to understand how the wake changes in three dimensions and the impact on separation on the cylinder surface due to the harmonic forcing. Results show that pulsed forcing causes vortices from one side of the wake to cross the centerline. This crossing creates an effective jet-like velocity along the centerline, resulting in a W velocity profile. Such a W profile is observed at least up to a streamwise distance of five cylinder diameters. Additionally, the pulsed actuation significantly increases the magnitude of primary and secondary frequencies throughout the wake. Forcing caused a 50% increase in the transverse velocity fluctuations at the centerline of the wake at the streamwise location of x/d=5. There was a similar increase in 33% at the centerline in the streamwise velocity fluctuations at the same location.

Experimental Study on Wake Characteristics of Secondary Grooved Cylinders with Different Depths

In this study, the flow field of a new secondary-grooved cylinder is determined by using particle image velocimetry (PIV) to understand the wake characteristics at different depths of the secondary grooved cylinders. In order to analyze the wake characteristic behind the secondary grooved cylinder with different depths, time-averaged streamlines, time-averaged velocity, RMS velocity, Reynolds stress, turbulent kinetic energy, and instantaneous flow structures are employed. The recirculation zone for secondary grooved cylinders with different depths decreases when compared to the smooth cylinder; the peak magnitudes of flow velocity fluctuation intensity and transverse velocity fluctuation intensity for secondary grooved cylinders with different depths are reduced and the locations appear delayed. Furthermore, in contrast to the smooth cylinder, the secondary grooved cylinders with different depths' Reynolds stress and turbulent kinetic energy are increased by the wake flow, and the transient large-scale vortex is split into several smaller-scale vortices behind the secondary grooved cylinders. The results obtained for the above flow structure are more significant when h/D = 0.05 for the secondary grooved cylinder.

Investigations of thickness effects on the acoustic characteristics of symmetric and asymmetric airfoils

The present paper provides a detailed acoustic characterization of symmetric and asymmetric NACA airfoils for various thickness ratios to determine the best thickness ratio and geometry which provide lower acoustic radiations with respect to the standard NACA0010 airfoil. The studies are conducted for various t/c values of 0.12, 0.15 and 0.21, where t is the airfoil thickness and c is the airfoil chord. The far-field acoustic emissions are observed to decrease with increase in t/c ratios for both the symmetric and asymmetric airfoils. For all the t/c values and jet velocities studied, the asymmetric airfoils show higher noise reductions from mid to high frequencies as compared to the symmetric ones, which might be due to the reduced transverse velocity fluctuations as a result of the large distortions imparted to oncoming turbulent gust by the formation of the larger stagnation pressure zone. The symmetric airfoils show a maximum reduction up to 3 dB from mid to high frequencies while asymmetric ones show a reduction up to about 5 dB. An empirical expression is developed for the ΔOAPWL as a function of t/c only for both the symmetric and asymmetric airfoils, where ΔOAPWL is the overall sound power reduction level in dB. It reveals that the ΔOAPWL follow a second order polynomial for both the symmetric and asymmetric airfoils at all jet velocities studied. It is observed that thicker (i.e., t/c = 0.21) symmetric and asymmetric airfoils show lower acoustic radiations as compared to the thinner ones for all the emission angles. In general, it is observed that the thinner airfoils show higher directivity as compared thicker ones, albeit they show a common trait of downstream directivity. Further the highest directivity is seen at an emission angle of 67.5° for both the symmetric and asymmetric airfoils. Thus, the present study clearly demonstrates that the airfoils with higher t/c ratios could be considered as the best passive means for achieving substantial reductions of airfoil broadband noise over a wide range of frequencies.

Laminar and turbulent flow development study in a rectangular duct with 180° sharp bend by using stereo particle image velocimetry and liquid crystal thermography measurements

This work presents a detailed insight into the flow progression and surface heat transfer distribution across the sharp 180° bend of a two-pass rectangular duct for laminar (Re = 800) and turbulent (Re = 6500) in-flow conditions. Stereoscopic particle image velocimetry (stereo PIV) as well as two-dimensional and two-component PIV measurements and liquid crystal thermography techniques are appropriately used for flow and heat transfer characterization across the complete sharp 180° bend. The centrifugal instabilities arise due to the sharp bend, which induces the secondary flows in the form of counter-rotating vortex pairs commonly known as Dean vortices. These secondary vortices play a significant role in the localized laminar–turbulent transition and turbulence augmentations for laminar and turbulent inflow conditions. Subsequently, quantitative analysis shows that complete 180° turning of flow resulted in intense augmentation of spatially averaged turbulence quantities. Root mean square (RMS) fluctuations in the transverse direction V¯T|rms increase by 298% and 186% for respective flow conditions. Augmentation of ∼ 287% (laminar) and 260% (turbulent) in the wall-normal RMS fluctuations (V¯N|rms) are observed. These augments in transverse and wall-normal velocity fluctuations result in a very sharp amplification of spatially averaged turbulent kinetic energy (k¯), that is, 1825% for inlet laminar and 928% for inlet turbulent flow regimes.

On the wake of an isolated rotating wheel: An experimental and numerical investigation

The wake of an isolated, rotating wheel of a geometry typical of those used in open-wheel motorsport, is investigated. The CFD is validated by comparing the wake data gathered from this method with the data from the PIV wind tunnel experiments, where analysis of the data showed a good agreement between the two methods. A comparison of the mean and instantaneous flow-fields obtained from the CFD shows significant differences in the wake topology. The time-averaged illustration of the flow shows an inverted “T” shape, and consists of a pair of upper and lower counter-rotating vortices that merge downstream, with the upper being dominant. The instantaneous wake follows the same fundamental shape, but consists of incoherent macro-scale eddies, together with these counter-rotating vortices in a deformed state. Analysis of the unsteadiness of the wake via proper orthogonal decomposition reveals significant transverse and vertical velocity fluctuations. The transverse velocity fluctuations are driven by both the contraction and expansion of the contact patch wake and the instability of the merged counter-rotating vortex pair that eventually lead to a transverse flapping motion of the bulk wake. The instability of these vortices also leads to vertical velocity fluctuations in the vortex-induced downwash region.

Turbulent flows along a streamwise external corner

A numerical investigation of turbulent flows in straight pipes with a cross-section in the form of a circular sector at different values of the apex angle${\alpha }$is carried out. Main attention is paid to the cases${\alpha }>{\rm \pi}$when the cross-section boundary contains a convex external corner. An analytical solution to the problem of laminar flow in the geometry under consideration is given. The law of resistance is determined, and velocity distributions over the pipe cross-section are obtained. The singularity of wall shear stress$\tau _w\sim r^{{\rm \pi} /{\alpha }-1}$at${\alpha }>{\rm \pi}$is shown which persists in turbulent flows as well. Turbulent flows are simulated at$Re=2000$and four apex-angle values${\alpha }=5{\rm \pi} /4$,$3{\rm \pi} /2$,$7{\rm \pi} /4$and$2{\rm \pi}$, as well as at a larger$Re=4000$and${\alpha }=3{\rm \pi} /2$. The characteristic features of the mean-velocity distributions are outlined, and their relationship with secondary flows is shown. The velocity of the secondary flow in the vicinity of the external corner reaches the value$6.3\,\%$of the bulk flow velocity at the maximum${\alpha }=2{\rm \pi}$. A characteristic feature of the considered flows is the presence of intense transverse velocity fluctuations in the region above the apex corner. It is hypothesized that the cause of these fluctuations may be the linear instability of the mean flow field. The studies of linear stability confirm this hypothesis. Considerable attention is paid to the study of secondary flows in the vicinity of the external corner. In general, the formation of these flows fits into the scheme proposed earlier (Nikitin,J. Fluid Mech., vol. 917, 2021, A24; Nikitinet al.,Fluid Dyn., vol. 56, issue 4, 2021, pp. 513–538), according to which the main mechanism is the centrifugal force arising from the fluctuating flow over the corner in the transverse plane. It is shown that the shape of secondary flows is reproduced to a certain extent by the vortical part of the Reynolds-stress force field. The latter may be found from the Helmholtz decomposition. The features of the mean pressure distribution associated with the secondary flow and with the presence of a region of concentrated fluctuations above the external corner are explained.

Flow past a rotationally oscillating cylinder with an attached flexible filament

Experimental studies are conducted on a rotationally oscillating cylinder with an attached flexible filament at a Reynolds number of 150. Parametric studies are carried out to investigate the effect of cylinder forcing parameters and filament stiffness on the resultant wake structure. The diagnostics are flow visualization using the laser-induced fluorescence technique, frequency measurement using a hot film, and characterization of the velocity and vorticity field using planar particle image velocimetry. The streamwise force and power are estimated through control volume analysis, using a modified formulation, which considers the streamwise and transverse velocity fluctuations in the wake. These terms become important in a flow field where asymmetric wakes are observed. An attached filament significantly modifies the flow past a rotationally oscillating cylinder from a Bénard–Kármán vortex street to a reverse Bénard–Kármán vortex street, albeit over a certain range of Strouhal number, $St_{A} \sim 0.25\text {--}0.5$ , encountered in nature in flapping flight/fish locomotion and in the flow past pitching airfoils. The transition from a Kármán vortex street to a reverse Kármán vortex street precedes the drag-to-thrust transition. The mechanism of unsteady thrust generation is discussed. Maximum thrust is generated at the instants when vortices are shed in the wake from the filament tip. At $St_{A} > 0.4$ , a deflected wake associated with the shedding of an asymmetric vortex street is observed. Filament flexibility delays the formation of an asymmetric wake. Wake symmetry is governed by the time instant at which a vortex pair is shed in the wake from the filament tip.

Hydrodynamics of simple active liquids: the emergence of velocity correlations

We derive the hydrodynamics for a system of N active, spherical, underdamped particles, interacting through conservative forces. At the microscopic level, we represent the evolution of the particles in terms of the Kramers equation for the probability density distribution of their positions, velocities, and orientations, while at a mesoscopic level we switch to a coarse-grained description introducing an appropriate set of hydrodynamic fields given by the lower-order moments of the distribution. In addition to the usual density and polarization fields, the hydrodynamics developed in this paper takes into account the velocity and kinetic temperature fields, which are crucial to understanding new aspects of the behavior of active liquids. By imposing a suitable closure of the hydrodynamic moment equations and truncation of the Born–Bogolubov–Green–Kirkwood–Yvon hierarchy, we obtain a closed set of mesoscopic balance equations. At this stage, we focus our interest on the small deviations of the hydrodynamic fields from their averages and apply the methods of the theory of linear hydrodynamic fluctuations. Our treatment sheds light on the peculiar properties of isotropic active liquids and their emergent dynamical collective phenomena, such as the spontaneous alignment of the particle velocities. We predict the existence within the liquid phase of spatial equal-time Ornstein–Zernike-like velocity correlations both for the longitudinal and the transverse modes. At variance with active solids, in active liquids, the correlation length of the transverse velocity fluctuations is sensibly shorter than the length of the longitudinal fluctuations. In particular, the latter depends on the sound speed and increases with the persistence time, while the former displays a weaker dependence on these parameters. Finally, within the same framework, we derive the dynamical structure factors and the intermediate scattering functions and discuss how the velocity ordering persists in time. We find that the velocity decorrelates on a time-scale much longer than the one characteristic of passive fluids.

Flame response to transverse velocity excitation leading to frequency doubling and modal coupling

Transverse thermoacoustic modes may occur in gas turbines, aero-engines, and rocket engines. Various scenarios of flame excitation can be observed, depending on the type of transverse mode and the location of the flame relative to the mode shape. If an acoustically compact, symmetric flame is exposed to transverse velocity fluctuations of uniform strength and direction, the resulting modulation of the overall heat release rate is invariant to the direction of the velocity perturbation. It follows that the dominant flame response occurs at twice the forcing frequency, even for an infinitesimally small oscillation amplitude. The present study proposes a modeling framework for this inherently non-linear phenomenon, which relies on a second-order kernel of the Volterra series. As a possible realization of the Volterra series, an ad-hoc model is proposed and validated with CFD for mono-frequency forcing. Furthermore, a mechanism of modal interaction is established by which frequency doubling in the flame response causes an unstable transverse mode to drive a higher order stable mode, such that at near-resonance conditions the higher order mode exhibits elevated amplitude. This mechanism can explain the observations made by Urbano et al. (2016) in a small-scale rocket thrust chamber, where a radial mode appears at exactly twice the frequency of the dominant transverse mode. A simple representative setup of a cylindrical combustion chamber is used to explain this mechanism analytically.

Flow Turbulence Characteristics and Mass Transport in the Near-Wake Region of an Aquaculture Cage Net Panel

Cage-based aquaculture has been growing rapidly in recent years. In some locations, cage-based aquaculture has resulted in the clustering of large quantities of cages in fish farms located in inland lakes or reservoirs and coastal embayments or fjords, significantly affecting flow and mass transport in the surrounding waters. Existing studies have focused primarily on the macro-scale flow blockage effects of fish cages, and the complex wake flow and associated near-field mass transport in the presence of the cages remain largely unclear. As a first step toward resolving this knowledge gap, this study employed the combined Particle Image Velocimetry and Planar Laser Induced Fluorescence (PIV-PLIF) flow imaging technique to measure turbulence characteristics and associated mass transport in the near wake of a steady current through an aquaculture cage net panel in parametric flume experiments. In the near-wake region, defined as ~3M (mesh size) downstream of the net, the flow turbulence was observed to be highly inhomogeneous and anisotropic in nature. Further downstream, the turbulent intensity followed a power-law decay after the turbulence production region, albeit with a decay exponent much smaller than reported values for analogous grid-generated turbulence. Overall, the presence of the net panel slightly enhanced the lateral spreading of the scalar plume, but the lateral distribution of the scalar concentration, concentration fluctuation and transverse turbulent scalar flux exhibited self-similarity from the near-wake region where the flow was still strongly inhomogeneous. The apparent turbulent diffusivity estimated from the gross plume parameters was found to be in reasonable agreement with the Taylor diffusivity calculated as the product of the transverse velocity fluctuation and integral length scale, even when the plume development was still transitioning from a turbulent-convective to turbulent-diffusive regime. The findings of this study provide references to the near-field scalar transport of fish cages, which has important implications in the assessment of the environmental impacts and environmental carrying capacity of cage-based aquaculture.

Compressibility Effects on Large Structures and Entrainment Length Scales in Mixing Layers

In this work, three-component planar velocity measurements are analyzed to identify the effects of compressibility on mixing layer turbulence, with a focus on the evolution of large-scale structures, dominant spatial eigenmodes, and entrainment length scales. Velocity measurements obtained via stereoscopic particle image velocimetry for five different dual-stream air planar mixing layers with convective Mach numbers of , 0.38, 0.55, 0.69, and 0.88 are analyzed. Results of two-point correlations reveal that length scales of the streamwise velocity fluctuations increase in both the streamwise and transverse directions, whereas the length scales of the transverse velocity fluctuations decrease in the transverse direction. To further investigate these trends, the spatial organization, shape, and dynamics of large-scale turbulent structures are examined via two-dimensional spatial velocity correlations, proper orthogonal decomposition, and linear stochastic estimation. These quantitative techniques support qualitative findings in the literature that report coherent, round roller structures in incompressible mixing layers becoming flattened and elongated longitudinally with increased compressibility. This evolution is likely due to a dominant pulsing motion present for the higher cases and can be linked to compressibility effects on the entrainment mechanisms. Length scales of entrainment are determined using autocorrelations of normal flow velocity components along instantaneously identified turbulent/non-turbulent interfaces and are found to decrease with increasing . This result can heuristically be interpreted as small-scale nibbling being dominant for higher , whereas larger-scale engulfment contributes more in nearly incompressible mixing layers.

Numerical investigation of the accuracy of particle image velocimetry technique in gas-phase detonations

We numerically investigate the accuracy of the Particle Image Velocimetry (PIV) technique for the flow characterization in high-speed, compressible regimes, in particular in gas-phase detonations. We carry out synthetic PIV reconstruction of the flow field in a two-dimensional, planar detonation propagating under atmospheric conditions and modelled using single-step Arrhenius kinetics. The flow is uniformly seeded with monodispersed Al2O3 particles with sizes 50 and 200 nm, along with initially co-located massless Lagrangian tracer particles. The effect of massive particles on the detonation speed and thermodynamic state of the flow is investigated and is found to be negligible. We further assess the ability of massive particles to sample the flow field and while it is found that 50 nm particles sample the flow field better than the 200 nm ones, they also exhibit significant clustering. By comparing the trajectories of massive particles with those of massless tracers, it is shown that almost all massive particles rapidly diverge from the actual flow pathlines. Finally, we quantify the accuracy of the PIV reconstruction of the velocity field in comparison with the actual velocity field in the numerical simulations. It is shown that while PIV is generally capable of capturing the bulk flow features in the streamwise direction, its accuracy is not sufficient to characterize the transverse velocity component or velocity fluctuations.

Universality class for a nonequilibrium state of matter: A d=4-ε expansion study of Malthusian flocks.

We show that "Malthusian flocks"-i.e., coherently moving collections of self-propelled entities (such as living creatures) which are being "born" and "dying" during their motion-belong to a new universality class in spatial dimensions d>2. We calculate the universal exponents and scaling laws of this new universality class to O(ε) in a d=4-ε expansion and find these are different from the "canonical" exponents previously conjectured to hold for "immortal" flocks (i.e., those without birth and death) and shown to hold for incompressible flocks with spatial dimensions in the range of 2<d≤4. We also obtain a universal amplitude ratio relating the damping of transverse and longitudinal velocity and density fluctuations in these systems. Furthermore, we find a universal separatrix in real space (r) between two regions in which the equal-time density correlation 〈δρ(r,t)δρ(0,t)〉 has opposite signs. Our expansion should be quite accurate in d=3, allowing precise quantitative comparisons between our theory, simulations, and experiments.

Fluid Theory of Coherent Magnetic Vortices in High-β Space Plasmas

Abstract In situ observations in Earth’s and Saturn’s magnetosheaths and in the solar wind reveal the presence of Alfvén vortices as intermittent structures in the range of scales from fluid lengths down to a few ion lengths. The density and the magnetic field associated with them appear to be compressible for higher plasma betas. Until now, only incompressible Alfvén vortices have been known. Motivated by space plasma observations, we develop a new model of magnetic vortices in high-beta plasmas with anisotropic temperature, possessing compressible density and magnetic field, whose typical size ranges from fluid to ion scales. At magnetofluid scales, we find novel nonpropagating field-aligned cylindrical monopoles and inclined propagating dipoles. Their transverse magnetic and velocity fluctuations are aligned, but not identical, and they exhibit density and compressible magnetic field fluctuations δn and localized inside the vortex core. In the presence of thermal anisotropy and acoustic effects, they may be correlated or anticorrelated, fluctuations whose velocity along the magnetic field is below the ion thermal speed are always correlated. At ion or kinetic scales (with the smallest radii ) and in the absence of acoustic perturbations, only dipolar Alfvén vortices survive with properties similar to those at fluid scales, except that δn/n 0 reaches the level of . We also find pressure-balanced kinetic slow magnetosonic dipoles, possessing finite and purely compressional magnetic field perturbation, whose existence is facilitated by a strong ion temperature anisotropy.

Mesoscale numerical modeling of the boundary atmospheric layer adapted to the north-western Black Sea region. Part 1. Mathematical problem formulation

The article presents a complete mathematical formulation of the problem of the boundary layer of the atmosphere and the interacting surface layers of the soil with the active layer of the sea adapted to the North-Western Black Sea Region through the inclusion of the coastline shape, relief elevation angles and climatic characteristics of soil moisture. The numerical model is a three-dimensional, unsteady, hydrostatic model with one- or two-parameter closure. The paper presents a detailed description of the applied sub-grid processes parameterizations such as cloudiness in the lower tier, flows of short- and long-wave radiation throughout thickness of the boundary layer and near the Earth, antigradient migration for basic meteorological variables in the presence of neutral or weakly stable stratification, components of water, heat and radiation balance, phase transitions of moisture in the atmosphere, and different parameterizations of turbulent processes used in the model. The possibilities of the model include description of neutral and stable boundary layers with consideration of the kinetic energy of vertical velocity fluctuations instead of the kinetic energy of longitudinal and transverse velocity fluctuations. Identification of the type of the boundary layer at a particular point in time is estimated using values of the Richardson number. In addition, in case of convective conditions presence, parameterization of dry convection and wet-convective adaptation may be implemented. At the boundaries of "free boundary layer – surface or near-water layer of air, air-soil and air-water" certain bonding conditions are to be set to ensure continuity of meteorological parameters or their flows. On the upper boundary of the free boundary layer actual values of meteorological parameters and necessary parameters, or corresponding values from the global atmospheric model are to set. At the lower boundary of the deep soil layer the invariance of the vertical temperature gradient of the active layer of the sea – the value of temperature which is equal to the value of the latter according to its climatic values in the considered season of the year is to be set. The presented model is the first approximation in numerical modeling of the boundary layer over the adapted territory and is designed for studying the thermodynamic structure of the boundary layer of the adapted territory, as well as for identifying the breeze effects over the terrain.

Coexistence of acoustic waves and turbulence in low Mach number compressible flows

In this work, direct numerical simulations of the compressible fluid equations in turbulent regimes are performed. The behavior of the flow is either dominated by purely turbulent phenomena or by the generation of sound waves in it. Previous studies suggest that three different types of turbulence may happen at the low Mach number limit in polytropic flows: Nearly incompressible, modally equipartitioned compressible, and compressible wave. The distinction between these types of turbulence is investigated here applying different kinds of forcing. Scaling of density fluctuations with Mach number, comparison of the ratio of transverse velocity fluctuations to longitudinal fluctuations, and spectral decomposition of fluctuations are used to distinguish the nature of these solutions. From the study of the spatio-temporal spectra and correlation times, we quantify the contribution of the waves to the total energy of the system. Also, in the dynamics of a compressible flow, three associated correlation times are considered: the non-linear time of local interaction between scales, the sweeping time or non-local time of large scales on small scales, and the time associated with acoustic waves (sound). We observed that different correlation times dominate depending on the wave number (k), the Mach number, and the type of forcing.