Hydrodynamic Turbulence Research Articles

Sand barrier morphological evolution based on time series remote sensing images: a case study of Anhaiao, Pingtan

The morphological evolution of the sand barrier in the Anhaiao coastal zone of Pingtan from 1996 to 2018 was studied. Tidal correction was used to refine the location of the coastline. A standard deviation ellipse method was applied to further analyze the movement of the barrier head with the axis and rotation angle. A natural neighbor interpolation (NNI) method was carried out to calculate the terrain of the intertidal area, and the erosion and deposition characteristics were illustrated based on the terrain. The results showed that the northern part of the sand barrier facing the lagoon area was deposited over the whole studied period, while erosion has always occurred in the southern part of the sand barrier facing the open sea. The erosion and deposition were slightly different on both sides of the barrier head due to hydrodynamic turbulence. The middle sand barrier moved 102.60 m away from its original location in 1996, and the end of the barrier moved 65.45 m. The head of the sand barrier continued moving 379 m to the northwest. Consequently, the preliminary morphological evolution of the sand barrier corresponding to the distance and direction of movement was detected.

Compressible Turbulence in the Interstellar Medium: New Insights from a High-resolution Supersonic Turbulence Simulation

Abstract The role of supersonic turbulence in structuring the interstellar medium (ISM) remains an unsettled question. Here, this problem is investigated using a new exact law of compressible isothermal hydrodynamic turbulence, which involves two-point correlations in physical space. The new law is shown to have a compact expression that contains a single flux term reminiscent of the incompressible case and a source term with a simple expression whose sign is given by the divergence of the velocity. The law is then used to investigate the properties of such a turbulence at integral Mach number 4 produced by a massive numerical simulation with a grid resolution of points. The flux (resp. source) term was found to have positive (resp. negative) contribution to the total energy cascade rate, which is interpreted as a direct cascade amplified by compression, while their sum is constant in the inertial range. Using a local (in space) analysis it is shown that the source is mainly driven by filamentary structures in which the flux is negligible. Taking positive defined correlations reveals the existence of different turbulent regimes separated by the sonic scale, which determines the scale over which the nonnegligible source modifies the scaling of the flux. Our study provides new insight into the dynamics and structures of supersonic interstellar turbulence.

Scaling and hetero-/auto-Bäcklund transformations with solitons of an extended coupled (2+1)-dimensional Burgers system for the wave processes in hydrodynamics and acoustics

The Burgers-type equations are applied to oceanography, hydrodynamic turbulence, gas dynamics, shock-wave formation, acoustic transmission structure, boundary-layer behavior, continuum-traffic simulation, convection-dominated diffusion, wave formation in the thermo-elastic media, vorticity transport, dispersion in the porous media, particle sedimentation in fluid suspension, colloid evolution, and so forth. Hereby, taking into account the wave processes in hydrodynamics and acoustics, we investigate an extended coupled (2+1)-dimensional Burgers system, and with symbolic computation, work out a scaling transformation, two hetero-Bäcklund transformations and two auto-Bäcklund transformations, with the soliton solutions. Our results are dependent on the coefficients in the system.

Stability in turbulence: The interplay between shocks and vorticity in a superfluid with higher-order dispersion

Higher-order dispersion can lead to intriguing dynamics that are becoming a focus of modern hydrodynamics research. Such systems occur naturally, for example in shallow water waves and nonlinear optics, for which several types of novel dispersive shocks structures have been identified. Here we introduce ultracold atoms as a tunable quantum simulations platform for higher-order systems. Degenerate quantum gases are well controlled model systems for the experimental study of dispersive hydrodynamics in superfluids and have been used to investigate phenomena such as vortices, solitons, dispersive shock waves and quantum turbulence. With the advent of Raman-induced spin-orbit coupling, the dispersion of a dilute gas Bose-Einstein condensate can be modified in a flexible way, allowing for detailed investigations of higher-order dispersion dynamics. Here we present a combined experimental and theoretical study of shock structures generated in such a system. The breaking of Galilean invariance by the spin-orbit coupling allows two different types of shock structures to emerge simultaneously in a single system. Numerical simulations suggest that the behavior of these shock structures is affected by interactions with vortices in a manner reminiscent of emerging viscous hydrodynamics due to an underlying quantum turbulence in the system. This result suggests that spin-orbit coupling can be used as a powerful means to tun the effective viscosity in cold-atom experiments serving as quantum simulators of turbulent hydrodynamics, with applications from condensed matter and optics to quantum simulations of neutron stars.

Dust Growth by Accretion of Molecules in Supersonic Interstellar Turbulence

Abstract We show that the growth rate of dust grains in cold molecular clouds is enhanced by the high degree of compressibility of a turbulent, dilute gas. By means of high-resolution (10243) numerical simulations, we confirm the theory that the spatial mean growth rate is proportional to the gas-density variance. This also results in broadening of the grain-size distribution (GSD) due to turbulence-induced variation of the grain-growth rate. We show, for the first time in a detailed numerical simulation of hydrodynamic turbulence, that the GSD evolves toward a shape that is a reflection of the gas-density distribution, regardless of the initial distribution. That is, in case of isothermal, rotationally forced turbulence, the GSD tends to be a lognormal distribution. We also show that in hypersonic turbulence, decoupling of gas and dust becomes important and that this leads to an even further accelerated grain growth.

Compressible vortex structures and their role in the onset of hydrodynamic turbulence

We study the formation of quasi-two-dimensional (thin pancake) vortex structures in three-dimensional flows and of quasi-one-dimensional structures in two-dimensional hydrodynamics. These structures are formed at large Reynolds numbers, when their evolution is described in the leading order by the Euler equations for an ideal incompressible fluid. We show numerically and analytically that the compression of these structures and, as a consequence, the increase in their amplitudes are due to the compressibility of the frozen-in-fluid fields: the field of continuously distributed vortex lines in the three-dimensional case and the field of vorticity rotor lines (divorticity) for two-dimensional flows. We find that the growth of vorticity and divorticity can be considered to be a process of overturning the corresponding fields. At high intensities, this process demonstrates a Kolmogorov-type scaling relating the maximum amplitude to the corresponding thicknesses-to-width ratio of the structures. The possible role of these coherent structures in the formation of the Kolmogorov turbulent spectrum, as well as in the Kraichnan spectrum corresponding to a constant flux of enstrophy in the case of two-dimensional turbulence, is analyzed.

Сжимаемые вихревые структуры и их роль в зарождении гидродинамической турбулентности

Сжимаемые вихревые структуры и их роль в зарождении гидродинамической турбулентности

Dust coagulation feedback on magnetohydrodynamic resistivities in protostellar collapse

Context. The degree of coupling between the gas and the magnetic field during the collapse of a core and the subsequent formation of a disk depends on the assumed dust size distribution. Aims. We study the impact of grain–grain coagulation on the evolution of magnetohydrodynamic (MHD) resistivities during the collapse of a prestellar core. Methods. We use a 1D model to follow the evolution of the dust size distribution, out-of-equilibrium ionisation state, and gas chemistry during the collapse of a prestellar core. To compute the grain–grain collisional rate, we consider models for both random and systematic, size-dependent, velocities. We include grain growth through grain–grain coagulation and ice accretion, but ignore grain fragmentation. Results. Starting with a Mathis-Rumpl-Nordsieck (MRN) size distribution (Mathis et al. 1977, ApJ, 217, 425), we find that coagulation in grain–grain collisions generated by hydrodynamical turbulence is not efficient at removing the smallest grains and, as a consequence, does not have a large effect on the evolution of the Hall and ambipolar diffusion MHD resistivities, which still drop significantly during the collapse like in models without coagulation. The inclusion of systematic velocities, possibly induced by the presence of ambipolar diffusion, increases the coagulation rate between small and large grains, removing small grains earlier in the collapse and therefore limiting the drop in the Hall and ambipolar diffusion resistivities. At intermediate densities (nH ~ 108 cm−3), the Hall and ambipolar diffusion resistivities are found to be higher by 1 to 2 orders of magnitude in models with coagulation than in models where coagulation is ignored, and also higher than in a toy model without coagulation where all grains smaller than 0.1 μm would have been removed in the parent cloud before the collapse. Conclusions. When grain drift velocities induced by ambipolar diffusion are included, dust coagulation happening during the collapse of a prestellar core starting from an initial MRN dust size distribution appears to be efficient enough to increase the MHD resistivities to the values necessary to strongly modify the magnetically regulated formation of a planet-forming disk. A consistent treatment of the competition between fragmentation and coagulation is, however, necessary before reaching firm conclusions.

Intermittency of many-particle dispersion in anisotropic magnetohydrodynamic turbulence

Intermittent deviation from average dispersion curves reveals differences between the dynamics of magnetohydrodynamic turbulence and hydrodynamic turbulence. Turbulent dispersion is typically measured by the average separation of a group of Lagrangian tracer particles from each other as the particles move in a turbulent flow. On average, the particles will increase their separation as time evolves. However, due to the intermittent nature of turbulence, radical deviations from this behavior can be observed when considering individual groups of particles. When the group consists only of two particles, those two particles sometimes can move toward each other for short periods of time, decreasing their separation. When the group consists instead of many particles that are initially densely packed, similar results can be obtained using the convex hull of the group of particles. We examine this intermittency of many-particle dispersion in incompressible isotropic hydrodynamic turbulence, incompressible isotropic magnetohydrodynamic turbulence, and incompressible anisotropic magnetohydrodynamic turbulence. We interpret periods of decreasing separation physically in terms of anisotropic dispersion due to a large-scale static magnetic field, interactions with local magnetic fields and current sheets, and interactions with Alfvénic fluctuations.

Hydrodynamic Turbulence: Sweeping Effect and Taylor’s Hypothesis via Correlation Function

Hydrodynamic Turbulence: Sweeping Effect and Taylor’s Hypothesis via Correlation Function

Mitigation of Darrieus–Landau instability effects on turbulent premixed flames

Theoretical considerations on the competition between the most amplified modes for Darrieus–Landau (DL) hydrodynamic instability and turbulence timescales, show that, two extremal regimes can be identified: the instability-dominated and turbulence-dominated regimes. In the latter, also denoted as unified regime, both experiments and numerical simulations give evidence showing how the large scale, cusp-like structures of the flame front surface, typical of DL instability, are hindered by turbulent fluctuations. The result is that quantities such as turbulent flame propagation and front curvature statistics, which in the instability dominated regime are enhanced or modified by the overwhelming presence of hydrodynamic instability, are now mitigated and a unified regime is reached in which the characteristics of DL unstable and stable flame configurations become indistinguishable. In this work we analyze the concealing effects of increasing level of turbulence over the hydrodynamic Darrieus–Landau instability, and we show that, although some global indices such as the skewness of the curvature p.d.f. suggest that a unified regime is reached, others show the persistence of residual differences: in particular, the power spectral density of the flame front curvature. We use both experimental and numerical datasets of stable and unstable (based on linear stability analysis) flames, in conditions ranging from quasi laminar to significantly turbulent regimes.

Turbulent hydrodynamics in strongly correlated Kagome metals

A current challenge in condensed matter physics is the realization of strongly correlated, viscous electron fluids. These fluids can be described by holography, that is, by mapping them onto a weakly curved gravitational theory via gauge/gravity duality. The canonical system considered for realizations has been graphene. In this work, we show that Kagome systems with electron fillings adjusted to the Dirac nodes provide a much more compelling platform for realizations of viscous electron fluids, including non-linear effects such as turbulence. In particular, we find that in Scandium Herbertsmithite, the fine-structure constant, which measures the effective Coulomb interaction, is enhanced by a factor of about 3.2 as compared to graphene. We employ holography to estimate the ratio of the shear viscosity over the entropy density in Sc-Herbertsmithite, and find it about three times smaller than in graphene. These findings put the turbulent flow regime described by holography within the reach of experiments.

Effects of Solar Activity on Taylor Scale and Correlation Scale in Solar Wind Magnetic Fluctuations

Abstract The correlation scale and the Taylor scale are evaluated for interplanetary magnetic field fluctuations from two-point, single time correlation function using the Advanced Composition Explorer (ACE), Wind, and Cluster spacecraft data during the time period from 2001 to 2017, which covers over an entire solar cycle. The correlation scale and the Taylor scale are respectively compared with the sunspot number to investigate the effects of solar activity on the structure of the plasma turbulence. Our studies show that the Taylor scale increases with the increasing sunspot number, which indicates that the Taylor scale is positively correlated with the energy cascade rate, and the correlation coefficient between the sunspot number and the Taylor scale is 0.92. However, these results are not consistent with the traditional knowledge in hydrodynamic dissipation theories. One possible explanation is that in the solar wind, the fluid approximation fails at the spatial scales near the dissipation ranges. Therefore, the traditional hydrodynamic turbulence theory is incomplete for describing the physical nature of the solar wind turbulence, especially at the spatial scales near the kinetic dissipation scales.

Seagrass and rhodolith beds are important seascapes for the development of fish eggs and larvae in tropical coastal areas

In this study, the ichthyoplankton in two distinct tropical seascapes, gravelly sand with rhodolith beds (SRB) and muddy sand with seagrasses, were compared. The number of eggs was higher in the seagrass beds; however, the number of fish larvae was slightly higher in the SRB. Seagrass beds present less turbulent hydrodynamics and favor the retention of eggs and spawning. A more structured habitat provides better shelter, especially for eggs. However, as ontogeny progresses, the fish can explore areas with less shelter. This behavior was observed in this study, where the less structured SRB habitat had a high density of larvae in the later developmental stage. The dominance of earlier larval stages demonstrates a preference for more protected and less turbulent seascapes for nursery and offspring rearing. The results highlight that mapping of these seascapes (e.g., seagrass and rhodolith beds) will help to establish conservation measures to protect ecological connectivity and important tropical species.

Elastic Turbulence: An Experimental View on Inertialess Random Flow

A viscous solvent laminar flow may be strongly modified by the addition of a tiny amount of long polymer molecules, resulting in a chaotic flow called elastic turbulence (ET). ET is attributed to polymer stretching, which generates elastic stress and its back reaction on the flow. Its properties are analogous to those observed in hydrodynamic turbulence, although the formal similarity does not imply a similarity in physical mechanisms underlining these two types of random motion. Here we review the statistical and spectral properties and the spatial structure of the velocity field, the statistical and spectral properties of pressure fluctuations, and scaling of the friction factor of ET in wall-bounded and unbounded flow geometries, as observed in experiments and numerical simulations and described by theory for a wide range of control parameters and polymer concentrations.

Review of Non-Actual Problems: Unexpected fragmentation of light in the rib of a soap film. Stoilov’s phenomenon

An unexpected chaotic fragmentation of light was detected in its passage through the liquid waveguide of a conventional soap film rib, which was associated with the extraordinary turbulent hydrodynamics of inaccessible for direct observation collecting solution into the film rib

Modeling of Hydrodynamics and Mass Transfer Processes in KDP Crystal Growth

The turbulent hydrodynamics in a conventional operating crystallizer for growing kalium dihydrophosphate crystals is analyzed by physical modeling methods. The potentialities of an axisymmetric crystallizer, which has similar tools for stirring solution but is able to ensure controlled laminar hydrodynamic flows are considered. A combined mathematical model is formulated, which takes into account both the convective salt transfer in the crystallizer on the basis of solving the Navier–Stokes and diffusion equations and the kalium dihydrophosphate crystal growth on the basis of the theoretical model. A parametric calculation is performed to determine the effect of each mechanism of solution motion, including the directed solution outflow from a tube into the crystallizer and the rotation of crystal and stirrer.

Hydrodynamical instability with noise in the Keplerian accretion discs: modified Landau equation

ABSTRACT Origin of hydrodynamical instability and turbulence in the Keplerian accretion disc as well as similar laboratory shear flows, e.g. plane Couette flow, is a long-standing puzzle. These flows are linearly stable. Here we explore the evolution of perturbation in such flows in the presence of an additional force. Such a force, which is expected to be stochastic in nature hence behaving as noise, could be result of thermal fluctuations (however small be), Brownian ratchet, grain–fluid interactions, feedback from outflows in astrophysical discs, etc. We essentially establish the evolution of nonlinear perturbation in the presence of Coriolis and external forces, which is modified Landau equation. We show that even in the linear regime, under suitable forcing and Reynolds number, the otherwise least stable perturbation evolves to a very large saturated amplitude, leading to nonlinearity and plausible turbulence. Hence, forcing essentially leads a linear stable mode to unstable. We further show that nonlinear perturbation diverges at a shorter time-scale in the presence of force, leading to a fast transition to turbulence. Interestingly, emergence of nonlinearity depends only on the force but not on the initial amplitude of perturbation, unlike original Landau equation based solution.

Modeling oil dispersion under breaking waves. Part I: Wave hydrodynamics

The dispersion (transport and breakup) of oil droplets under breaking waves is essential for evaluating the impact of oil spills on the environment, and for designing countermeasures. In this part of the work (Part I), the hydrodynamics of a wave breaker in a 1.0 m deep tank obtained experimentally by Rapp and Melville (Philos Trans R Soc Lond A Math Phys Eng Sci 331(1622):735–800, 1990) using the dispersive focusing method was investigated numerically using Reynold-averaged Navier–Stokes (RANS) within the CFD code ANSYS Fluent. The renormalization group (RNG) k–e turbulence closure model was adopted to simulate wave turbulence, and the transient water–air interface was captured using volume of fluid (VOF) method. The simulated surface excursion and velocity fields matched closely the experimental observations during wave breaking. The energy dissipation of the wave crest showed good agreement with recent laboratory work and numerical simulations through evaluating the breaking parameter. The RANS approach was able to reproduce the turbulent kinetic energy field engendered by the breakers and simulated the residual turbulence within about two wave periods after the passage of the wave train. The VOF scheme Compressive provided a better agreement with the observation than the Geo-reconstruct scheme. The approach herein suggests that RANS method coupled with VOF in ANSYS Fluent is capable of capturing the major hydrodynamic forces and turbulence, and thus could be used to predict environmental processes within the breaking waves such as oil droplet formation and transport.

On the Closure Problem of the Coarse-Grained Hydrodynamics of Turbulent Superfluids

The coarse-grained hydrodynamics of turbulent superfluid fluids describes the fluid flow in terms of two equations for the averaged normal and superfluid velocities. These two equations are coupled via the mutual friction term, which contains the quantity $${\mathcal {L}}(r,t)$$ –the vortex line density (VLD) of the vortex tangle. The question of how to treat the quantity $${\mathcal {L}}(r,t)$$ –the so-called closure procedure is crucial for the correct description of flow of turbulent superfluids. The article provides a critical analysis of several approaches to the closure procedure. The first one, which is usually referred to as HVBK method suggests to express the quantity $${\mathcal {L}}(r,t)$$ via coarse-grained vorticity $$\nabla \times {\mathbf {v}}_{s}$$ using the famous Feynman rule. This method and idea on the vortex bundle structure, which justifies the use of the HVBK approach, are analyzed and discussed in detail. Another approach that has been popular before, but is still used sometimes, is called the Gorter–Mellink relation. This method suggests that the VLD $${\mathcal {L}}(r,t)$$ is proportional to the squared relative velocity between normal and superfluid components $$\propto (v_{n}-v_{s})^{2}$$ . One more variant of the closure procedure, discussed in the paper, is based on the method in which the vortex line density $${\mathcal {L}}(r,t)$$ is not expressed directly via the velocity (and/or vorticity) field, but is an independent equipollent variable, controlled by a separate equation. The latter approach is called as hydrodynamics of superfluid turbulence (HST). The advantages and disadvantages of each method are discussed.