Effects Of Stable Stratification Research Articles

Stratified Resistive Tearing Instability

Resistive tearing instabilities are common in fluids that are highly electrically conductive and carry strong currents. We determine the effect of stable stratification on the tearing instability under the Boussinesq approximation. Our results generalise previous work that considered only specific parameter regimes, and we show that the length scale of the fastest-growing mode depends non-monotonically on the stratification strength. We confirm our analytical results by solving the linearised equations numerically, and we discuss whether the instability could operate in the solar tachocline.

Tidal Dissipation in Stably Stratified and Semiconvective Regions of Rotating Giant Planets: Incorporating Coriolis Forces

We study how stably stratified or semiconvective layers alter tidal dissipation rates associated with the generation of inertial, gravito-inertial, interfacial, and surface gravity waves in rotating giant planets. We explore scenarios in which stable (nonconvective) layers contribute to the high rates of tidal dissipation observed for Jupiter and Saturn in our solar system. Our model is an idealized spherical Boussinesq system incorporating Coriolis forces to study effects of stable stratification and semiconvective layers on tidal dissipation. Our detailed numerical calculations consider realistic tidal forcing and compute the resulting viscous and thermal dissipation rates. The presence of an extended stably stratified fluid core significantly enhances tidal wave excitation of both inertial waves (due to rotation) in the convective envelope and gravito-inertial waves in the dilute core. We show that a sufficiently strongly stratified fluid core enhances inertial wave dissipation in a convective envelope much like a solid core does. We demonstrate that efficient tidal dissipation rates (and associated tidal quality factors )—sufficient to explain the observed migration rates of Saturn's moons—are predicted at the frequencies of the orbiting moons due to the excitation of inertial or gravito-inertial waves in our models with stable layers (without requiring resonance locking). Stable layers could also be important for tidal evolution of hot and warm Jupiters and hot Neptunes, providing efficient tidal circularization rates. Future work should study more sophisticated planetary models that also account for magnetism and differential rotation, as well as the interaction of inertial waves with turbulent convection.

Horizontal meandering in direct numerical simulations of the stable boundary layer

AbstractLarge‐scale nonturbulent motions are investigated using high‐resolution direct numerical simulations of the turbulent Ekman layer at a moderate Reynolds number. In particular, the role of stable stratification effects in the generation and amplification of large‐scale oscillations in the wind‐speed components and buoyancy is analysed. Eulerian autocorrelation functions (EAFs) and spectral analysis help to describe and characterize such modes as meandering‐like structures. Focus is given to the strong stability cases, where vertical turbulent motions are damped and large‐scale modes drive near‐wall patterns of flow laminarization. Horizontal meandering arises in the near‐wall region when the ratio of vertical wind‐speed variance to horizontal wind‐speed variance decreases to small orders of magnitude. In the case of strong stratification, the characteristic features of meandering motion were identified as negative lobes in the EAF, with corresponding low‐frequency peaks in the horizontal wind speed and buoyancy spectra. The Ekman configuration used reproduced the development of meandering‐like structures satisfactorily in strong stable conditions, as indicated by field observations of the stable boundary layer and its dependence on the level of stratification. At strong stability, the Rotta model constant, which represents the relationship between the dissipation and return to isotropy terms in the velocity variance budget, is shown to vary with stability.

On large-scale dynamos with stable stratification and the application to stellar radiative zones

Abstract Our understanding of large-scale magnetic fields in stellar radiative zones remains fragmented and incomplete. Such magnetic fields, which must be produced by some form of dynamo mechanism, are thought to dominate angular-momentum transport, making them crucial to stellar evolution. A major difficulty is the effect of stable stratification, which generally suppresses dynamo action. We explore the effects of stable stratification on mean-field dynamo theory with a particular focus on a non-helical large-scale dynamo (LSD) mechanism known as the magnetic shear-current effect. We find that the mechanism is robust to increasing stable stratification as long as the original requirements for its operation are met: a source of shear and non-helical magnetic fluctuations (e.g. from a small-scale dynamo). Both are plausibly sourced in the presence of differential rotation. Our idealized direct numerical simulations, supported by mean-field theory, demonstrate the generation of near equipartition large-scale toroidal fields. Additionally, a scan over magnetic Reynolds number shows no change in the growth or saturation of the LSD, providing good numerical evidence of a dynamo mechanism resilient to catastrophic quenching, which has been an issue for helical dynamos. These properties – the absence of catastrophic quenching and robustness to stable stratification – make the mechanism a plausible candidate for generating in situ large-scale magnetic fields in stellar radiative zones.

Numerical study of stable stratification effects on the wind over simplified tall building models using large-eddy simulations

Atmospheric stratification is a critical factor affecting wind around buildings. However, very few studies have dealt with the atmosphere under stable stratification. In addition, the building model is typically simplified as a cubic block in previous studies concerning stable stratifications; however, the building aspect ratio (height/width) in the downtown area is often larger than 1. Furthermore, the spatial correlation of the velocities in tall buildings, which is important in determining the length scale of the flow and in evaluating pollutant dispersion, has seldom been studied. Therefore, in the present study, the flow around a simplified tall building and the flow around two groups of buildings with the plan area densities of 12.5% and 25.0%, were investigated under stable stratifications with stratified numbers K equaling to 0, 1, 2, and 3, using large eddy simulations (LES). The aspect ratio of the building models is 2. It was found that, for a single building model, the average wind acceleration above the building is directly proportional to K. Regarding the fluctuating wind velocity, the stratification effect has a weak impact. For building groups, the impact region of stratified flow usually appears when z/H < 1.2. A higher building density reduces the streamwise fluctuating wind velocity and the streamwise velocity spatial correlation.

Numerical Investigation of Stable Stratification Effects on Wind Resource Assessment in Complex Terrain

In the present study, we perform numerical simulations considering various stable atmospheric conditions for a small-scale simple topography. Based on the obtained simulation results, we visualize the flow field and discuss drastic changes in the flow patterns. A flow pattern similar to the potential flow suddenly appears around an isolated hill as the stability increases, regardless of the inclination angle of the hill. We show that a critical Richardson number clearly exists. Furthermore, the effect of stable stratification on the evaluation of power generation is shown for typical complex terrain. We evaluate the capacity factor (%) of a 2 MW large wind turbine based on one-year virtual mast data and consider the effect of stable stratification. It is shown, in the case of stable stratification, that the capacity factor is 2.775 times greater than that under neutral stratification.

Horizontal shear instabilities in rotating stellar radiation zones

Context. Rotational mixing transports angular momentum and chemical elements in stellar radiative zones. It is one of the key processes for modern stellar evolution. In the past two decades, an emphasis has been placed on the turbulent transport induced by the vertical shear instability. However, instabilities arising from horizontal shear and the strength of the anisotropic turbulent transport that they may trigger remain relatively unexplored. The weakest point of this hydrodynamical theory of rotational mixing is the assumption that anisotropic turbulent transport is stronger in horizontal directions than in the vertical one. Aims. This paper investigates the combined effects of stable stratification, rotation, and thermal diffusion on the horizontal shear instabilities that are obtained and discussed in the context of stellar radiative zones. Methods. The eigenvalue problem describing linear instabilities of a flow with a hyperbolic-tangent horizontal shear profile was solved numerically for a wide range of parameters. When possible, the Wentzel–Kramers–Brillouin–Jeffreys (WKBJ) approximation was applied to provide analytical asymptotic dispersion relations in both the nondiffusive and highly diffusive limits. As a first step, we consider a polar f-plane where the gravity and rotation vector are aligned. Results. Two types of instabilities are identified: the inflectional and inertial instabilities. The inflectional instability that arises from the inflection point (i.e., the zero second derivative of the shear flow) is the most unstable when at a zero vertical wavenumber and a finite wavenumber in the streamwise direction along the imposed-flow direction. While the maximum two-dimensional growth rate is independent of the stratification, rotation rate, and thermal diffusivity, the three-dimensional inflectional instability is destabilized by stable stratification, while it is stabilized by thermal diffusion. The inertial instability is rotationally driven, and a WKBJ analysis reveals that its growth rate reaches the maximum value of √f(1 − f) in the inviscid limit as the vertical wavenumber goes to infinity, where f is the dimensionless Coriolis parameter. The inertial instability for a finite vertical wavenumber is stabilized as the stratification increases, whereas it is destabilized by the thermal diffusion. Furthermore, we found a selfsimilarity in both the inflectional and inertial instabilities based on the rescaled parameter PeN2 with the Péclet number Pe and the Brunt–Väisälä frequency N.

Reproduction of Local Strong Wind Area Induced in the Downstream of Small-Scale Terrain by Computational Fluid Dynamic (CFD) Approach

In this research, the computational fluid dynamic (CFD) approach was applied for the solution of the problems of local strong wind areas in railway fields, and the mechanism of wind generation was discussed. The problem of local wind occurring on a railway line in winter was taken up in this research. A computational simulation for the prediction of wind conditions by large-eddy simulation (LES) was implemented, and it was clarified that local strong wind areas are mainly caused by separated flows originating from small-scale terrain positioned at its upstream (at approximately 180 m above sea level). Meanwhile, the effects of the size of the calculation area and spatial grid resolution on the result of calculation and the effect of atmospheric stability were also discussed. It was clarified that in order to simulate the air flow characteristic of the separated flow originating from the small-scale terrain (at an altitude of approximately 180 m) targeted in the present research, approximately 10 m of spatial resolution of computational cell in the horizontal direction is required. In addition, the effect of stable stratification on the flow was also examined. As a result, lee waves were excited at the downstream of the terrain over time in the case of stably stratified flow (Fr = 1.0). The reverse-flow region lying behind the terrain, which had been observed at a neutral time, was strongly inhibited. Consequently, a local strong wind area was generated at the downstream of the terrain, and a strong wind area passing through the observation mast was observed. By investigating the increasing rate of speed of the local strong wind area induced at the time of stable stratification, it was found that the wind was approximately 1.2 times stronger than what was generated at a neutral time.

Layer formation and relaminarisation in plane Couette flow with spanwise stratification

In this paper we investigate the effect of stable stratification on plane Couette flow when gravity is oriented in the spanwise direction. When the flow is turbulent we observe near-wall layering and associated new mean flows in the form of large-scale spanwise-flattened streamwise rolls. The layers exhibit the expected buoyancy scaling $l_{z}\sim U/N$ where $U$ is a typical horizontal velocity scale and $N$ the buoyancy frequency. We associate the new coherent structures with a stratified modification of the well-known large-scale secondary circulation in plane Couette flow. We find that the possibility of the transition to sustained turbulence is controlled by the relative size of this buoyancy scale to the spanwise spacing of the streaks. In parts of parameter space transition can also be initiated by a newly discovered linear instability in this system (Facchini et al., J. Fluid Mech., vol. 853, 2018, pp. 205–234). When wall turbulence can be sustained the linear instability opens up new routes in phase space for infinitesimal disturbances to initiate turbulence. When the buoyancy scale suppresses turbulence the linear instability leads to more ordered nonlinear states, with the possibility for intermittent bursts of secondary shear instability.

The effects of stable stratification on the decay of initially isotropic homogeneous turbulence

We report on direct numerical simulations of the decay of initially isotropic, homogeneous turbulence subject to the application of stable density stratification. Flows were simulated for three different initial Reynolds numbers, but for the same initial Froude number. We find that the flows pass through three different dynamical regimes as they decay, depending on the local values of the Froude number and activity parameter. These regimes are analogous to those seen in the experimental study of Spedding (J. Fluid Mech., vol. 337, 1997, pp. 283–301) for the wake of a sphere. The flows initially decay with little influence of stratification, up to approximately one buoyancy period, when the local Froude number has dropped below 1. At this point the flows have adjusted to the density stratification, and, if the activity parameter is large enough, begin to decay at a slower rate and spread horizontally at a faster rate, consistent with the predictions of Davidson (J. Fluid Mech., vol. 663, 2010, pp. 268–292) and the scaling arguments of Billant &amp; Chomaz (Phys. Fluids, vol. 13, 2001, pp. 1645–1651). We refer to this second regime as the stratified turbulence regime. As the flows continue to decay, ultimately the activity parameter drops below approximately 1 as viscous effects begin to dominate. In this regime, the flows have become quasi-horizontal, and approximately obey the scaling arguments of Godoy-Diana et al. (J. Fluid Mech., vol. 504, 2004, pp. 229–238).

The effect of stable stratification on vortex stretching in open channel flow

We present the results of direct numerical simulation of stably stratified open channel flow. The main goal of the paper is to check the effect of thermal stratification on the dynamics of vortex interactions. By comparing the vortex stretching in neutral and stratified cases we show that imposing the stratification leads to an increase of the ratio between positive and negative vortex stretching magnitudes in the flow. That indicates the change in spectral transfer of turbulent energy.

Effect of stable stratification on dispersion within urban street canyons: A large-eddy simulation

This study employs a validated large-eddy simulation (LES) code with high tempo-spatial resolution to investigate the effect of a stably stratified roughness sublayer (RSL) on scalar transport within an urban street canyon. The major effect of stable stratification on the flow and turbulence inside the street canyon is that the flow slows down in both streamwise and vertical directions, a stagnant area near the street level emerges, and the vertical transport of momentum is weakened. Consequently, the transfer of heat between the street canyon and overlying atmosphere also gets weaker. The pollutant emitted from the street level ‘pools’ within the lower street canyon, and more pollutant accumulates within the street canyon with increasing stability. Under stable stratification, the dominant mechanism for pollutant transport within the street canyon has changed from ejections (flow carries high-concentration pollutant upward) to unorganized motions (flow carries high-concentration pollutant downward), which is responsible for the much lower dispersion efficiency under stable stratifications.

Effects of stable stratification on turbulent/nonturbulent interfaces in turbulent mixing layers

Numerical simulations of the turbulent/nonturbulent interface in stably stratified turbulent mixing layers determine the statistical properties near the interface, such as the inner structure of the interface, the characteristic length scales and buoyancy Reynolds number, and the effects of buoyancy on the small-scale turbulence dynamics.

Numerical study of unsteady, thermally-stratified shear flows in superposed porous and pure-fluid domains

In this paper we report on numerical simulations of temporally evolving, thermally stratified shear flows in superposed porous and pure-fluid domains. In particular, we study two different types of flows, namely, pressure-driven channel flows and unforced shear layers. Our study is based on a recently developed thermo-mechanical model for flows in the domains of interest. This model follows a mixture-theoretic approach, according to which the medium’s porosity is introduced as a concentration parameter, thus allowing the derivation of a single set of equations that is valid simultaneously in both domains. For the types of flows examined herein, our simulations predict the formation of spanwise vortical structures (rollers) at the porous–pure fluid interface. These rollers grow in time thereby inducing fluid circulation inside the porous medium. For the case of pressure-driven channel flows, our simulations further predict the development of plumes of hot and cold fluid due to convective instabilities that interact with the rollers. In the case of unforced shear layers, unstable stratification accelerates the growth of the rollers, which soon start to merge, and enhances fluid mixing. By contrast, the effect of stable stratification is exactly the opposite. Herein we discuss in detail the temporal evolution of the predicted flow structures and the interactions between them, as well as the mechanisms that induce thermal non-equilibrium inside the porous medium.

Stable Stratification Effects on Flow and Pollutant Dispersion in Boundary Layers Entering a Generic Urban Environment

Large-eddy simulations (LES) are used to investigate the effect of stable stratification on rural-to-urban roughness transitions. Smooth-wall turbulent boundary layers are subjected to a generic urban roughness consisting of cubes in an in-line arrangement. Two line sources of pollutant are added to investigate the effect on pollutant dispersion. Firstly, the LES method is validated with data from wind-tunnel experiments on fully-developed flow over cubical roughness. Good agreement is found for the vertical profiles of the mean streamwise velocity component and mean Reynolds stress. Subsequently, roughness transition simulations are done for both neutral and stable conditions. Results are compared with fully-developed simulations with conventional double-periodic boundary conditions. In stable conditions, at the end of the domain the streamwise velocity component has not yet reached the fully-developed state even though the surface forces are nearly constant. Moreover, the internal boundary layer is shallower than in the neutral case. Furthermore, an investigation of the turbulence kinetic energy budget shows that the buoyancy destruction term is reduced in the internal boundary layer, above which it is equal to the undisturbed (smooth wall) value. In addition, in stable conditions pollutants emitted above the urban canopy enter the canopy farther downstream due to decreased vertical mixing. Pollutants emitted below the top of the urban canopy are 85 % higher in concentration in stable conditions mostly due to decreased advection. If this is taken into account concentrations remain 17 % greater in stable conditions due to less rapid internal boundary-layer growth. Finally, it is concluded that in the first seven streets the vertical advective pollutant flux is significant, in contrast to the fully-developed case.

Vanishing viscosity limits of mixed hyperbolic–elliptic systems arising in multilayer channel flows

This study considers the spatially periodic initial value problem of 2 × 2 quasi-linear parabolic systems in one space dimension having quadratic polynomial flux functions. These systems arise physically in the interfacial dynamics of viscous immiscible multilayer channel flows. The equations describe the spatiotemporal evolution of phase-separating interfaces with dissipation arising from surface tension (fourth-order) and/or stable stratification effects (second-order). A crucial mathematical aspect of these systems is the presence of mixed hyperbolic–elliptic flux functions that provide the only source of instability. The study concentrates on scaled spatially 2π-periodic solutions as the dissipation vanishes, and in particular the behaviour of such limits when generalized dissipation operators (spanning second to fourth-order) are considered. Extensive numerical computations and asymptotic analysis suggest that the existence (or not) of bounded vanishing viscosity solutions depends crucially on the structure of the flux function. In the absence of linear terms (i.e. homogeneous flux functions) the vanishing viscosity limit does not exist in the L∞-norm. On the other hand, if linear terms in the flux function are present the computations strongly suggest that the solutions exist and are bounded in the L∞-norm as the dissipation vanishes. It is found that the key mechanism that provides such boundedness centres on persistent spatiotemporal hyperbolic–elliptic transitions. Strikingly, as the dissipation decreases, the flux function becomes almost everywhere hyperbolic except on a fractal set of elliptic regions, whose dimension depends on the order of the regularized operator. Furthermore, the spatial structures of the emerging weak solutions are found to support an increasing number of discontinuities (measure-valued solutions) located in the vicinity of the fractally distributed elliptic regions. For the unscaled problem, such spatially oscillatory solutions can be realized as extensive dynamics analogous to those found in the Kuramoto–Sivashinsky equation.

Simulating Dispersion in the Evening-Transition Boundary Layer

We investigate dispersion in the evening-transition boundary layer using large-eddy simulation (LES). In the LES, a particle model traces pollutant paths using a combination of the resolved flow velocities and a random displacement model to represent subgrid-scale motions. The LES is forced with both a sudden switch-off of the surface heat flux and also a more gradual observed evolution. The LES shows ‘lofting’ of plumes from near-surface releases in the pre-transition convective boundary layer; it also shows the subsequent ‘trapping’ of releases in the post-transition near-surface stable boundary layer and residual layer above. Given the paucity of observations for pollution dispersion in evening transitions, the LES proves a useful reference. We then use the LES to test and improve a one-dimensional Lagrangian Stochastic Model (LSM) such as is often used in practical dispersion studies. The LSM used here includes both time-varying and skewed turbulence statistics. It is forced with the vertical velocity variance, skewness and dissipation from the LES for particle releases at various heights and times in the evening transition. The LSM plume spreads are significantly larger than those from the LES in the post-transition stable boundary-layer trapping regime. The forcing from the LES was thus insufficient to constrain the plume evolution, and inclusion of the significant stratification effects was required. In the so-called modified LSM, a correction to the vertical velocity variance was included to represent the effect of stable stratification and the consequent presence of wave-like motions. The modified LSM shows improved trapping of particles in the post-transition stable boundary layer.

Non-equilibrium processes in non-homogeneous fluids under the action of external forces

This paper is devoted to the investigation of stable stratification effects that arise as a result of the combined influence of the external forces and environmental media's non-homogeneity due to the non-uniform distribution of dissolved or suspended matter, temperature, gas bubbles and so on. Such a medium is a thermodynamically non-equilibrium system where non-uniformity of the density flux causes the formation of specific fluid motions that are diffusion-induced flows and internal waves (IW), which are non-existent in a homogeneous fluid. In this paper, we demonstrate numerical calculations on flows’ fine structure around impermeable motionless plates with finite length and uniformly moving sloping plates in the interior of a continuously stratified fluid. The flow patterns are investigated both in the direct vicinity of the plate where compact non-wave boundary layer-like components and jet flows are observed and at long distances from the obstacle where sharp horizontal interfaces and groups of IW are revealed. The flows’ properties are analyzed as a function of the dimensional parameters of the problem, i.e. the value of stratification, the plate's length and its slope angle to the horizon. The calculated flow patterns are compared with the earlier obtained asymptotic approximation of small and large times and high-resolution schlieren images of stratified flows around both motionless and moving sloping plates in the laboratory.

ROTATION AND STABILITY OF THE TOROIDAL MAGNETIC FIELD IN STELLAR RADIATION ZONES

The stability of the magnetic field in radiation zones is of crucial importance for mixing and angular momentum transport in the stellar interior. We consider the stability properties of stars containing a predominant toroidal field in spherical geometry by means of a linear stability in the Boussinesq approximation taking into account the effect of thermal conductivity. We calculate the growth rate of instability and analyze in detail the effects of stable stratification and heat transport. We argue that the stabilizing influence of gravity can never entirely suppress the instability caused by electric currents in radiation zones. However, the stable stratification can essentially decrease the growth rate of instability.

Linearized potential vorticity mode and its role in transition to baroclinic instability

In addition to the effect of stable stratification and uniform shear in turbulent flows, a case which has already been modelled using linear approaches (rapid distortion theory) and direct numerical simulations, we introduce the effect of uniform rotation. Assuming the rotation axis to be vertical, and aligned with the gradients of density and mean velocity, an enslaved horizontal stratification is forced and baroclinic instability can occur. In that case, the linear analysis shows an extension of the unstable domain up to a gradient Richardson number \documentclass[12pt]{minimal}\begin{document}$\textit {Ri}$\end{document}Ri of 1 for kx = 0 modes. First, we extend this asymptotic analysis at t → ∞ to kx ≠ 0 modes. We show that these modes lead asymptotically to oscillating bounded solutions whose frequency depend only on the rotation number \documentclass[12pt]{minimal}\begin{document}$R=1/\textit {Ro}$\end{document}R=1/Ro. The analysis of the transition to baroclinic instability is then completed with a discussion of the role of kx ≈ 0 modes—small streamwise wavenumbers—and of the importance of coupling with the potential vorticity mode \documentclass[12pt]{minimal}\begin{document}$u^{(\Omega _{pot})}$\end{document}u(Ωpot) or Ertel's mode. The latter is shown to be determinant for dramatic transient growth at intermediate times. The structure of the stratified, sheared, rotating flow is predicted using a stochastic linear approach (referred to as kinematic simulation) to complete the rapid distortion theory analysis.