Effects Of Density Stratification Research Articles

Effect of atmospheric density stratification on the generation of water waves by wind

The critical level instability mechanism for the generation of water waves by wind is re-examined for the situation when the atmosphere is density stratified. The density stratification is confined to the middle and upper atmosphere and then two cases are investigated. In case (A) no internal gravity waves are generated in the upper atmosphere and the effect of the density stratification is very small. In case (B) vertically propagating internal gravity waves form in the upper atmosphere and travel to infinity causing an energy loss, thus inhibiting the critical level instability in the lower atmosphere. Both cases are examined quantitatively for a logarithmic wind shear profile.

Investigating the influence of stepped roofs on wind dynamics using large eddy simulation

This study investigates airflow and turbulence within varying roof configurations in urban boundary layers by using the parallelized large-eddy simulation model (PALM). Key findings reveal stark contrasts in airflow between stepped and flat roof arrangements, with the former presenting dual counter-rotating vortices and enhanced vertical motion in one street, while the latter exhibited a primary vortex and several secondary vortices. Additionally, normalized turbulence kinetic energy (TKE) was markedly lower in flat roof configurations, with stepped roofs fostering more significant turbulence and small-scale turbulent motion. This variability intensified with decreasing step height and quantity. Vertical profiles further disclosed considerable velocity disturbances and larger Reynolds numbers in one street of stepped roofs, affirming the roof’s influence on turbulence generation and transport. Dispersive stress also displayed differing characteristics in various canyons. Turbulent momentum transport through eddies significantly differs between the windward and leeward streets of flat and stepped roofs. Further exploration into density stratification effects and scalar transport in stepped roofs would enhance practical implications.

Densitaxis: Active particle motion in density gradients

Organisms often swim through density-stratified fluids. Here, we investigate the dynamics of active particles swimming in fluid density gradients and report theoretical evidence of taxis as a result of these gradients (densitaxis). Specifically, we calculate the effect of density stratification on the dynamics of a force- and torque-free spherical squirmer and show that density gradients induce reorientation that tends to align swimming either parallel or normal to the gradient depending on the swimming gait. In particular, swimmers that propel by generating thrust in the front (pullers) rotate to swim parallel to gradients and hence display (positive or negative) densitaxis, while swimmers that propel by generating thrust in the back (pushers) rotate to swim normal to the gradients. This work could be useful to understand the motion of marine organisms in ocean or be leveraged to sort or organize a suspension of active particles by modulating density gradients.

On the limitations of the complex wave velocity for the heterogeneous swirling flows

Abstract The hydrodynamic instability of variable density swirling flows under gravity between two infinite coaxial cylinders is investigated for axisymmetric disturbances. It is shown that the complex wave velocity of any arbitrary unstable axisymmetric mode must lie within the semi-elliptical region whose minor axis depends on the density stratification parameter J(r). The stabilizing effect of density stratification is shown by reducing the semi-circular instability region of [G. K. Batchelor and A. E. Gill, “Analysis of the stability of axisymmetric jets,” J. Fluid Mech., vol. 14, p. 529, 1962]. Furthermore, we have obtained two parabolic instability regions which intersect and reduce the semi-elliptical instability region for density-stratified flows. These parabolic instability regions are uniformly valid for both variable density and density homogeneous flows also.

Three-dimensional Simulations of Massive Stars. II. Age Dependence

We present 3D full star simulations, reaching up to 90% of the total stellar radius, for three 7 M ⊙ stars of different ages: zero-age main sequence (ZAMS), mid–main sequence (midMS), and terminal-age main sequence (TAMS). A comparison with several theoretical prescriptions shows that the generation spectra for all three ages are dominated by convective plumes. Two distinct overshooting layers are observed, with most plumes stopped within the layer situated directly above the convective boundary; overshooting to the second, deeper layer becomes progressively more infrequent with increasing stellar age. Internal gravity wave (IGW) propagation is significantly impacted in the midMS and TAMS models as a result of some IGWs getting trapped within their Brunt–Väisälä frequency spikes. A fundamental change in the wave structure across radius is also observed, driven by the effect of density stratification on IGW propagation causing waves to become evanescent within the radiative zone, with older stars being affected more strongly. We find that the steepness of the frequency spectrum at the surface increases from ZAMS to the older models, with older stars also showing more modes in their spectra.

A Bingham Plastic Fluid Solver for Turbulent Flow of Dense Muddy Sediment Mixtures

We have developed and tested a numerical model for turbulence resolving simulations of dense mud–water mixtures in oscillatory bottom boundary layers, based on a low Stokes number formulation of the two-phase equations. The resulting non-Boussinesq equation for the fluid momentum is coupled to a transport equation for the mud volumetric concentration, giving rise to a volume-averaged fluid velocity that is non-solenoidal, and the model was implemented as a new compressible flow solver. An oscillating pressure gradient force was implemented in the correction step of the standard semi-implicit method for pressure linked equations (SIMPLE), for consistency with the treatment of other volume forces (e.g., gravity). The flow solver was further coupled to a new library for Bingham plastic materials, in order to model the rheological properties of dense mud mixtures using empirically determined concentration-dependent yield stress and viscosity. We present three direct numerical simulation tests to validate the new MudMixtureFoam solver against previous numerical solutions and experimental data. The first considered steady flow of Bingham plastic fluid with uniform concentration around a sphere, with Bingham numbers ranging from 1 to 100 and Reynolds numbers ranging from 0.1 to 100. The second considered the development of turbulence in oscillatory bottom boundary layer flow, and showed the formation of an intermittently turbulent layer with peak velocity perturbations exceeding 10 percent of the freestream flow velocity and occurring at a distance from the bottom comparable to the Stokes boundary layer thickness. The third considered the effects of density stratification due to resuspended sediment on turbulence in oscillatory bottom boundary layer flow with a bulk Richardson number of 1×10−4 and a Stokes–Reynolds number of 1000, and showed the formation of a lutocline between 20 and 40 Stokes boundary layer depths. In all cases, the new solver produced excellent agreement with the previous results.

Hydrodynamic behavior of a circular floating solar pond with an entrapped two-layer fluid

The resonant behavior in a moonpool of a floating circular solar pond, with an entrapped two-layer fluid, is studied. The problem is solved by applying a domain-decomposition method using eigenfunction matching. The surface- and internal-wave elevations and the hydrodynamic coefficients of a typical floating solar pond under forced heave or surge motion are computed. The effects of density stratification on surface-wave elevation, added mass, and damping coefficients are analyzed. A collection of resonance frequencies of surface and internal waves is examined, together with the corresponding variations of modal shapes. For heave resonance, the surface and internal waves are characterized by axisymmetric sloshing modes, as opposed to antisymmetric sloshing modes under surge resonances. A frozen-mode approximation method that treats the moonpool fluid as a density-stratified solid is developed to estimate piston-mode frequencies. Non-dimensional resonance frequencies corresponding to antisymmetric and axisymmetric sloshing modes are estimated based on the standing-wave approximation and reciprocity relations between surface and internal wavenumbers. Satisfactory agreement between the estimated resonance frequencies and those computed by eigenfunction matching method is achieved. It is found that the first resonance of the internal wave, rather than higher-order resonances, is more likely to affect the surface-wave behavior, whereas resonances of the surface-wave modes have significant effects on the internal waves. Parametric analyses are performed to study the effects of geometry configurations of the pond. It is found that the resonance frequencies of internal waves under forced heave or surge motion decrease with an increasing density ratio.

On the Dynamics of Overshooting Convection in Spherical Shells: Effect of Density Stratification and Rotation.

Overshooting of turbulent motions from convective regions into adjacent stably stratified zones plays a significant role in stellar interior dynamics, as this process may lead to mixing of chemical species and contribute to the transport of angular momentum and magnetic fields. We present a series of fully nonlinear, three-dimensional (3D) anelastic simulations of overshooting convection in a spherical shell that are focused on the dependence of the overshooting dynamics on the density stratification and the rotation, both key ingredients in stars that however have not been studied systematically together via global simulations. We demonstrate that the overshoot lengthscale is not simply a monotonic function of the density stratification in the convective region, but instead it depends on the ratio of the density stratifications in the two zones. Additionally, we find that the overshoot lengthscale decreases with decreasing Rossby number Ro and scales as Ro0.23 while it also depends on latitude with higher Rossby cases leading to a weaker latitudinal variation. We examine the mean flows arising due to rotation and find that they extend beyond the base of the convection zone into the stable region. Our findings may provide a better understanding of the dynamical interaction between stellar convective and radiative regions, and motivate future studies particularly related to the solar tachocline and the implications of its overlapping with the overshoot region.

Numerical modeling of the flow of polluted groundwater into the Vyatka River

In the formation of the hydrochemical regime of water bodies and adjacent territories, a significant role is played by the density stratification effects caused by the heterogeneity of the distribution of mineralization fields. When the concentration of the heavy solute is larger than one ppm under terrestrial conditions, these effects have a great influence on the nature of the flow. Such effects can not be described using hydrodynamic models within the framework of shallow water equations; for their correct description, it is necessary to use hydrodynamic models in a full three-dimensional non-hydrostatic formulation. The present paper presents the results of numerical modeling of the formation of diffuse pollution of the Vyatka River during washing of floodplain water bodies (quarries, lakes) in the region of the Kirovo-Chepetsk industrial complex. The assessment of the scale and intensity of the supply of nitrogen-containing compounds was made. The calculation results form the basis for the development of a number of possible measures aimed at both reducing diffuse runoff and ensuring the standard water quality at the main drinking water intake in Kirov, Russia.

Modeling the vertical structure of the ice shelf–ocean boundary current under supercooled condition with suspended frazil ice processes: A case study underneath the Amery Ice Shelf, East Antarctica

In contrast with the severe thinning of ice shelves along the coast of West Antarctica, large ice shelves (specifically, the Filchner–Ronne and Amery Ice Shelves) with deep grounding lines gained mass during the period 1994–2012. This positive mass budget is potentially associated with the marine ice production, which originates from the supercooled Ice Shelf Water plume carrying suspended frazil ice along the ice shelf base. In addition, the outflow of this supercooled plume from beneath the ice shelf arguably exerts a significant impact on the properties of Antarctic Bottom Water, as well as its production. However, knowledge of this buoyant and supercooled shear flow is still limited, let alone its structure that is generally assumed to be vertically uniform. In this study we extended the vertical one-dimensional model of ice shelf–ocean boundary current from Jenkins (2016) by incorporating a frazil ice module and a fairly sophisticated turbulence closure (i.e., k-ε model) with the effects of density stratification. On the basis of this extended model, the study reproduced the measured thermohaline properties of a perennially-prominent supercooled ice shelf–ocean​ boundary current underneath the Amery Ice Shelf in East Antarctica, and conducted extensive sensitivity runs to a wide range of factors, including advection of scalar quantities, far-field geostrophic currents, basal slope, and the distribution of frazil ice crystal size. Based on the simulation results, the following conclusions can be drawn: Firstly, it can be difficult to reasonably reproduce the vertical structure of the ice shelf–ocean boundary current using a constant eddy viscosity/diffusivity near the ice shelf base. Secondly, although there are no direct observations of the size of frazil ice crystals beneath the ice shelves, the size of the finest ice crystals that play an important role in controlling the ice shelf–ocean boundary current is strongly suggested. Lastly, but most importantly, the ice shelf–ocean boundary layer response to the vertical gradient of frazil ice concentration will significantly reduce the level of turbulence. Therefore, this study highlights the importance of the strong interaction between frazil ice formation and the hydrodynamics and thermodynamics of ice shelf–ocean boundary layer. This interaction must not only be included, but also be resolved at high resolutions in three-dimensional coupled ice shelf–ocean models applied to cold ice cavities, which will have a potential impact on the overall ice shelf mass balance and the Antarctic Bottom Water production.

Nonlinear dynamics of two-layer channel flow with soluble surfactant below or above the critical micelle concentration

Abstract

On the inertial effects of density variation in stratified shear flows

In this paper, we first revisit the celebrated Boussinesq approximation in stratified flows. Using scaling arguments we show that when the background shear is weak, the Boussinesq approximation yields either (i) At≪O(1) or (ii) Frc2≪O(1), where At is the ratio of density variation to the mean density and Frc is the ratio of the phase speed to the long wave speed. The second clause implies that, in contrast to the commonly accepted notion, a flow with large density variations can also be Boussinesq. Indeed, we show that deep water surface gravity waves are Boussinesq, while shallow water surface gravity waves are not. However, in the presence of moderate/strong shear, the Boussinesq approximation implies the conventionally accepted At≪O(1). To understand the inertial effects of density variation, our second objective is to explore various non-Boussinesq shear flows and study different kinds of stably propagating waves that can be present at an interface between two fluids of different background densities and vorticities. Furthermore, three kinds of density interfaces—neutral, stable, and unstable—embedded in a background shear layer are investigated. Instabilities ensuing from these configurations, which include Kelvin-Helmholtz, Holmboe, Rayleigh-Taylor, and triangular-jet, are studied in terms of resonant wave interactions. The effects of density stratification and the shear on the stability of each of these flow configurations are explored. Some of the results, e.g., the destabilizing role of density stratification, stabilizing role of shear, etc., are apparently counter-intuitive, but physical explanations are possible if the instabilities are interpreted from wave interaction perspective.In this paper, we first revisit the celebrated Boussinesq approximation in stratified flows. Using scaling arguments we show that when the background shear is weak, the Boussinesq approximation yields either (i) At≪O(1) or (ii) Frc2≪O(1), where At is the ratio of density variation to the mean density and Frc is the ratio of the phase speed to the long wave speed. The second clause implies that, in contrast to the commonly accepted notion, a flow with large density variations can also be Boussinesq. Indeed, we show that deep water surface gravity waves are Boussinesq, while shallow water surface gravity waves are not. However, in the presence of moderate/strong shear, the Boussinesq approximation implies the conventionally accepted At≪O(1). To understand the inertial effects of density variation, our second objective is to explore various non-Boussinesq shear flows and study different kinds of stably propagating waves that can be present at an interface between two fluids of different background densities ...

The modeling of the formation of technogenic thermal pollution zones in large reservoirs

Thermal pollution of water bodies is an unavoidable consequence of thermal or nuclear power plant operation. To minimize the detrimental effects of these plants, one should assess the nature of dangerous zones. The most effective approach to solving these problems is the computational experiment. This paper presents the results of a numerical study of thermal pollution in one of the largest thermal power plants of Europe - Permskaya TPP, using the Kama Reservoir as a natural cooling system. Such problems are traditionally solved in 2D formulation using the “shallow water” approximation. However, with this approach it is impossible to take into account the vertical inhomogeneity of the temperature field. On the other hand, 3D models, which can take into account the effect of density stratification, require very large computational resources. In this work, a combined approach, based on a combination of computational models in the 1D, 2D and 3D formulations, is applied.

Instability of two-layer film flows due to the interacting effects of surfactants, inertia, and gravity

We consider a two-fluid shear flow where the interface between the two fluids is coated with an insoluble surfactant. An asymptotic model is derived in the thin-layer approximation, consisting of a set of nonlinear partial differential equations describing the evolution of the film and surfactant disturbances at the interface. The model includes important physical effects such as Marangoni forces (caused by the presence of surfactant), inertial forces arising in the thick fluid layer, as well as gravitational forces. The aim of this study is to investigate the effect of density stratification or gravity—represented through the Bond number Bo—on the flow stability and the interplay between the different (de)stabilisation mechanisms. It is found that gravity can either stabilise or destabilise the interface (depending on fluid properties) but not always as intuitively anticipated. Different traveling-wave branches are presented for varying Bo, and the destabilising mechanism associated with the Marangoni forces is discussed.

Reinvestigation on mixing length in an open channel turbulent flow

The present study proposes a model on vertical distribution of streamwise velocity in an open channel turbulent flow through a newly proposed mixing length, which is derived for both clear water and sediment-laden turbulent flows. The analysis is based on a theoretical consideration which explores the effect of density stratification on the streamwise velocity profile. The derivation of mixing length makes use of the diffusion equation where both the sediment diffusivity and momentum diffusivity are taken as a function of height from the channel bed. The damping factor present in the mixing length of sediment-fluid mixture contains velocity and concentration gradients. This factor is capable of describing the dip-phenomenon of velocity distribution. From the existing experimental data of velocity, the mixing length data are calculated. The pattern shows that mixing length increases from bed to the dip-position, having a larger value at dip-position and then decreases up to the water surface with a zero value thereat. The present model agrees well with these data sets and this behavior cannot be described by any other existing model. Finally, the proposed mixing length model is applied to find the velocity distribution in wide and narrow open channels. The derived velocity distribution is compared with laboratory channel data of velocity, and the comparison shows good agreement.

Scattering of flexural–gravity waves by a group of elastic plates floating on a stratified fluid

A hydroelastic problem of flexural–gravity wave scattering by a demarcation between two floating elastic plates is investigated within the frame of linear potential-flow theory, where the method of matched eigenfunction expansions is employed for analysis. The formulations are subsequently generalized to the case of multiple elastic plates on a stratified fluid with multiple layers, which is helpful to the study of the hydrodynamic behaviors of inhomogeneous floating covers as well as the effects of density stratification in seawater. The eigenfunction expansions are numerically calculated by an inner product technique, in which an orthogonal definition involving an explicit differential term exhibits the effectiveness in dealing with the multi-layer matching relations between adjacent regions covered by different elastic plates. By use of Green’s theorem, an energy conversation relation is deduced to assure the convergence of the calculation. The high converging rates are exhibited afterwards. The correctness of numerical results are also verified by comparing with a previous analytical method. The details of the hydrodynamic responses of the generalized extension, especially the impact of the fluid stratification on the inner forces of the elastic plates, are discussed for different situations.

The effect of density stratification on the prediction of global storm surges

With the long-term goal of developing an operational forecast system for total water level, we conduct a hindcast study of global storm surges for Fall 2014 using a baroclinic ocean model based on the NEMO framework. The model has 19 vertical levels, a horizontal resolution of 1/12°, and is forced by hourly forecasts of atmospheric wind and air pressure. Our first objective is to evaluate the model’s ability to predict hourly sea levels recorded by a global array of 257 tide gauges. It is shown that the model can provide reasonable predictions of surges for the whole test period at tide gauges with relatively large tidal residuals (i.e., gauges where the standard deviation of observed sea level, after removal of the tide, exceeds 5 cm). Our second objective is to quantify the effect of density stratification on the prediction of global surges. It is found that the inclusion of density stratification increases the overall predictive skill at almost all tide gauges. The increase in skill for the instantaneous peak surge is smaller. The location for which the increase in overall skill is largest (east coast of South Africa) is discussed in detail and physical reasons for the improvement are given.

Особенности численного моделирования плотностных стратификационных эффектов в динамике крупных водохранилищ

Density stratification effects determined by temperature fields and mineralization fields’ distribution heterogeneity can play an essential role in formation of both hydrological and hydro/chemical regime of surface water bodies. At that, they cannot be described within the frameworks of hydrodynamic models in a shallow water statement. Description of these processes within the framework of the combined approach based on the models conjunction in 1D,2D,3D statement with the study cases (water quality formation downstream the Chusvaya and the Sylva rivers confluence in the Kama thermal electro station backwater; features of the Kama reservoir thermal contamination zones formation due to the Kama thermal electro station operation; special features of the high density waste waters diffusion in water bodies) has been made. It has been demonstrated that the proposed calculation scheme will enable to reproduce effectively the processes of the Sylva River more dense water mass dribbling under the Chusovaya waters during winter periods. This has a critical significance for the city of Perm sustainable drinking water supply. It has been shown (with the thermal contamination zones formed by the Perm thermal power station as a study case) that the proposed approach much more reliable in reproduction and assessment of the temperature fields under study than traditional hydro/dynamic shallow water model in 2D statement. Estimation of the potassium industry excessive brines impact on the Kama reservoir has demonstrated higher effectiveness of the proposed method in comparison with those defined by the currently in force regulatory guidelines.

Effect of stratification on wind drift of river runoff in the Kara Sea

The formation mechanism of the Yenisei and Ob Rivers floodwater lens (detected in the Kara Sea near the eastern coast of Novaya Zemlya in September to October 2007) by wind drift is examined. Numerical calculations of the trajectories of Lagrangian floats launched at the north part of the Yenisei and Ob seaside and transported by drift currents have been performed using actual wind-forcing data. Four different algorithms have been used for calculating the surface drift velocity and the relative wind direction; two account for the effect of density stratification due to the presence of a layer of fresh water on the sea surface. It has been shown that only wind-drift models that take into account the presence of stratification are able to explain the transport of the Yenisei and Ob floodwater to the point of lens detection.

Effects of density stratification on the frequencies of the inertial-gravity modes of the Earth's fluid core

Effects of density stratification on the frequencies of the inertial-gravity modes of the Earth's fluid core