Next Issue
Previous Issue

Table of Contents

Fluids, Volume 2, Issue 3 (September 2017)

  • Issues are regarded as officially published after their release is announced to the table of contents alert mailing list.
  • You may sign up for e-mail alerts to receive table of contents of newly released issues.
  • PDF is the official format for papers published in both, html and pdf forms. To view the papers in pdf format, click on the "PDF Full-text" link, and use the free Adobe Readerexternal link to open them.
View options order results:
result details:
Displaying articles 1-14
Export citation of selected articles as:

Research

Jump to: Review

Open AccessArticle An Oceanic Ultra-Violet Catastrophe, Wave-Particle Duality and a Strongly Nonlinear Concept for Geophysical Turbulence
Fluids 2017, 2(3), 36; doi:10.3390/fluids2030036
Received: 12 March 2017 / Revised: 14 June 2017 / Accepted: 16 June 2017 / Published: 29 June 2017
PDF Full-text (4727 KB) | HTML Full-text | XML Full-text
Abstract
There is no theoretical underpinning that successfully explains how turbulent mixing is fed by wave breaking associated with nonlinear wave-wave interactions in the background oceanic internal wavefield. We address this conundrum using one-dimensional ray tracing simulations to investigate interactions between high frequency internal
[...] Read more.
There is no theoretical underpinning that successfully explains how turbulent mixing is fed by wave breaking associated with nonlinear wave-wave interactions in the background oceanic internal wavefield. We address this conundrum using one-dimensional ray tracing simulations to investigate interactions between high frequency internal waves and inertial oscillations in the extreme scale separated limit known as “Induced Diffusion”. Here, estimates of phase locking are used to define a resonant process (a resonant well) and a non-resonant process that results in stochastic jumps. The small amplitude limit consists of jumps that are small compared to the scale of the resonant well. The ray tracing simulations are used to estimate the first and second moments of a wave packet’s vertical wavenumber as it evolves from an initial condition. These moments are compared with predictions obtained from the diffusive approximation to a self-consistent kinetic equation derived in the ‘Direct Interaction Approximation’. Results indicate that the first and second moments of the two systems evolve in a nearly identical manner when the inertial field has amplitudes an order of magnitude smaller than oceanic values. At realistic (oceanic) amplitudes, though, the second moment estimated from the ray tracing simulations is inhibited. The transition is explained by the stochastic jumps obtaining the characteristic size of the resonant well. We interpret this transition as an adiabatic ‘saturation’ process which changes the nominal background wavefield from supporting no mixing to the point where that background wavefield defines the normalization for oceanic mixing models. Full article
(This article belongs to the collection Geophysical Fluid Dynamics)
Figures

Figure 1

Open AccessArticle Interaction between a Quasi-Geostrophic Buoyancy Filament and a Heton
Fluids 2017, 2(3), 37; doi:10.3390/fluids2030037
Received: 15 June 2017 / Revised: 27 June 2017 / Accepted: 28 June 2017 / Published: 3 July 2017
Cited by 1 | PDF Full-text (17405 KB) | HTML Full-text | XML Full-text
Abstract
We investigate the interaction between a heton and a current generated by a filament of buoyancy anomaly at the surface. Hetons are baroclinic dipoles consisting of a pair of vortices of opposite signs lying at different depths. Such structures have self-induced motion whenever
[...] Read more.
We investigate the interaction between a heton and a current generated by a filament of buoyancy anomaly at the surface. Hetons are baroclinic dipoles consisting of a pair of vortices of opposite signs lying at different depths. Such structures have self-induced motion whenever the pair of vortices are offset horizontally. A surface buoyancy filament generates a shear flow since the density perturbation locally modifies the pressure field. The vertical shear induced by the filament offsets the vortices of the heton if vertically aligned initially. Moreover, if the vortex nearer the surface is in adverse horizontal shear with the buoyancy filament, the heton tends to move towards the filament. Conversely, if the upper vortex is in cooperative horizontal shear with the buoyancy filament, the heton moves away from it. The filament is also naturally unstable and eventually breaks into a series of billows as it is perturbed by the heton. Moderate to large intensity surface buoyancy distributions separate the vortices of the heton, limiting its advection as a baroclinic dipole. Instead, the vortices of the heton start to interact strongly with surface billows. Additionally, the vortices of the heton can be partially destroyed by the filament if the shear it induces is sufficiently large. Full article
(This article belongs to the collection Geophysical Fluid Dynamics)
Figures

Figure 1

Open AccessArticle The Reduced NS-α Model for Incompressible Flow: A Review of Recent Progress
Fluids 2017, 2(3), 38; doi:10.3390/fluids2030038
Received: 3 June 2017 / Revised: 19 June 2017 / Accepted: 30 June 2017 / Published: 6 July 2017
PDF Full-text (1403 KB) | HTML Full-text | XML Full-text
Abstract
This paper gives a review of recent results for the reduced Navier–Stokes-α (rNS-α) model of incompressible flow. The model was recently developed as a numerical approximation to the well known Navier–Stokes-α model, for the purpose of more efficiently computations in the C0
[...] Read more.
This paper gives a review of recent results for the reduced Navier–Stokes-α (rNS-α) model of incompressible flow. The model was recently developed as a numerical approximation to the well known Navier–Stokes-α model, for the purpose of more efficiently computations in the C0 finite element setting. Its performance in initial numerical tests was remarkable, which led to analytical studies and further numerical tests, all of which provided excellent results. This paper reviews the main results established thus far for rNS-α, and presents some open problems for future work. Full article
(This article belongs to the Special Issue Turbulence: Numerical Analysis, Modelling and Simulation)
Figures

Figure 1

Open AccessArticle Interaction of the Longwave and Finite-Wavelength Instability Modes of Convection in a Horizontal Fluid Layer Confined between Two Fluid-Saturated Porous Layers
Fluids 2017, 2(3), 39; doi:10.3390/fluids2030039
Received: 2 May 2017 / Revised: 6 July 2017 / Accepted: 14 July 2017 / Published: 16 July 2017
PDF Full-text (1449 KB) | HTML Full-text | XML Full-text
Abstract
The onset of convection in a three-layer system consisting of two fluid-saturated porous layers separated by a homogeneous fluid layer is studied. It is shown that both a longwave convective regime developing in the whole system and a finite-wavelength regime of convection concentrated
[...] Read more.
The onset of convection in a three-layer system consisting of two fluid-saturated porous layers separated by a homogeneous fluid layer is studied. It is shown that both a longwave convective regime developing in the whole system and a finite-wavelength regime of convection concentrated in the homogeneous fluid layer are possible. Due to the hydraulic resistance of the porous matrix, the flow intensity in the longwave convective regime is much lower than that in the finite-wavelength regime. Moreover, it grows at a much slower pace with the increase of the Grashof number. Because of that, the long-wave convective regime becomes unstable at small supercriticalities and is replaced by a finite-wavelength regime. Full article
(This article belongs to the Special Issue Convective Instability in Porous Media)
Figures

Figure 1

Open AccessArticle Regimes of Axisymmetric Flow and Scaling Laws in a Rotating Annulus with Local Convective Forcing
Fluids 2017, 2(3), 41; doi:10.3390/fluids2030041
Received: 8 June 2017 / Revised: 14 July 2017 / Accepted: 16 July 2017 / Published: 19 July 2017
PDF Full-text (8182 KB) | HTML Full-text | XML Full-text | Supplementary Files
Abstract
We present a numerical study of axisymmetric flow in a rotating annulus in which local thermal forcing, via a heated annular ring on the outside of the base and a cooled circular disk in the centre of the top surface, drives convection. This
[...] Read more.
We present a numerical study of axisymmetric flow in a rotating annulus in which local thermal forcing, via a heated annular ring on the outside of the base and a cooled circular disk in the centre of the top surface, drives convection. This new configuration is a variant of the classical thermally-driven annulus, where uniform heating and cooling are applied through the outer and inner sidewalls respectively. The annulus provides an analogue to a planetary circulation and the new configuration, with its more relaxed vertical thermal boundary conditions, is expected to better emulate vigorous convection in the tropics and polar regions as well as baroclinic instability in the mid-latitude baroclinic zone. Using the Met Office/Oxford Rotating Annulus Laboratory (MORALS) code, we have investigated a series of equilibrated, two dimensional axisymmetric flows across a large region of parameter space. These are characterized in terms of their velocity and temperature fields. When rotation is applied several distinct flow regimes may be identified for different rotation rates and strengths of differential heating. These regimes are defined as a function of the ratio of the horizontal Ekman layer thickness to the non-rotating thermal boundary layer thickness and are found to be similar to those identified in previous annulus experiments. Convection without rotation is also considered and the scaling of the heat transport with Rayleigh number is calculated. This is then compared with existing work on the classical annulus as well as horizontal and Rayleigh-Bénard convection. As with previous studies on both rotating and non-rotating convection the system’s behaviour is found to be aspect ratio dependent. This dependence is seen in the scaling of the non-rotating Nusselt number and in transitions between regimes in the rotating case although further investigation is required to fully explain these observations. Full article
(This article belongs to the collection Geophysical Fluid Dynamics)
Figures

Figure 1

Open AccessArticle Onset of Primary and Secondary Instabilities of Viscoelastic Fluids Saturating a Porous Layer Heated from below by a Constant Flux
Fluids 2017, 2(3), 42; doi:10.3390/fluids2030042
Received: 3 April 2017 / Revised: 4 July 2017 / Accepted: 19 July 2017 / Published: 22 July 2017
PDF Full-text (418 KB) | HTML Full-text | XML Full-text
Abstract
We analyze the thermal convection thresholds and linear characteristics of the primary and secondary instabilities for viscoelastic fluids saturating a porous horizontal layer heated from below by a constant flux. The Galerkin method is used to solve the eigenvalue problem by taking into
[...] Read more.
We analyze the thermal convection thresholds and linear characteristics of the primary and secondary instabilities for viscoelastic fluids saturating a porous horizontal layer heated from below by a constant flux. The Galerkin method is used to solve the eigenvalue problem by taking into account the elasticity of the fluid, the ratio between the viscosity of the solvent and the total viscosity of the fluid and the lateral confinement of the medium. For the primary instability, we found out that depending on the rheological parameters, two types of convective structures may appear when the basic conductive solution loses its stability: stationary long wavelength instability as for Newtonian fluids and oscillatory convection. The effect of the lateral confinement of the porous medium by adiabatic walls is to stabilize the oblique and longitudinal rolls and therefore selects transverse rolls at the onset of convection. In the range of the rheological parameters where stationary long wave instability develops first, we use a parallel flow approximation to determine analytically the velocity and temperature fields associated with the monocellular convective flow. The linear stability analysis of the monocellular flow is performed, and the critical conditions above which the flow becomes unstable are determined. The combined influence of the viscoelastic parameters and the lateral confinement on the characteristics of the secondary instability is quantified. The major new findings concerning the secondary instabilities may be summarized as follows: (i) For concentrated viscoelastic fluids, computations showed that the most amplified mode of convection corresponds to oscillatory transverse rolls, which appears via a Hopf bifurcation. This pattern selection is independent of both the fluid elasticity and the lateral confinement of the porous medium. (ii) For diluted viscoelastic fluids, the preferred mode of convection is found to be oscillatory transverse rolls for a very laterally-confined medium. Otherwise, stationary or oscillatory longitudinal rolls may develop depending on the fluid elasticity. Results also showed the destabilizing effect of the relaxation fluid elasticity and the stabilizing effect of the viscosity ratio for the onset of both primary and secondary instabilities. Full article
(This article belongs to the Special Issue Convective Instability in Porous Media)
Figures

Figure 1

Open AccessArticle Stable Vortices in a Continuously Stratified Ocean with Thin Active Layer
Fluids 2017, 2(3), 43; doi:10.3390/fluids2030043
Received: 27 June 2017 / Revised: 9 July 2017 / Accepted: 20 July 2017 / Published: 25 July 2017
PDF Full-text (257 KB) | HTML Full-text | XML Full-text
Abstract
This paper presents a model which yields examples of stable vortices in a continuously stratified rotating fluid, thus providing a possible explanation of the observed longevity of oceanic eddies. The model is based on two assumptions. Firstly, the ocean comprises a thin upper
[...] Read more.
This paper presents a model which yields examples of stable vortices in a continuously stratified rotating fluid, thus providing a possible explanation of the observed longevity of oceanic eddies. The model is based on two assumptions. Firstly, the ocean comprises a thin upper (active) layer and a thick lower (passive) one, with large and small vertical gradients of density, respectively. Secondly, the Rossby number is small, justifying the use of the geostrophic and quasi-geostrophic approximations for the active and passive layers (the two are treated differently because the vortex-induced displacement of the isopycnal surfaces is comparable to the depth of the active layer, but is much smaller than that of the passive one). Using the asymptotic equations derived on the basis of the above assumptions, we prove a stability criterion and thus identify a class of stable vortex profiles. This class is much wider than the one following from the standard requirement that the potential vorticity be monotonic in the whole bulk of the fluid. Full article
(This article belongs to the collection Geophysical Fluid Dynamics)
Open AccessArticle Thermal Convection in a Rotating Anisotropic Fluid Saturated Darcy Porous Medium
Fluids 2017, 2(3), 44; doi:10.3390/fluids2030044
Received: 8 April 2017 / Revised: 11 August 2017 / Accepted: 15 August 2017 / Published: 21 August 2017
PDF Full-text (339 KB) | HTML Full-text | XML Full-text
Abstract
The stability of the thermal convection in a fluid-saturated rotating anisotropic porous material is investigated. We take into account the rotation of a layer of saturated porous medium about an axis orthogonal to the planes bounding the layer. The permeability is allowed to
[...] Read more.
The stability of the thermal convection in a fluid-saturated rotating anisotropic porous material is investigated. We take into account the rotation of a layer of saturated porous medium about an axis orthogonal to the planes bounding the layer. The permeability is allowed to be an anisotropic tensor. In particular, we restrict our attention to the case where the permeability in the vertical direction is different to that in the horizontal plane. The linear instability and nonlinear stability analysis, in the case where the inertial term vanishes, are performed. It is shown, by using an energy method, that the nonlinear critical Rayleigh numbers coincide with those of the linear analysis. The results reveal that the system becomes more stable when the rotation is present. Full article
(This article belongs to the Special Issue Convective Instability in Porous Media)
Figures

Figure 1

Open AccessArticle The Impact of Horizontal Resolution on Energy Transfers in Global Ocean Models
Fluids 2017, 2(3), 45; doi:10.3390/fluids2030045
Received: 15 July 2017 / Revised: 15 August 2017 / Accepted: 24 August 2017 / Published: 28 August 2017
PDF Full-text (5934 KB) | HTML Full-text | XML Full-text
Abstract
The ocean is a turbulent fluid with processes acting on a variety of spatio-temporal scales. The estimates of energy fluxes between length scales allows us to understand how the mean flow is maintained as well as how mesoscale eddies are formed and dissipated.
[...] Read more.
The ocean is a turbulent fluid with processes acting on a variety of spatio-temporal scales. The estimates of energy fluxes between length scales allows us to understand how the mean flow is maintained as well as how mesoscale eddies are formed and dissipated. Here, we quantify the kinetic energy budget in a suite of realistic global ocean models, with varying horizontal resolution and horizontal viscosity. We show that eddy-permitting ocean models have weaker kinetic energy cascades than eddy-resolving models due to discrepancies in the effect of wind forcing, horizontal viscosity, potential to kinetic energy conversion, and nonlinear interactions on the kinetic energy (KE) budget. However, the change in eddy kinetic energy between the eddy-permitting and the eddy-resolving model is not enough to noticeably change the scale where the inverse cascade arrests or the Rhines scale. In addition, we show that the mechanism by which baroclinic flows organise into barotropic flows is weaker at lower resolution, resulting in a more baroclinic flow. Hence, the horizontal resolution impacts the vertical structure of the simulated flow. Our results suggest that the effect of mesoscale eddies can be parameterised by enhancing the potential to kinetic energy conversion, i.e., the horizontal pressure gradients, or enhancing the inverse cascade of kinetic energy. Full article
(This article belongs to the collection Geophysical Fluid Dynamics)
Figures

Figure 1

Open AccessArticle Lagrangian Modeling of Turbulent Dispersion from Instantaneous Point Sources at the Center of a Turbulent Flow Channel
Fluids 2017, 2(3), 46; doi:10.3390/fluids2030046
Received: 5 August 2017 / Revised: 30 August 2017 / Accepted: 6 September 2017 / Published: 8 September 2017
PDF Full-text (1733 KB) | HTML Full-text | XML Full-text
Abstract
The paper is focused on the simulation and modeling of the dispersion from an instantaneous source of heat or mass located at the center of a turbulent flow channel. The flow is modeled with a direct numerical simulation, and the dispersion is modeled
[...] Read more.
The paper is focused on the simulation and modeling of the dispersion from an instantaneous source of heat or mass located at the center of a turbulent flow channel. The flow is modeled with a direct numerical simulation, and the dispersion is modeled with Lagrangian methods based on Lagrangian scalar tracking (LST). The LST technique allows the simulation of scalar sources that span a range of Prandtl or Schmidt numbers that cover orders of magnitude. The trajectories of individual heat or mass markers are tracked, generating a probability distribution function that describes the behavior of instantaneous point sources of a scalar in the turbulent field. The effect of the Prandtl or Schmidt number on turbulent dispersion is examined, with emphasis on the dispersion pattern. Results for Prandtl or Schmidt numbers between 0.1 and 15,000 are presented. For an instantaneous source at the channel center, it is found that there are two zones of cloud development: one where molecular diffusion plays a role at very small times (early stage of the dispersion), and one where turbulent convection dominates. The asphericity of the scalar marker cloud is found to increase monotonically, in contrast to published results for isotropic, homogenous turbulence, where the asphericity goes through a maximum. Full article
(This article belongs to the Special Issue Turbulence: Numerical Analysis, Modelling and Simulation)
Figures

Open AccessArticle Non-Iterative Partitioned Methods for Uncoupling Evolutionary Groundwater–Surface Water Flows
Fluids 2017, 2(3), 47; doi:10.3390/fluids2030047
Received: 1 July 2017 / Revised: 22 August 2017 / Accepted: 26 August 2017 / Published: 10 September 2017
PDF Full-text (824 KB) | HTML Full-text | XML Full-text
Abstract
We present an overview of a modern, efficient approach for uncoupling groundwater–surface water flows governed by the fully evolutionary Stokes–Darcy equations. Referred to as non-iterative partitioned methods, these algorithms treat the coupling terms explicitly and at each time level require only one Stokes
[...] Read more.
We present an overview of a modern, efficient approach for uncoupling groundwater–surface water flows governed by the fully evolutionary Stokes–Darcy equations. Referred to as non-iterative partitioned methods, these algorithms treat the coupling terms explicitly and at each time level require only one Stokes and one Darcy sub-physics solve, thus taking advantage of existing solvers optimized for each sub-flow. This strategy often results in a time-step condition for stability. Furthermore, small problem parameters, specifically those related to the physical characteristics of the porous media domain, can render certain time-step conditions impractical. Despite these obstacles, researchers have made significant progress towards efficient, stable, and accurate partitioned methods. Herein, we provide a comprehensive survey and comparison of recent developments utilizing these non-iterative numerical schemes. Full article
(This article belongs to the Special Issue Turbulence: Numerical Analysis, Modelling and Simulation)
Figures

Figure 1

Open AccessArticle Modelling Bidispersive Local Thermal Non-Equilibrium Flow
Fluids 2017, 2(3), 48; doi:10.3390/fluids2030048
Received: 1 August 2017 / Revised: 12 September 2017 / Accepted: 13 September 2017 / Published: 18 September 2017
PDF Full-text (233 KB) | HTML Full-text | XML Full-text
Abstract
In this work, we present a system of equations which describes non-isothermal flow in a bidispersive porous medium under conditions of local thermal non-equilibrium. The porous medium consists of macro pores, and in the solid skeleton are cracks or fissures which give rise
[...] Read more.
In this work, we present a system of equations which describes non-isothermal flow in a bidispersive porous medium under conditions of local thermal non-equilibrium. The porous medium consists of macro pores, and in the solid skeleton are cracks or fissures which give rise to micro pores. The temperatures in the solid skeleton and in the fluids in the macro and micro pores are all allowed to be independent. After presenting the general model, we derive a result of universal stability, which guarantees exponential decay of the solution for all initial data. We further present a concrete example by specializing the model to the problem of thermal convection in a layer heated from below. Full article
(This article belongs to the Special Issue Convective Instability in Porous Media)

Review

Jump to: Research

Open AccessReview A Short Review of Advances in the Modelling of Blood Rheology and Clot Formation
Fluids 2017, 2(3), 35; doi:10.3390/fluids2030035
Received: 21 May 2017 / Revised: 19 June 2017 / Accepted: 20 June 2017 / Published: 28 June 2017
PDF Full-text (277 KB) | HTML Full-text | XML Full-text
Abstract
Several advances have taken place since the early 2000s in the field of blood flow modelling. These advances have been driven by the development of assist devices such as Left Ventricular Assist Devices (LVADs), etc., and by the acceptance of in silico tests
[...] Read more.
Several advances have taken place since the early 2000s in the field of blood flow modelling. These advances have been driven by the development of assist devices such as Left Ventricular Assist Devices (LVADs), etc., and by the acceptance of in silico tests for the generation of hypotheses concerning clot formation and lysis. We give an overview of the developments in modelling of blood rheology and clot formation/lysis in the last 10 to 15 years. In blood rheology, advances are increasingly supplemented by flow simulation studies. In clot formation (or coagulation), advances have taken place in both single-scale modeling under quiescent conditions as well as in multi-scale modeling in the presence of flow. The future will possibly see more blood flow simulations in complex geometries and, simultaneously, development and simulation of multi-scale models for clot formation and lysis. Full article
Figures

Figure 1

Open AccessReview A Review of Time Relaxation Methods
Fluids 2017, 2(3), 40; doi:10.3390/fluids2030040
Received: 20 June 2017 / Revised: 7 July 2017 / Accepted: 10 July 2017 / Published: 17 July 2017
PDF Full-text (3524 KB) | HTML Full-text | XML Full-text
Abstract
The time relaxation model has proven to be effective in regularization of Navier–Stokes Equations. This article reviews several published works discussing the development and implementations of time relaxation and time relaxation models (TRMs), and how such techniques are used to improve the accuracy
[...] Read more.
The time relaxation model has proven to be effective in regularization of Navier–Stokes Equations. This article reviews several published works discussing the development and implementations of time relaxation and time relaxation models (TRMs), and how such techniques are used to improve the accuracy and stability of fluid flow problems with higher Reynolds numbers. Several analyses and computational settings of TRMs are surveyed, along with parameter sensitivity studies and hybrid implementations of time relaxation operators with different regularization techniques. Full article
(This article belongs to the Special Issue Turbulence: Numerical Analysis, Modelling and Simulation)
Figures

Figure 1

Back to Top