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The background potential energy (BPE) is the only reservoir that double diffusive instabilities can tap their energy from when developing from an unforced motionless state with no available potential energy (APE). Recently, Middleton and Taylor linked the extraction of BPE into APE to the sign of the diapycnal component of the buoyancy flux, but their criterion can predict only diffusive convection instability, not salt finger instability. Here, we show that the problem can be corrected if the sign of the APE dissipation rate is used instead, making it emerge as the most fundamental criterion for double diffusive instabilities. A theory for the APE dissipation rate for a two-component fluid relative to its single-component counterpart is developed as a function of three parameters: the diffusivity ratio, the density ratio, and a spiciness parameter. The theory correctly predicts the occurrence of both salt finger and diffusive convection instabilities in the laminar unforced regime, while more generally predicting that the APE dissipation rate for a two-component fluid can be enhanced, suppressed, or even have the opposite sign compared to that for a single-component fluid, with important implications for the study of ocean mixing. Because negative APE dissipation can also occur in stably stratified single-component and doubly stable two-component stratified fluids, we speculate that only the thermodynamic theory of exergy can explain its physics; however, this necessitates accepting that APE dissipation is a conversion between APE and the internal energy component of BPE, in contrast to prevailing assumptions. [ABSTRACT FROM AUTHOR]

This study proposes a new mechanism that can lead to layering or convection from the finite amplitude perturbation acting on the double diffusive convection with uniform background shear. We focus on the double diffusive convection in the diffusive regime with the cold fresh water laying above the warm salty water. We demonstrate that, although the unperturbed system is linearly stable, the finite amplitude perturbation can trigger the initial flow motions which subsequently obtain energy from the gravitational potential energy and from the uniform background shear, and evolve to layering or convection. By using the linear stability analysis for the initial growth stage and the energy analysis for the following transitional stage, the critical Richardson number can be predicted theoretically. Here the Richardson number measures the relative strength of stratification to the background shear. The dominant wavenumbers and the growth rates of the corresponding modes given by linear theory agree well with the two-dimensional direct numerical simulations, and so does the critical Richardson number predicted by the theoretical model. The layering state is dominated by the double diffusion process, while the convection state at smaller Richardson number exhibits stronger influences from shear and generates smaller heat and salinity fluxes. The theoretical model is further applied to the parameter range which is relevant to the real oceanic environments and reveals that for the typical density ratio observed in the staircase regions in the Arctic Ocean, the current mechanism can lead to layering for relatively weak shear. [ABSTRACT FROM AUTHOR]

The Soret effect, also known as thermal diffusion, plays a crucial role in the phenomenon of double diffusion convection in liquids. This study investigates Soret-driven convection within a vertical double-diffusive layer of Maxwell-Cattaneo (M-C) fluids, where the boundaries maintain constant temperatures and solute concentrations that are distinct from each other. The heat transfer equation for Maxwell-Cattaneo fluids is governed by a hyperbolic rule of heat conduction, rather than the typical Fourier parabolic one. The Chebyshev collocation method is employed to solve the corresponding stability eigenvalue problem. The neutral stability curve shows significant fluctuation responses due to the M-C effect. When the Cattaneo number (C) reaches 0.02, multiple local minima appear in the critical Grashof number (Gr). The instability the thermal convection is found to be amplified by the combined effects of Maxwell-Cattaneo and Soret, along with the Grashof number, while the double diffusion effect appears to suppress the instability of convective system. The influence of Soret effect on convective instability will diminish dramatically as the Gr number rises above 8200. [ABSTRACT FROM AUTHOR]

The convection stability of Maxwell–Cattaneo fluids in a vertical double-diffusive layer is investigated. Maxwell–Cattaneo fluids mean that the response of the heat flux with respect to the temperature gradient satisfies a relaxation time law rather than the classical Fourier one. The Chebyshev collocation method is used to resolve the linearized forms of perturbation equations, leading to the formulation of stability eigenvalue problem. By numerically solving the eigenvalue problem, the neutral stability curves in the a–Gr plane for the different values of solute Rayleigh number RaS are obtained. Results show that increasing the double diffusion effect and Louis number Le can suppress the convective instability. Furthermore, compared with Fourier fluid, the Maxwell–Cattaneo fluids in a vertical slot cause an oscillation on the neutral stability curve. The appearance of Maxwell–Cattaneo effect enhances the convection instability. Meanwhile, it is interesting to find that the Maxwell–Cattaneo effect for convective instability becomes stronger as the Prandtl number rises. That means Prandtl number (Pr) also has a significant effect on convective instability. Moreover, the occurrence of two minima on the neutral curve can be found when Pr reaches 12.

In this study, the effect of throughflow and variable gravity field on the stability of double diffusive convection in a fluid layer for the system when heating and salting both are done from below, are investigated. The linear and energy techniques are regulated to check the stability characteristics of the system. The numerical results of linear and non-linear techniques are compared to check the subcritical region. The Chebyshev pseudo-spectral technique is applied to find the influences of distinct physical parameters on the stability of the system. [ABSTRACT FROM AUTHOR]

The present study reports the linear stability analysis of cross diffusive free colivective thermosolutal flow of viscoelastic Maxwell fluid in a horizontal layer with chemical reaction in porous medium. The flow is driven with external heat source. The solutal transfer effect is supported by chemical reaction. The temperature gradient is also used as a flow supportive component. The onset of flow stability is calculated analytically with free-free boundaries.The neutral stability curves are plotted graphically with respect to distinguished physical parameters. Stabilizing and destabilizing characteristics of Soret parameter, Dufour parameter and Lewis number are observed during stationary convection. The impact of chemically reacting parameter Kr in delaying the commencement of convection is analysed in the oscillatory mode analysis. [ABSTRACT FROM AUTHOR]

Numerical simulations have been conducted to examine the structure of diffusive-convection staircases in the presence of vortical-mode-induced turbulent forcing. By modulating the input power $P$ and the background density ratio $R_\rho$ , we have identified three distinct types of staircase structures in these simulations: namely staircases maintained in the system driven by double-diffusion, by turbulence or by a combination of both double-diffusion and turbulence. While we showed that staircases maintained in the double-diffusion-dominated system are accurately characterised by the existing model originally proposed by Linden & Shirtcliffe (J. Fluid Mech. , vol. 87, no. 3, 1978, pp. 417–432), we introduced new physical models to describe the staircase structures maintained in the turbulence-dominated system and the system driven by both turbulence and double-diffusion. Our integrated model reveals that turbulence fundamentally governs the entire life cycle of the diffusive-convection staircases, encompassing their formation, maintenance and eventual disruption in the Arctic Ocean's thermohaline staircases. While our previous work of Ma & Peltier (J. Fluid Mech. , vol. 931, 2022 b) demonstrated that turbulence could initiate the formation of Arctic staircases, these staircases are sustained by both turbulence and double-diffusion acting together after formation has occurred. Strong turbulence may disrupt staircase structures; however, the presence of weak turbulence could lead to unstable stratification within mixed layers of the staircases, as well as enhancing vertical heat and salt fluxes. Turbulence can even sustain a stable staircase structure factor when $R_\rho$ is relatively large, following a similar mechanism to the density staircases observed in laboratory experiments. Consequently, previous parameterisations (e.g. Kelley, J. Geophys. Res.: Oceans , vol. 95, no. C3, 1990, pp. 3365–3371) on the vertical heat flux across the diffusive-convection staircases may provide a significant underestimation of the heat transport by ignoring the influences of turbulence. [ABSTRACT FROM AUTHOR]

Melting icebergs provide nearly half of the total freshwater flux from ice shelves to the ocean, but the availability of accurate, data-constrained melting rate parametrisations limits the correct representation of this process in ocean models. Here, we investigate the melting of a vertical ice face in a warm, salt-stratified environment in a laboratory setting. Observations of the depth-dependent melting rates ${m}$ and boundary layer flow speed $U$ are reported for a range of initially uniform far-field ambient temperatures $T_a$ above ${10}\,^{\circ }{\rm C}$. Ice scallops are characteristic features observed in all experiments, with the width of the scallops consistent with the theory of double-diffusive layers. The morphology of the scallops changes from symmetric about the scallop centre in the colder experiments to asymmetric in the warmer experiments. Observed melting rates are consistent with a melting rate scaling of the form ${m}\propto U\,\Delta T_a$ proposed by previous work in less extreme parameter regimes, where $\Delta T_a$ is the magnitude of thermal driving between the ambient and ice–fluid interface. Our results indicate that ice scalloping is closely linked to the naturally convecting flow of the ambient fluid. Depth-averaged melting rates depend on the buoyancy frequency in the ambient fluid, and double-diffusive convection promotes a turbulent-flux regime distinct from that explained previously in an unstratified regime. These findings have implications for parametrising melting rates of icebergs and glaciers in numerical models or potential freshwater harvesting operations, and provide insights into the interplay between stratification and ice melting. [ABSTRACT FROM AUTHOR]

This article aims to study double-diffusive magneto-convective flow of electrically conducting and Newtonian fluid in the presence of throughflow and concentration modulation. Here, two infinite horizontal plates have been considered with heated from below and cooled and salted from above. The flow is also influenced by the induced magnetic field for which a constant magnetic field is applied in the perpendicular direction to the plates and vertically upward direction. A weakly nonlinear analysis is used to obtain the expression of heat and mass transport rate using Ginzburg–Landau equation. The influence of various physical parameters on Nusselt and Sherwood numbers is presented by graphs. From the numerical outcome, it is found that Péclet, Chandrasekhar, and magnetic Prandtl numbers enhance the mass and heat transport rate, while Lewis number increases only the rate of mass transport. The major result of this study is that the onset of convection postpones in the presence of throughflow and magnetic field.

In numerical studies of thermal convection that includes a layer of lighter surface fluid, the light fluid naturally forms clusters that bulge downward at downwelling sites. A curious result is that in some cases, the clusters have maximum bulging downward near the sides of the cluster instead of a single bulge downward centred above the downwelling. The fluid mechanics leading to this 'double bulge' formation is analysed. To accomplish this, a simplified model replaces the thermally driven convection cells with driving cells with a fixed speed. Adding a layer of dense fluid on the bottom to the previous configuration leads to bulges along the top and bottom. More importantly, this allows a new scaling that reduces the number of governing parameters from four to three and even to two in this study. The mechanism for the double bulges comes from buoyancy of the clusters. This produces localized vorticity at the sides of the cluster that has the opposite sign of the driving cells. When this vorticity is approximately the same order of magnitude as the driving cell vorticity, a divergence in the middle of each cluster leads to the double bulges. The effect can be so great that the underlying flow cells are tilted so that vertical motion is reversed under the middle of each bulge. [ABSTRACT FROM AUTHOR]

Thermal radiations are extensively utilized in the medical sciences, and the investigation of thermal radiation combined with double diffusive phenomena is the burning research area because of its enormous applications in treatment of various diseases. Cilia play significant part in many physiological processes of animal and humans. A novel mathematical prodigy for Prandtl nanofluid with thermal radiations and double diffusion convection by implementing slip at boundaries is presented for cilia induce flow in an asymmetric microchannel. Mathematical scheme for the physiological flow is developed and then pertinent equations are designed exploiting low Reynolds number and long wavelength simplifications. Solution for the physiological nanofluid is gathered by emphasizing on the novel BVP4C technique in MATLAB and resulting outcomes are elaborated with aid of graphical illustrations. Pros and cons of various physical flow parameters like thermal slip parameters, Prandtl fluid parameters, Grashof parameter, Prandtl parameter , Brownian motion parameter, thermal radiation parameter, Brinkmann number, Soret parameter are examined on the velocity, magnetic force function, temperature profile, concentration and nanoparticles volume fraction. It is reported that slip parameter really effects the nanofluid transport within the ciliated microchannel, it reduces the fluid flow, diffusion phenomena of the nanoparticles in the ciliated microchannel surges when radiation parameter is strengthened. The reported investigation will be instrumental in heat radiation effect for regulation of blood circulation to cure the cancer tissues in multiple drug delivery systems and will pave the way for the designs of certain diagnostic and pharmacological devices.

The magnetic and chemical reaction effects on the onset of thermosolutal convection in a penetrative internally heated fluid are investigated for the case when the plane layer has a constant temperature and salt concentration on the upper surface and a specified heat flux and salt flux on the bottom surface. The linear instability and nonlinear stability boundaries are analyzed using the Chebyshev collocation method to calculate the corresponding eigenvalue systems according to the boundary conditions. Two distinct internal heat source functions are examined: the first kind is a constant, and the second kind is to heat the bottom half of the surface while cooling the rest. The Rayleigh number is graphically represented with the various parameter effects. The outcomes indicate that utilizing magnetic, chemical reactions, and internal heat sources has a significant influence on defining the thermosolutal convection stabilization and destabilization thresholds. For all types of internal heat sources, it is found that the magnetic field has a stabilizing effect. It is also noted that the effects of chemical reaction, heat flux, and salt flux play important factors in the stability region. [ABSTRACT FROM AUTHOR]

The present work aims at clarifying the effects of a solid boundary on the salt fingers in the wall-bounded double diffusive convection turbulence driven by the salinity and temperature differences between the top and bottom plates. The fluid properties are the same as the seawater, and two-dimensional direct numerical simulations are conducted over a wide range of the thermal and salinity Rayleigh numbers which measure the strength of driving salinity difference and stabilising temperature difference. We find that the bulk density ratio ?b, defined by the mean temperature and salinity gradients at the bulk, controls the flow morphology. As ?b exceeds unity, the bulk flow shifts from wide convection rolls to slender salt fingers. Two different regimes are further identified for the cases of salt-finger type. One is the confined salt-finger regime where the characteristic height of salt fingers is comparable to the bulk height and the influences of the solid boundary are noticeable. The other is the free salt-finger regime where the salt fingers are much shorter than the bulk height. In this latter regime, the transport properties versus ?b are in quantitative agreement with those obtained in the fully periodic domain (e.g. Traxler et al., J. Fluid Mech., vol. 677, 2011, pp. 530-553). For a limited range of density ratio at the highest salinity Rayleigh number considered here, multiple states can be obtained from different initial conditions. The large-scale secondary instability and spontaneous formation of staircase from finger layers are not observed in the current study. [ABSTRACT FROM AUTHOR]

Understanding the dynamics of staircases in salt fingering convection presents a long-standing theoretical challenge to fluid dynamicists. Although there has been significant progress, particularly through numerical simulations, there are a number of conflicting theoretical explanations as to the driving mechanism underlying staircase formation. The Phillips effect proposes that layering in stirred stratified flow is due to an antidiffusive process, and it has been suggested that this mechanism may also be responsible for salt fingering staircases. However, the details of this process, as well as mathematical models to predict the evolution and merger dynamics of staircases, have yet to be established. We generalise the theory of the Phillips effect to a three-component system (e.g. temperature, salinity, energy) and demonstrate a regularised nonlinear model of layering based on mixing length parametrisations. The model predicts both the inception of layering and its long-term evolution through mergers, while generalising, and remaining consistent with, previous results for double-diffusive layering based on flux ratios. Our model of salt fingering is formulated using spatial averaging processes, and closed by a mixing length parametrised in terms of the kinetic energy and the ratio of the temperature and salt gradients. The model predicts a layering instability for a bounded range of parameter values in the salt fingering regime. Nonlinear solutions show that an initially unstable linear buoyancy gradient develops into layers, which proceed to merge through a process of stronger interfaces growing at the expense of weaker ones. Our results indicate that these mergers are responsible for the characteristic increase of buoyancy flux through thermohaline staircases. [ABSTRACT FROM AUTHOR]

To improve the heat storage capacity of a salt gradient solar pond(SGSP), a full understanding on the thermal and solutal transfer characteristics is needed. Lattice Boltzmann method was adopted to numerically simulate the double diffusive convection and entropy generation inside an internal heating enclosure attaching with a porous layer. The influence of internal heat generation, Darcy number, Soret and Dufour effect on heat and mass transfer rates and entropy generation was deeply discussed. Results show that attaching a porous layer at the bottom is beneficial to inhibit the heat and mass transfer rates, and blindly reducing Darcy number has no significant influence. Increasing internal heat generation can also suppress the heat and mass transfer rates. Soret effect can improve the solutal transfer process, while Dufour effect has positive influence on thermal transfer process. Furthermore, porous layer for lower Darcy number can inhibit the entropy generation. Internal heat generation can enhance the entropy generation, and thermal irreversibility has dominant effect for large internal heat generation. Soret effect has no mild influence on entropy generation, while Dufour effect promotes the entropy generation. Under the stronger Dufour effect, thermal irreversibility dominates the total entropy generation. [ABSTRACT FROM AUTHOR]

Abstract:

We study the diffusive instability subject to a solid–liquid interface and a Kolmogorov flow using modal, non-modal analyses and energy analysis. It is found that the phase boundary has different effects on the threshold of diffusive convection for weak and strong salinity stratification. In the context of oceanography where the salinity Rayleigh number RS is very high, the ice–water interface has negligible influence on the onset of diffusive convection. In the presence of shear, the diffusive convection for RS  < 106 tends to be inhibited and with the increase of shear intensity, the oscillatory, steady convective and Kelvin–Helmholtz instabilities will be successively dominant. For RS  > 106, the shear has a destabilizing effect on the diffusive convection, due to the generation of thermohaline-sheared instability found by Radko (J. Fluid Mech. , vol. 805, 2016, pp. 147–170). Non-modal analysis indicates that for realistic parameters of high-latitude oceans, with the transition of the ultimate energy source of instability from the density gradient to background current, the thermohaline-shear instability is expected to transition from oscillatory to steady instability. The initial transient amplification due to double diffusion has also been studied, which is due to the generation of overstable instability at the initial phase. For RS  < 106, the optimal initial condition to achieve the maximum transient growth favours longitudinal rolls. For thermohaline-shear instability, however, it favours transverse rolls and specifically, in oscillatory thermohaline-shear instability, the transient amplification can be enhanced by the shear by one order of magnitude, thus having important influence on the stability of the system. [ABSTRACT FROM AUTHOR]

The internal heat source and reaction effects on the onset of thermosolutal convection in a local thermal non-equilibrium porous medium are examined, where the temperature of the fluid and the solid skeleton may differ. The linear instability and nonlinear stability theories of Darcy–Brinkman type with fixed boundary condition are carried out where the layer is heated and salted from below. The D 2 Chebyshev tau technique is used to calculate the associated system of equations subject to the boundary conditions for both theories. Three different types of internal heat source function are considered, the first type increases across the layer, while the second decreases, and the third type heats and cools in a nonuniform way. The effect of different parameters on the Rayleigh number is depicted graphically. Moreover, the results detect that utilizing the internal heat source, reaction, and non-equilibrium have pronounced effects in determining the convection stability and instability thresholds. [ABSTRACT FROM AUTHOR]

We investigate thermal convection in two horizontal layers of miscible fluids with an initial state in which the fluids are at rest and the temperature has a linear continuous vertical distribution, but the concentration takes different constant values in each layer. Because the initial layered state is not a stationary state, most theoretical methods available for immiscible fluids are not applicable to the miscible case. Here we propose a new model of the thermal convection of miscible fluids, which is devised in such a way that the horizontal average of the width of the transitional layer is kept constant. Both the stability of the stationary state in the linear stage and the asymptotic attractors in the nonlinear stage of the model closely describe the transition of the convection pattern in the original system, which is associated with the change of the width of the transitional layer. [ABSTRACT FROM AUTHOR]

The present investigation is aimed to study the joint effect of the variable gravity field and chemical reaction on the onset of convection in a sparsely packed porous layer. Linear, parabolic, cubic and exponential functions are considered to account for the variable gravity field. The normal mode technique is used to study the linear stability of the problem. The corresponding eigenvalue problem is solved for the free-free, rigid-free, and rigid-rigid boundaries. The influence of the Damkohler number Dm, the solutal Rayleigh number Rs, the Lewis number Le, the Darcy number Da and the variable gravity field parameter on stability of the system in a sparsely packed porous layer is investigated. The results show that the onset of convection is delayed due to increase in the solutal Rayleigh number, the variable gravity parameter, and the Lewis number. In contrast, the onset of convection is enhanced by increase in the Darcy number and the Damkohler number. It is also observed that the system becomes more stable for exponential variation in the gravity field and less stable for cubic variation in the gravity field. [ABSTRACT FROM AUTHOR]

This paper deals with developing a numerical boundary layer flow model to analyze convective heat transfer characteristics of a micropolar fluid past a vertical plate in a composite material with viscous-Ohmic dissipations in the presence of a transverse magnetic field. The basic governing equations are solved numerically by using the Runge-Kutta-Fehlberg method. The computed results reveal a reduction in the velocity, temperature, and microrotation profiles by increasing the Prandtl number. Also, the concentration distribution is enhanced by enhancing or decreasing Soret-Dufour parameter, and there seems to be decremented in the skin-friction coefficient values with Schmidt number.

Current disquisition is aimed to adumbrate thermosolutal convective diffusion transport in Casson fluid filled in hexagonal enclosure under effectiveness of inclined magnetic field. Partially iso-concentration and iso-temperature distributions at base wall of enclosure is provided along with incorporation of fillets at corners of flow domain. Governing formulation in 2D are expressed in a velocity-pressure, energy and concentration balance equations. Numerical computations are executed by employing COMSOL Multiphysics software based on finite element scheme. Domain discretization in manifested by performing hybrid meshing in view of 2D elements. Linear and quadric interpolating polynomials for pressure and other associated distributions are capitalized. Non-linearized discretization system is handled by non-linear solver renowned as PARADISO. Results and code validation is assured by performing comparison and grid convergence test respectively. The impact of flow concerning variables by considering wide ranges like Casson parameter (0.1≤β≤10), Rayleigh number (104≤Ra≤107), Hartmann number (20≤Ha≤80) and Lewis number (0.1≤Le≤10) on velocity, isothermal and isoconcentration fields are visualized through graphs and tables. Visualization about kinetic energy along with heat and mass transfer rates are disclosed through graphs and tables.

Double diffusive convection is the phenomena that describes the convection driven by two different densities which have different rates of diffusion. A comparison of two temperature boundaries when i) both the surfaces are set at adiabatic temperature, and ii)upper free surface is adiabatic and lower rigid surface is isothermal cases, on surface tension driven double diffusive convection in a horizontal composite layer is studied analytically using exact method. For both cases i) and ii), the thermal Marangoni number (Tmn) is determined, which is the eigen value, for upper free and lower rigid velocity boundary conditions. The results indicate that the given system is a fluid dominant composite system and adiabatic-isothermal thermal boundary is more stable compare to adiabatic-adiabatic boundary condition. [ABSTRACT FROM AUTHOR]

When particles settle through a stable temperature or salinity gradient they can drive an instability known as sedimentary fingering convection. This phenomenon is thought to occur beneath sediment-rich river plumes in lakes and oceans, in the context of marine snow where decaying organic materials serve as the suspended particles or in the atmosphere in the presence of aerosols or volcanic ash. Laboratory experiments of Houk & Green (Deep-Sea Res., vol. 20, 1973, pp. 757–761) and Green (Sedimentology, vol. 34(2), 1987, pp. 319–331) have shown sedimentary fingering convection to be similar to the more commonly known thermohaline fingering convection in many ways. Here, we study the phenomenon using three-dimensional direct numerical simulations. We find evidence for layer formation in sedimentary fingering convection in regions of parameter space where it does not occur for non-sedimentary systems. This is due to two complementary effects. Sedimentation affects the turbulent fluxes and broadens the region of parameter space unstable to the $\unicode[STIX]{x1D6FE}$-instability (Radko, J. Fluid Mech., vol. 497, 2003, pp. 365–380) to include systems at larger density ratios. It also gives rise to a new layering instability that exists in $\unicode[STIX]{x1D6FE}$-stable regimes. The former is likely quite ubiquitous in geophysical systems for sufficiently large settling velocities, while the latter probably grows too slowly to be relevant, at least in the context of sediments in water.

We analyse the linear stability of stably stratified fluids whose density depends on two scalar fields where one of the scalar fields is unstably stratified and involves a settling velocity. Such conditions may be found, for example, in flows involving the transport of sediment in addition to heat or salt. A linear stability analysis for constant-gradient base states demonstrates that the settling velocity generates a phase shift between the perturbation fields of the two scalars, which gives rise to a novel, settling-driven instability mode. This instability mechanism favours the growth of waves that are inclined with respect to the horizontal. It is active for all density and diffusivity ratios, including for cases in which the two scalars diffuse at identical rates. If the scalars have unequal diffusivities, it competes with the elevator mode waves of the classical double-diffusive instability. We present detailed linear stability results as a function of the governing dimensionless parameters, including for lateral gradients of the base state density fields that result in predominantly horizontal intrusion instabilities. Highly resolved direct numerical simulation results serve to illustrate the nonlinear competition of the various instabilities for such flows in different parameter regimes.

The linear and nonlinear stability analyses of thermosolutal convection in a non-Newtonian Navier-Stokes-Voigt fluid, considering Soret and Ekman damping effects, are conducted analytically. Instability thresholds are determined for thermosolutal convection within a viscoelastic fluid of the Kelvin-Voigt type, wherein a dissolved salt field exists. Two scenarios are examined: one where the fluid layer is heated from the bottom and concurrently salted from the bottom, and the other where the fluid layer is heated from the bottom and concurrently salted from the top. The governing partial differential equations system includes conservation laws of mass, momentum, energy, and salt concentration. Using the energy method, the disturbances to the fluid system are shown to decay exponentially. Analytical expressions are developed for the eigenvalue as a function of Soret, Lewis, Prandtl, Kelvin-Voigt, and Rayleigh friction numbers. The study illustrates the shift from a stationary mode of convection to an oscillatory mode and provides thresholds that indicate these transitions. It is found that the viscoelastic property of the fluid acts as a stabilizing agent for oscillatory mode convection. Rayleigh friction substantially controls the convection threshold. Upon comparing threshold values between linear and nonlinear theories, a subcritical instability region is observed in the heating bottom-salting bottom case (case-1), whereas such a region is absent in the heating bottom-salting top case (case-2). • Influence of Ekman damping on the convection in Kelvin-Voight fluid is highlighted. • Global nonlinear stability analysis of conduction solution has been performed. • Analytical expressions for the eigenvalue are obtained. • Conditions for the onset of convection are provided. • Transition from stationary convection to oscillatory convection is demonstrated. [ABSTRACT FROM AUTHOR]

Doubly diffusive convection is considered in a vertical slot where horizontal temperature and solutal variations provide competing effects to the fluid density while allowing the existence of a conduction state. In this configuration, the linear stability of the conductive state is known, but the convection patterns arising from the primary instability have only been studied for specific parameter values. We have extended this by determining the nature of the primary bifurcation for all values of the Lewis and Prandtl numbers using a weakly nonlinear analysis. The resulting convection branches are extended using numerical continuation and we find large-amplitude steady convection states can coexist with the stable conduction state for sub- and supercritical primary bifurcations. The stability of the convection states is investigated and attracting travelling waves and periodic orbits are identified using time stepping when these steady states are unstable. [ABSTRACT FROM AUTHOR]

The major finding of this paper is studying the stability of a double diffusive convection using the so-called local thermal non-equilibrium (LTNE) effects. A new combined model that we call it a Brinkmann-Forchheimer model was considered in this inquiry. Using both linear and non-linear stability analysis, a double diffusive convection is used in a saturated rotating porous layer when fluid and solid phases are not in the state of local thermal non-equilibrium. In addition, we discussed several related topics such as the effect of solute Rayleigh number, symmetric properties, Brinkman coefficient, Taylor number, inter-phase heat transfer coefficient on the stability of the system, and porosity modified conductivity ratio. Moreover, two cases were investigated in non-linear theory, the case of the Forchheimer coefficient F = 0 and the case of the Taylor-Darcy number τ = 0 . For the validation of this work, some numerical experiments were made in the non-linear energy stability and the linear instability theories. [ABSTRACT FROM AUTHOR]

The investigation of thermal modulation on double-diffusive stationary convection in the presence of an applied magnetic field and internal heating is carried out. A weakly nonlinear stability analysis has been performed using the finite-amplitude Ginzburg-Landau model. This finite amplitude of convection is obtained at the third order of the system. The study considers three different forms of temperature modulations. OPM-out of phase modulation, LBMO-lower boundary modulation, IPM-in phase modulation. The finite-amplitude is a function of amplitude δ T , frequency ω and the phase difference θ. The effects of δ T and ω on heat/mass transports have been analyzed and depicted graphically. The study shows that heat/mass transports can be controlled effectively by thermal modulation. Further, it is found that the internal Rayleigh number Ri enhances heat transfer and reduces the mass transfer in the system.

A sequence of two- and three-dimensional simulations are conducted for the double-diffusive convection (DDC) flows in the diffusive regime subjected to an imposed shear. For a wide range of control parameters, and for sufficiently strong perturbation of the conductive initial state, staircase-like structures spontaneously develop, with relatively well-mixed layers separated by sharp interfaces of enhanced scalar gradient. Such staircases appear to be robust even in the presence of strong shear over very long times, with early-time coarsening of the observed layers. For the same set of control parameters, different asymptotic layered states, with markedly different vertical scalar fluxes, can arise for different initial perturbation structures. The imposed shear significantly spatio-temporally modifies the vertical transport of the various scalars. The flux ratio γ* (i.e. the ratio between the density fluxes due to the total salt flux and the total heat flux) is found, at steady state, to be essentially equal to the square root of the ratio of the salt diffusivity to the thermal diffusivity, consistent with the physical model proposed by Linden & Shirtcliffe (J. Fluid Mech., vol. 87, 1978, pp. 417-432) and the variational arguments presented by Stern (J. Fluid Mech., vol. 114, 1982, pp. 105-121) for unsheared double-diffusive convection. [ABSTRACT FROM AUTHOR]

The effect of thermal diffusion on the onset of double‐diffusive convection is analyzed by considering a composite system of the fluid‐saturated porous layer. The porous layer of the composite system is modeled employing the Darcy–Brinkman–Rayleigh–Benard model. The boundaries of the composite system are assumed to be rigid‐rigid under normal gravitational force. The governing equations satisfying the Darcy–Brinkman–Rayleigh–Benard model are solved using the regular perturbation method. A mathematical expression is derived for the critical thermal Rayleigh number by solving the coupled equation. The impact of various physical parameters on the onset of convection is graphically represented under the influence of the Soret effect and the stability of the system is analyzed. [ABSTRACT FROM AUTHOR]

The effect of hall current on a couple-stress ferromagnetic fluid heated and soluted from below in the presence of varying gravitational field and horizontal magnetic field through a porous media is considered. A linearized hypothesis and normal mode procedure are utilized to get dispersion relation. For the case of stationary convection, stable solute gradient has a stabilizing effect on the system. Medium permeability and couple-stress both have stabilizing and destabilizing effects under specific conditions. Additionally, magnetic field and hall current have both stabilizing as well as a destabilizing effect on the system under some conditions. It is likewise discovered that in the absence of stable solute gradient, magnetization has a stabilizing effect on the system. Oscillatory modes are introduced in the system in the presence of magnetic field (hence hall current) and stable solute gradient, though in their nonappearance, the principle of exchange of stabilities is satisfied in the system. Graphs also have been plotted by giving some numerical values to the parameters. [ABSTRACT FROM AUTHOR]

In this work we show that horizontal gradients of temperature and salinity with compensating effects on density can drive thermohaline intrusion in the fluid layer below. Specifically, different types of double diffusive convection generate differential vertical fluxes from the top boundary, which then sustain horizontal temperature and salinity gradients within the bulk. Interleaving layers develop in the bulk and slope downward towards the cold fresh side, which are of the diffusive type. New layers emerge near the bottom boundary and shift the existing layers upward due to the density difference induced by the divergence of the vertical fluxes through the top surface. Detailed analyses reveal that the present intrusion is consistent with those in the narrow fronts, and both layer thickness and current velocity follow the corresponding scaling laws. Such intrusion process provides an extra path to transfer heat and salinity horizontally towards the cold and fresh side, but transfer the density anomaly towards the warm and salty side. These findings extend the circumstances where thermohaline intrusions may be observed. [ABSTRACT FROM AUTHOR]

Double-diffusive convection, in which a fluid is acted upon by two fields (such as temperature and salinity) that affect the density, has been widely studied in areas as diverse as the oceans and stellar atmospheres. Assuming classical Fickian diffusion for both heat and salt, the evolution of temperature and salinity are governed by parabolic advection–diffusion equations. In reality, there are small extra terms in these equations that render the equations hyperbolic (the Maxwell–Cattaneo effect). Although these corrections are nominally small, they represent a singular perturbation and hence can lead to significant effects when the underlying differences of salinity and temperature are large. In this paper, we investigate the linear stability of a double-diffusive fluid layer and show that amending Fick's law for the temperature, or the salinity, alone can lead to new modes of oscillation and to very large changes in the preferred wavelength of oscillatory convection at onset. In particular, the salt finger regime of classical double diffusion is here replaced by Maxwell–Cattaneo oscillations when the salt concentration is very high. The more complicated case when both laws are amended is left to a future paper, now in preparation. [ABSTRACT FROM AUTHOR]

The problem of non-Darcian-Bènard double diffusive magneto-Marangoni convection is considered in a horizontal infinite two layer system. The system consists of a two-component fluid layer placed above a porous layer, saturated with the same fluid with a constant heat sources/sink in both the layers, in the presence of a vertical magnetic field. The lower porous layer is bounded by rigid boundary, while the upper boundary of the fluid region is free with the presence of Marangoni effects. The system of ordinary differential equations obtained after normal mode analysis is solved in a closed form for the eigenvalue and the Thermal Marangoni Number (TMN) for two cases of Thermal Boundary Combinations (TBC); these are type (i) Adiabatic-Adiabatic and type (ii) Adiabatic-Isothermal. The corresponding two TMNs are obtained and the impacts of the porous parameter, solute Marangoni number, modified internal Rayleigh numbers, viscosity ratio, and the diffusivity ratios on the non-Darcian-Bènard double diffusive magneto - Marangoni convection are studied in detail. [ABSTRACT FROM AUTHOR]

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This paper considers analytically and numerically the curvature-based stabilization method for double-diffusive natural convection flows in the presence of magnetic field. Unconditionally stable and optimally accurate second-order approximations are obtained. The impact of curvature stabilization on different flow fields are presented for several numerical test problems. [ABSTRACT FROM AUTHOR]

Current analysis presents the mathematical modeling for peristaltic transport of nanofluid with applications of double-diffusive convection and Hall features. The flow has been induced by a convergent channel due to peristaltic propulsion. These rheological equations are transformed from fixed to wave frames by using a linear mathematical relation between these two frames. The dimensionless variables are used to transform these rheological equations into nondimensional forms. The flow analysis is carried out under two distinct scientific biological assumptions, one is known as long wavelength and the second one is low Reynolds number. The analytical solutions of these rheological equations are obtained with the help of a rigorous analytical method known as integration in the term of stream function. The physical effects of magnetic and Hall devices, respectively, on the flow features are also considered in the present analysis. The physical influences of dominant hydro-mechanical parameters on the axial velocity, pressure gradient, trapping, volumetric fraction of nanofluid, heat and mass transfer phenomena are studied. The complex scenario of biomimetic propulsions are considered in boundary walls to boost the proficiency of peristaltic micropumps. [ABSTRACT FROM AUTHOR]

The present article deals with Soret Dufour free convective heat and mass transfer of a micropolar fluid over vertical stretching and shrinking sheets embedded in a Darcian porous medium with thermal radiation and magnetic field. We have obtained numerical solutions for the velocity, temperature, microrotation, and solute concentration fields for various values of the thermal radiation and microrotation material parameters, Prandtl number, chemical reaction, magnetic parameter, and Soret-Dufour number. Present results are obtained by using Runge-Kutta Fehlberg method with shooting technique and they are presented graphically and in tabular form for performing a critical analysis of various parametric values. It is explored that the velocity and temperature distribution decrease with enhancement in the Prandtl number and having reverse effects on the concentration distribution. Further, it is noticed that by increasing the values of the thermal radiation parameter, there is a rise in the velocity and temperature distributions. This work would find applications in the field of chemical engineering systems and magnetic materials processing. [ABSTRACT FROM AUTHOR]

The effects of cross-diffusion on linear and weak nonlinear stability of double diffusive convection in an electrically conducting horizontal fluid layer with an imposed vertical magnetic field are investigated. The criterion for the onset of stationary and oscillatory convection is obtained analytically by performing the linear instability analysis. Several noteworthy departures from those of doubly diffusive fluid systems are unveiled under certain parametric conditions. It is shown that (i) disconnected closed convex oscillatory neutral curve separated from the stationary neutral curve exists requiring three critical thermal Rayleigh numbers to completely specify the linear instability criteria instead of a usual single critical value, (ii) an electrically conducting fluid layer in the presence of magnetic field can be destabilized by stable solute concentration gradient, and (iii) a doubly diffusive conducting fluid layer can be destabilized in the presence of magnetic field. It is demonstrated that small variations in the off-diagonal elements enforce discrepancies in the instability criteria. A weak nonlinear stationary stability analysis has been performed using a perturbation method and a cubic Landau equation is derived and the stability of bifurcating equilibrium solution is discussed. It is found that subcritical bifurcation occurs depending on the choices of governing parameters. [ABSTRACT FROM AUTHOR]

A miscible horizontal interface separating two solutions of different solutes in the gravity field can deform into convective finger structures due to the Rayleigh–Taylor (RT) instability, or the double-diffusive (DD) and diffusive-layer-convection (DLC) instabilities, triggered by differential diffusion of the solutes. We analyse here numerically the nonlinear dynamics of these buoyancy-driven instabilities in porous medium flows by an integration of Darcy’s law coupled to advection–diffusion equations for the concentrations of the two solutes. After a diffusive growth, the mixing length L, defined as the vertical extent of the mixing zone, starts to grow linearly when convection sets in. We compute the mixing velocity U as the slope of this linear growth. In the one-species RT regime, U is proportional to Δρ0, the initial density difference between the two layers. In the two-species problem, differential diffusion effects can induce non-monotonic density profiles characterised by an adverse density difference, defined as the density jump across the spatial domain where the density decreases along the direction of gravity. We find that, in the parameter space spanned by the buoyancy ratio R, and the ratio δ of diffusion coefficients of the two species, the mixing velocity scales linearly with this dynamic density difference. It is computed analytically from the diffusive base-state density profile and can be significantly larger than Δρ0. Our results evidence the possibility of controlling the mixing of RT, DD and DLC instabilities in two-species stratifications by a careful choice of the nature and thus diffusivity of the species involved. [ABSTRACT FROM AUTHOR]

We employ direct numerical simulations of salt fingering engendered turbulent mixing to derive a parameterization scheme for the representation of this physical process in low-resolution ocean models and compare the results with those previously suggested on empirical grounds. In this analysis we differentiate between the reversible and irreversible contributions to diapycnal diffusivity associated with the turbulence generated by this mechanism. The necessity of such a distinction has been clearly recognized in connection with shear-driven density stratified turbulence processes: only irreversible processes can contribute to the effective turbulent diapycnal diffusivity. We expand the formalism herein to the more complicated salt-fingering case as a first step towards analysis of the general case. The irreversible fluxes are determined in the case of salt fingering related turbulence by examining high-resolution direct numerical simulation (DNS)-derived turbulence data sets based upon two different models: namely the 'unbounded gradient model' and the 'interface model' with depth-dependent gradients of temperature and salinity. By fitting the irreversible diapycnal fluxes in the unbounded gradient model (for equilibrium states) as a function of density ratio (the governing non-dimensional parameter), we derive a functional form that can be used as a basis for a next generation salt-fingering parametrization scheme. By applying this scheme to the interface model, we demonstrate that the local fluxes predicted agree well with those obtained from the numerical simulations based upon this more complex model. We compare this new DNS-derived turbulence parameterization with those that have been derived empirically. [ABSTRACT FROM AUTHOR]

The major finding of this paper is studying the stability of a double diffusive convection using the so-called local thermal non-equilibrium (LTNE) effects. A new combined model that we call it a Brinkmann-Forchheimer model was considered in this inquiry. Using both linear and non-linear stability analysis, a double diffusive convection is used in a saturated rotating porous layer when fluid and solid phases are not in the state of local thermal non-equilibrium. In addition, we discussed several related topics such as the effect of solute Rayleigh number, symmetric properties, Brinkman coefficient, Taylor number, inter-phase heat transfer coefficient on the stability of the system, and porosity modified conductivity ratio. Moreover, two cases were investigated in non-linear theory, the case of the Forchheimer coefficient F=0 and the case of the Taylor-Darcy number τ=0. For the validation of this work, some numerical experiments were made in the non-linear energy stability and the linear instability theories.

When body of fluid with a salinity gradient is heated from an isolated vertical wall instabilities can form. These have been observed in many experiments. The evolving temperature boundary layer causes the fluid to rise and generates horizontal salinity gradients and vertical shear. These background temperature and salinity gradients and the shear can all drive (or inhibit) the instabilities. The time-dependent nature of the background gradients has previously restricted linear stability analysis to some limits where a quasi-static assumption could be made. However, in many of the experiments this assumption is not valid. We investigate the instabilities over the full range of salinity gradients and applied heating, from what is essentially the thermal problem to the strong salinity gradient limit, with two different heating rates. The approach taken is to find the optimal evolution of a quadratic energy-like measure of the amplitude of the instabilities as the background state evolves. This involves a matrix optimization problem. The choice of quadratic measure is not predetermined, but selected to minimize this optimal growth. This approach has been developed previously for the purely thermal case of heating from isolated horizontal and vertical boundaries, and to the double-diffusive problem of heating a salinity gradient from a horizontal lower boundary. We show that there are three regimes of instability when a salinity gradient is heated from a sidewall. There are the small and large Prandtl number regimes observed previously in the purely thermal problem. As the salinity gradient increases the shear-driven small Prandtl number mode is suppressed and only the large Prandtl number mode is observed. For larger salinity gradients a double-diffusive mode of instability appears, which initially has an order-one aspect ratio. As the salinity gradient further increases it evolves into the thin almost horizontal intrusions of the quasi-static analysis. These findings are in line with experimental observations. [ABSTRACT FROM AUTHOR]

A numerical computation is performed to analyze the double diffusive convection in micropolar nanofluids flow governed by peristaltic pumping in an asymmetric microchannel, in the presence of thermal radiation and an external magnetic field. The highly nonlinear governing equations are diluted by using desirable physical assumptions such as lubrication approximation and low zeta potential. Convective boundary conditions are employed. This enables us to determine numerical estimates of various physical flow variables such as velocity, pressure gradient, spin velocity, temperature of the nanofluid, concentration of solute, and volume fraction of nanoparticles for sundry parameters like micropolar parameter, coupling parameter, solutal Grashof number, thermophoretic diffusion coefficient, Grashof number, thermal radiation parameter and Helmholtz–Smoluchowski velocity with the aid of bvp4c function built-in command of MATLAB 2012b. Influence of each relevant parameter on flow, thermal and species characteristics are computed in this study. Influence of Soret and Dufour parameters are also simulated. This model is applicable to the study of chemical fraternization/separation procedures and various thermal management systems like of heat sinks, thermoelectric coolers, forced air systems and fans, heat pipes, and many more. [ABSTRACT FROM AUTHOR]

This paper presents a numerical study of a double diffusive convection in an inclined square porous cavity filled with an electrically conducting binary mixture. The upper and bottom walls are maintained at a constant temperatures and concentrations whereas the left and right walls are assumed to be adiabatic and impermeable. A uniform and tilted magnetic field is applied at an angle, γ, about the horizontal, it is obvious that this is related to the orientation of the magnetic force that can help or oppose the buoyant force. The Dupuit-Darcy flow model, which includes effects of the inertial parameter, with the Boussinesq approximation, energy, and species transport equations are solved numerically using the classical finite difference method. Governing parameters of the problem under study are the thermal Rayleigh number, Hartmann number, Lewis number, the buoyancy ratio, inclination angle, and tilting angle of the magnetic field. The numerical results are reported on the contours of streamline, temperature, and concentration and for the average Nusselt and Sherwood numbers for various parametric conditions. It is demonstrated that both the inertial effect parameter and the magnetic field, have a strong influence on the strength of the natural convection heat and mass transfer within the porous layer. [ABSTRACT FROM AUTHOR]

We investigate experimentally the effect of double diffusion on the dynamics of initially neutrally buoyant warm and salty turbulent jets discharged horizontally into stationary cooler freshwater ambient. Jets over a range of source Reynolds numbers and source temperature/salinity combinations are examined. In all cases, we observed sinking jet trajectories and the formation of salt fingers along the lower surface of the jet. Increasing the source concentration of both scalar properties led to more pronounced jet sinking trajectories, and to a reduction in the distance between the source and the onset point of salt fingers, demonstrating the significance of the double-diffusive processes. We propose that is it the differential double-diffusive fluxes across the jet–ambient turbulent/non-turbulent interfaces that causes the build-up of negative buoyancy and hence the sinking motion. In addition, we make predictions on the onset point of the salt fingers based on the balance between diffusive processes and the jet entrainment, and compare them with the experimental observations. [ABSTRACT FROM AUTHOR]