Spatial Decay Bounds for the Brinkman Fluid Equations in Double-Diffusive Convection

In this paper, we consider the Brinkman equations pipe flow, which includes the salinity and the temperature. Assuming that the fluid satisfies nonlinear boundary conditions at the finite end of the cylinder, using the symmetry of differential inequalities and the energy analysis methods, we establish the exponential decay estimates for homogeneous Brinkman equations. That is to prove that the solutions of the equation decay exponentially with the distance from the finite end of the cylinder. To make the estimate of decay explicit, the bound for the total energy is also derived.

Layering and vertical transport in sheared double-diffusive convection in the diffusive regime

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 $\gamma ^*$ (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.

Double diffusion, shear instabilities, and heat impacts of a Pacific Summer Water intrusion in the Beaufort Sea

Pacific Summer Water eddies and intrusions transport heat and salt from boundary regions into the western Arctic basin. Here we examine concurrent effects of lateral stirring and vertical mixing using microstructure data collected within a Pacific Summer Water intrusion with a length scale of ∼20 km. This intrusion was characterized by complex thermohaline structure in which warm Pacific Summer Water interleaved in alternating layers of O(1 m) thickness with cooler water, due to lateral stirring and intrusive processes. Along interfaces between warm/salty and cold/fresh water masses, the density ratio was favorable to double-diffusive processes. The rate of dissipation of turbulent kinetic energy (ε) was elevated along the interleaving surfaces, with values up to 3×10−8 W kg−1 compared to background ε of less than 10−9 W kg−1. Based on the distribution of ε as a function of density ratio Rρ , we conclude that double-diffusive convection is largely responsible for the elevated ε observed over the survey. The lateral processes that created the layered thermohaline structure resulted in vertical thermohaline gradients susceptible to double-diffusive convection, resulting in upward vertical heat fluxes. Bulk vertical heat fluxes above the intrusion are estimated in the range of 0.2-1 W m−2, with the localized flux above the uppermost warm layer elevated to 2- 10 W m−2. Lateral fluxes are much larger, estimated between 1000-5000 W m−2, and set an overall decay rate for the intrusion of 1-5 years.

Slip boundaries effects on double-diffusive convection of magneto-pseudoplastic nanofluid on peristaltic flux in an inclined asymmetric channel

The implications of double-diffusive convection and an inclined magnetic field on the peristaltic transport of a pseudoplastic nanofluid in an inclined asymmetric channel with slip boundaries were investigated in this research. The present problem is mathematically modeled using lubrication techniques, which results in highly nonlinear equations for the proposed problem that is solved using a numerical technique. The graphical findings show how temperature, pressure rise, concentration, pressure gradient, nanoparticle fraction, and stream functions affect key physical parameters of interest. It is revealed that the velocity value rises as the velocity slip parameter, temperature, and solutal Grashof number rise. Furthermore, increasing thermal slip, Dufour, Soret, Brownian motion, and thermophoresis factors increase the temperature profile. If [Formula: see text] [Formula: see text] [Formula: see text] and [Formula: see text] the viscous model of classical Newtonian fluid is a special case of the preceding model.

Partial Slip Impact on Double Diffusive Convection Flow of Magneto-Carreau Nanofluid through Inclined Peristaltic Asymmetric Channel

The significance of partial slip on double diffusive convection on magneto-Carreau nanofluid through inclined peristaltic asymmetric channel is examined in this paper. The two-dimensional and directional flow of a magneto-Carreau nanofluid is mathematically described in detail. Under the lubrication technique, the proposed model is simplified. The solutions of extremely nonlinear partial differential equations are calculated using a numerical technique. Graphical data are displayed using Mathematica software and Matlab to examine how temperature, pressure rise, concentration, pressure gradient, velocity profile, nanoparticle volume fraction, and stream functions behave on emerging parameters. It is noticed that as the velocity slip parameter is increased, the axial velocity at the channel’s center increases. Additionally, near the boundary, opposite behavior is observed. The temperature, concentration, and nanoparticle profile drops by increasing thermal slip, concentration slip, and nanoparticle slip parameter.