Gyrotactic bioconvection at pycnoclines

2013 ◽  
Vol 733 ◽  
pp. 245-267 ◽  
Author(s):  
A. Karimi ◽  
A. M. Ardekani
Keyword(s):  
Boundary Conditions ◽  
Large Scale ◽  
Stokes Equations ◽  
Lewis Number ◽  
Boussinesq Approximation ◽  
Dynamical Behaviour ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
The Stability ◽  
Micro Organisms

AbstractBioconvection is an important phenomenon in aquatic environments, affecting the spatial distribution of motile micro-organisms and enhancing mixing within the fluid. However, stratification arising from thermal or solutal gradients can play a pivotal role in suppressing the bioconvective flows, leading to the aggregation of micro-organisms and growth of their patchiness. We investigate the combined effects by considering gyrotactic motility where the up-swimming cells are directed by the balance of the viscous and gravitational torques. To study this system, we employ a continuum model consisting of Navier–Stokes equations with the Boussinesq approximation coupled with two conservation equations for the concentration of cells and stratification agent. We present a linear stability analysis to determine the onset of bioconvection for different flow parameters. Also, using large-scale numerical simulations, we explore different regimes of the flow by varying the corresponding boundary conditions and dimensionless variables such as Rayleigh number and Lewis number ($\mathit{Le}$) and we show that the cell distribution can be characterized using the ratio of the buoyancy forces as the determinant parameter when $\mathit{Le}\lt 1$ and the boundaries are insulated. But, in thermally stratified fluids corresponding to $\mathit{Le}\gt 1$, temperature gradients are demonstrated to have little impact on the bioconvective plumes provided that the walls are thermally insulated. In addition, we analyse the dynamical behaviour of the system in the case of persistent pycnoclines corresponding to constant salinity boundary conditions and we discuss the associated inhibition threshold of bioconvection in the light of the stability of linearized solutions.

Heat Pollution by Large Buildings and the Effects upon Astrometric Observations

1991 ◽  
Vol 112 ◽  
pp. 326-326
Author(s):  
James A. Hughes ◽  
Calvin A. Kodres
Keyword(s):  
Real Estate ◽  
Boundary Conditions ◽  
Large Scale ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Real Estate Development ◽  
Atmospheric Effects ◽  
Navier Stokes Equations ◽  
Naval Observatory ◽  
The U.S

ABSTRACTRecent, large scale, real estate development near the U.S. Naval Observatory has led to an investigation of the systematic atmospheric effects which heat from large buildings can cause. Results show that non-negligible slopes of the atmospheric layers can be induced which cause a surprisingly large anomalous refraction. The Navier-Stokes equations were numerically integrated using the appropriate boundary conditions and the resulting isopycnic tilts using the appropriate boundary conditions and the resulting isopycnic tilts charted. Rays were then essentially traced through the perturbed atmosphere to determine the magnitude of the anomalous refraction.

scholarly journals Two-Level Brezzi-Pitkäranta Discretization Method Based on Newton Iteration for Navier-Stokes Equations with Friction Boundary Conditions

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Rong An ◽  
Xian Wang
Keyword(s):  
Boundary Conditions ◽  
Iteration Method ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Newton Iteration ◽  
Navier Stokes ◽  
Discretization Method ◽  
Navier Stokes Equations ◽  
Stabilized Finite Element Method ◽  
The Stability

We present a new stabilized finite element method for Navier-Stokes equations with friction slip boundary conditions based on Brezzi-Pitkäranta stabilized method. The stability and error estimates of numerical solutions in some norms are derived for standard one-level method. Combining the techniques of two-level discretization method, we propose two-level Newton iteration method and show the stability and error estimate. Finally, the numerical experiments are given to support the theoretical results and to check the efficiency of this two-level iteration method.

Unstably Stratified Homogeneous Turbulence as a Tool for Turbulent Mixing Modeling

2014 ◽  
Vol 136 (9) ◽  
Author(s):  
J. Griffond ◽  
B. J. Gréa ◽  
O. Soulard
Keyword(s):  
Turbulent Mixing ◽  
Large Scale ◽  
Stokes Equations ◽  
Boussinesq Approximation ◽  
Inertial Range ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Scale Characteristics ◽  
Rt Instability ◽  
Spectrum Structure

In this paper, we propose a kind of buoyancy-driven flow leading to unstably stratified homogeneous (USH) turbulence. This approach is developed in the context of incompressible Navier–Stokes equations under Boussinesq approximation. We show that USH turbulence is a valuable tool for understanding and modeling turbulent mixing induced by Rayleigh-Taylor (RT) instability. It is a much simpler configuration than “RT turbulence” which is in fact inhomogeneous. Thus, it gives insights in the basic mechanisms of buoyancy-driven turbulence, namely the interplay between buoyancy production, nonlinearities and dissipation. Besides, despite their differences both types of turbulence share very similar features for the large scale characteristics as well as for the inertial range spectrum structure.

scholarly journals Ensemble Algorithm for Parametrized Flow Problems with Energy Stable Open Boundary Conditions

2020 ◽  
Vol 20 (3) ◽  
pp. 531-554
Author(s):  
Aziz Takhirov ◽  
Jiajia Waters
Keyword(s):  
Boundary Conditions ◽  
Stokes Equations ◽  
Initial Conditions ◽  
Navier Stokes ◽  
Open Boundary ◽  
Open Boundary Conditions ◽  
Navier Stokes Equations ◽  
Flow Problems ◽  
The Stability ◽  
Ensemble Calculation

AbstractWe propose novel ensemble calculation methods for Navier–Stokes equations subject to various initial conditions, forcing terms and viscosity coefficients. We establish the stability of the schemes under a CFL condition involving velocity fluctuations. Similar to related works, the schemes require solution of a single system with multiple right-hand sides. Moreover, we extend the ensemble calculation method to problems with open boundary conditions, with provable energy stability.

Convection-Free Thermodiffusion in a Water-Ethanol Mixture Subject to Varying Thermal Boundary Conditions

2005 ◽  
Author(s):  
M. Chacha ◽  
M. Z. Saghir
Keyword(s):  
Boundary Conditions ◽  
Stokes Equations ◽  
Thermal Control ◽  
Boussinesq Approximation ◽  
Transport Processes ◽  
Navier Stokes ◽  
Soret Coefficient ◽  
Navier Stokes Equations ◽  
Ethanol Mixture ◽  
Thermal Boundary Conditions

The paper presents a precise numerical simulation of the transport processes in a rectangular cavity saturated with a water-ethanol mixture. The full transient Navier-Stokes equations coupled with the heat and mass transfer equations are solved by the means of the finite volume method. The mixture properties are drawn from the recent work by Dutrieux et al. [1]. The density is assumed to vary linearly with temperature and concentration (Boussinesq approximation) in the working temperature range while other thermo physical properties are held constant. After validation the present code is used for a series of numerical experiments. Thermodiffusion in a liquid-mixture of Ethanol and Water is analyzed under zero gravity condition. Different thermal boundary conditions scenarios are considered to simulate possible thermal control system shortcomings. Results of investigations might help in the preparation and monitoring of the heat sources control systems during the direct Soret coefficient measurement experiments.

Large-scale instabilities of turbulent wakes

1972 ◽  
Vol 54 (3) ◽  
pp. 481-488 ◽  
Author(s):  
W. C. Reynolds
Keyword(s):  
Large Scale ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Turbulent Shear ◽  
Small Scale ◽  
General Interest ◽  
Turbulent Shear Flow ◽  
Navier Stokes Equations ◽  
Eddy Structures ◽  
The Stability

The equations describing the statistical features of small amplitude waves in a turbulent shear flow are derived from the Navier-Stokes equations. Closure is achieved through a postulated constitutive equation for the alteration of the statistical properties of the turbulence by the organized wave. The theory is applied in an examination of the stability of a hypothetical wake consisting of small-scale turbulence enclosed within a steady uncontorted superlayer. A set of superlayer jump conditions is derived from fundamental considerations, and these are of more general interest. For this hypothetical flow the analysis predicts largescale instabilities and superlayer contortions reminiscent of large-eddy structures observed in real flows. These instabilities therefore offer an explanation of the presence of large-scale organized motions in turbulent free shear flows.

scholarly journals A SUBGRID STABILIZED METHOD FOR NAVIER-STOKES EQUATIONS WITH NONLINEAR SLIP BOUNDARY CONDITIONS

2021 ◽  
Vol 26 (4) ◽  
pp. 528-547
Author(s):  
Xiaoxia Dai ◽  
Chengwei Zhang
Keyword(s):  
Boundary Conditions ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Slip Boundary Conditions ◽  
Navier Stokes Equations ◽  
Slip Boundary ◽  
Fine Mesh ◽  
High Reynolds ◽  
The Stability ◽  
Nonlinear Slip Boundary Conditions

In this paper, we consider a subgrid stabilized Oseen iterative method for the Navier-Stokes equations with nonlinear slip boundary conditions and high Reynolds number. We provide one-level and two-level schemes based on this stability algorithm. The two-level schemes involve solving a subgrid stabilized nonlinear coarse mesh inequality system by applying m Oseen iterations, and a standard one-step Newton linearization problems without stabilization on the fine mesh. We analyze the stability of the proposed algorithm and provide error estimates and parameter scalings. Numerical examples are given to confirm our theoretical findings.

Parallel iterative finite-element algorithms for the Navier–Stokes equations with nonlinear slip boundary conditions

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Kangrui Zhou ◽  
Yueqiang Shang
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Parallel Algorithms ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Slip Boundary Conditions ◽  
Navier Stokes Equations ◽  
Slip Boundary ◽  
Parallel Iterative ◽  
Nonlinear Slip Boundary Conditions

AbstractBased on full domain partition, three parallel iterative finite-element algorithms are proposed and analyzed for the Navier–Stokes equations with nonlinear slip boundary conditions. Since the nonlinear slip boundary conditions include the subdifferential property, the variational formulation of these equations is variational inequalities of the second kind. In these parallel algorithms, each subproblem is defined on a global composite mesh that is fine with size h on its subdomain and coarse with size H (H ≫ h) far away from the subdomain, and then we can solve it in parallel with other subproblems by using an existing sequential solver without extensive recoding. All of the subproblems are nonlinear and are independently solved by three kinds of iterative methods. Compared with the corresponding serial iterative finite-element algorithms, the parallel algorithms proposed in this paper can yield an approximate solution with a comparable accuracy and a substantial decrease in computational time. Contributions of this paper are as follows: (1) new parallel algorithms based on full domain partition are proposed for the Navier–Stokes equations with nonlinear slip boundary conditions; (2) nonlinear iterative methods are studied in the parallel algorithms; (3) new theoretical results about the stability, convergence and error estimates of the developed algorithms are obtained; (4) some numerical results are given to illustrate the promise of the developed algorithms.

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