scholarly journals Gyrotactic swimmers in turbulence: shape effects and role of the large-scale flow

2018 ◽  
Vol 856 ◽  
Author(s):  
M. Borgnino ◽  
G. Boffetta ◽  
F. De Lillo ◽  
M. Cencini
Keyword(s):  
Large Scale ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Small Scale ◽  
Navier Stokes Equations ◽  
Preferential Sampling ◽  
Wide Range ◽  
Shape Effects ◽  
Dilute Suspensions ◽  
Large Scale Flow

We study the dynamics and the statistics of dilute suspensions of gyrotactic swimmers, a model for many aquatic motile microorganisms. By means of extensive numerical simulations of the Navier–Stokes equations at different Reynolds numbers, we investigate preferential sampling and small-scale clustering as a function of the swimming (stability and speed) and shape parameters, considering in particular the limits of spherical and rod-like particles. While spherical swimmers preferentially sample local downwelling flow, for elongated swimmers we observe a transition from downwelling to upwelling regions at sufficiently high swimming speed. The spatial distribution of both spherical and elongated swimmers is found to be fractal at small scales in a wide range of swimming parameters. The direct comparison between the different shapes shows that spherical swimmers are more clusterized at small stability and speed numbers, while for large values of the parameters elongated cells concentrate more. The relevance of our results for phytoplankton swimming in the ocean is briefly discussed.

Rayleigh number scaling in numerical convection

1996 ◽  
Vol 310 ◽  
pp. 139-179 ◽  
Author(s):  
Robert M. Kerr
Keyword(s):  
Boundary Layer ◽  
Rayleigh Number ◽  
Large Scale ◽  
Stokes Equations ◽  
Good Evidence ◽  
Navier Stokes ◽  
Fixed Temperature ◽  
Navier Stokes Equations ◽  
Local Boundary ◽  
Velocity Boundary Layer

Using direct simulations of the incompressible Navier-Stokes equations with rigid upper and lower boundaries at fixed temperature and periodic sidewalls, scaling with respect to Rayleigh number is determined. At large aspect ratio (6:6:1) on meshes up to 288 × 288 × 96, a single scaling regime consistent with the properties of ‘hard’ convective turbulence is found for Pr = 0.7 between Ra = 5 × 104 and Ra = 2 × 107. The properties of this regime include Nu ∼ RaβT with βT = 0.28 ≈ 2/7, exponential temperature distributions in the centre of the cell, and velocity and temperature scales consistent with experimental measurements. Two velocity boundary-layer thicknesses are identified, one outside the thermal boundary layer that scales as Ra−1/7 and the other within it that scales as Ra−3/7. Large-scale shears are not observed; instead, strong local boundary-layer shears are observed in regions between incoming plumes and an outgoing network of buoyant sheets. At the highest Rayleigh number, there is a decade where the energy spectra are close to k−5/3 and temperature variance spectra are noticeably less steep. It is argued that taken together this is good evidence for ‘hard’ turbulence, even if individually each of these properties might have alternative explanations.

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 On the analysis of a geometrically selective turbulence model

2020 ◽  
Vol 9 (1) ◽  
pp. 1402-1419 ◽  
Author(s):  
Nejmeddine Chorfi ◽  
Mohamed Abdelwahed ◽  
Luigi C. Berselli
Keyword(s):  
Turbulent Flows ◽  
Turbulence Model ◽  
Large Scale ◽  
Stokes Equations ◽  
A Priori ◽  
Strong Solutions ◽  
Navier Stokes ◽  
Smagorinsky Model ◽  
Navier Stokes Equations ◽  
Velocity Pressure

Abstract In this paper we propose some new non-uniformly-elliptic/damping regularizations of the Navier-Stokes equations, with particular emphasis on the behavior of the vorticity. We consider regularized systems which are inspired by the Baldwin-Lomax and by the selective Smagorinsky model based on vorticity angles, and which can be interpreted as Large Scale methods for turbulent flows. We consider damping terms which are active at the level of the vorticity. We prove the main a priori estimates and compactness results which are needed to show existence of weak and/or strong solutions, both in velocity/pressure and velocity/vorticity formulation for various systems. We start with variants of the known ones, going later on to analyze the new proposed models.

Navier–Stokes solutions of unsteady separation induced by a vortex

2002 ◽  
Vol 465 ◽  
pp. 99-130 ◽  
Author(s):  
A. V. OBABKO ◽  
K. W. CASSEL
Keyword(s):  
Boundary Layer ◽  
Large Scale ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Recirculation Region ◽  
Small Scale ◽  
Navier Stokes Equations ◽  
Scale Interaction

Numerical solutions of the unsteady Navier–Stokes equations are considered for the flow induced by a thick-core vortex convecting along a surface in a two-dimensional incompressible flow. The presence of the vortex induces an adverse streamwise pressure gradient along the surface that leads to the formation of a secondary recirculation region followed by a narrow eruption of near-wall fluid in solutions of the unsteady boundary-layer equations. The locally thickening boundary layer in the vicinity of the eruption provokes an interaction between the viscous boundary layer and the outer inviscid flow. Numerical solutions of the Navier–Stokes equations show that the interaction occurs on two distinct streamwise length scales depending upon which of three Reynolds-number regimes is being considered. At high Reynolds numbers, the spike leads to a small-scale interaction; at moderate Reynolds numbers, the flow experiences a large-scale interaction followed by the small-scale interaction due to the spike; at low Reynolds numbers, large-scale interaction occurs, but there is no spike or subsequent small-scale interaction. The large-scale interaction is found to play an essential role in determining the overall evolution of unsteady separation in the moderate-Reynolds-number regime; it accelerates the spike formation process and leads to formation of secondary recirculation regions, splitting of the primary recirculation region into multiple corotating eddies and ejections of near-wall vorticity. These eddies later merge prior to being lifted away from the surface and causing detachment of the thick-core vortex.

scholarly journals Direct numerical simulation of the oscillatory flow around a sphere resting on a rough bottom

2017 ◽  
Vol 822 ◽  
pp. 235-266 ◽  
Author(s):  
Marco Mazzuoli ◽  
Paolo Blondeaux ◽  
Julian Simeonov ◽  
Joseph Calantoni
Keyword(s):  
Reynolds Number ◽  
Large Scale ◽  
Oscillatory Flow ◽  
Stokes Equations ◽  
Coarse Sand ◽  
Spherical Particles ◽  
Navier Stokes ◽  
Sea Waves ◽  
Spherical Object ◽  
Navier Stokes Equations

The oscillatory flow around a spherical object lying on a rough bottom is investigated by means of direct numerical simulations of the continuity and Navier–Stokes equations. The rough bottom is simulated by a layer/multiple layers of spherical particles, the size of which is much smaller that the size of the object. The period and amplitude of the velocity oscillations of the free stream are chosen to mimic the flow at the bottom of sea waves and the size of the small spherical particles falls in the range of coarse sand/very fine gravel. Even though the computational costs allow only the simulation of moderate values of the Reynolds number characterizing the bottom boundary layer, the results show that the coherent vortex structures, shed by the spherical object, can break up and generate turbulence, if the Reynolds number of the object is sufficiently large. The knowledge of the velocity field allows the dynamics of the large-scale coherent vortices shed by the object to be determined and turbulence characteristics to be evaluated. Moreover, the forces and torques acting on both the large spherical object and the small particles, simulating sediment grains, can be determined and analysed, thus laying the groundwork for the investigation of sediment dynamics and scour developments.

Mechanics of thermohaline interleaving: beyond the empirical flux laws

2011 ◽  
Vol 675 ◽  
pp. 117-140 ◽  
Author(s):  
TIMOUR RADKO
Keyword(s):  
Large Scale ◽  
Stokes Equations ◽  
Equations Of Motion ◽  
Field Measurements ◽  
Navier Stokes ◽  
Homogeneous Field ◽  
Spontaneous Generation ◽  
Navier Stokes Equations ◽  
Salt Fingers ◽  
Stratified Ocean

An analytical theory is developed which illustrates the dynamics of the spontaneous generation of thermohaline intrusions in the stratified ocean with density compensated lateral temperature and salinity gradients. Intrusions in the model are driven by the interaction with the initially homogeneous field of salt fingers, whose amplitude and spatial orientation is weakly modulated by the long wavelength perturbations introduced into the system. The asymptotic multiscale analysis makes it possible to identify intrusive instabilities resulting from the positive feedback of salt fingers on large-scale perturbations and analyse the resulting patterns. The novelty of the proposed analysis is related to our ability to avoid using empirical double-diffusive flux laws – an approach taken by earlier models. Instead, we base our analytical explorations directly on the governing (Navier–Stokes) equations of motion. The model predictions of the growth rates and preferred slopes of intrusions are in general agreement with the laboratory and field measurements.

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.

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