Photo-gyrotactic bioconvection

2011 ◽  
Vol 678 ◽  
pp. 41-86 ◽  
Author(s):  
C. R. WILLIAMS ◽  
M. A. BEES
Keyword(s):  
Fluid Motion ◽  
Flagellar Apparatus ◽  
Finite Depth ◽  
Experimental Measurements ◽  
Hydrodynamic Instabilities ◽  
Centre Of Mass ◽  
Rational Models ◽  
The Third ◽  
Swimming Motion ◽  
Directional Stimulus

Many microorganisms exhibit taxes, biased swimming motion relative to a directional stimulus. Aggregations of cells with densities dissimilar to the medium in which they swim can induce hydrodynamic instabilities and bioconvection patterns. Here, three novel and mechanistically distinct models of the interaction of the two dominant taxes in suspensions of swimming phototrophic algae are presented: phototaxis, swimming towards or away from light, and gyrotaxis, a balance between viscous and gravitational torques. The descriptions are accordant with, and extend, recent rational models of bioconvection. In particular, the first model is for photokinesis–gyrotaxis, the second varies the cells' centre-of-mass offset, and the third introduces a reactive phototactic torque associated with the propulsive flagellar apparatus. Equilibria and linear-stability analysis in a layer of finite depth are analysed in detail using analytical and numerical methods. Results indicate that the first two models, despite their different roots, remarkably are in agreement. Penetrative and oscillatory modes are found and explained. Dramatically different behaviour is obtained for the model with phototactic torques: instabilities arise even in the absence of fluid motion due to induced gradients of light intensity. Typically, the response of microorganisms to light is multifaceted and thus some combination of the three models is appropriate. Encouragingly, qualitative agreement is found with recent experimental measurements on the effects of illumination on dominant pattern wavelength in bioconvection experiments. The theory may be of some interest in the emergent field of bioreactor design.

An integral-equation method for determining the fluid motion due to a cylinder heaving on water of finite depth

1980 ◽  
Vol 372 (1748) ◽  
pp. 93-110 ◽  
Keyword(s):  
Integral Equation ◽  
Fundamental Solution ◽  
Integral Equations ◽  
Fluid Motion ◽  
Integral Equation Method ◽  
Finite Depth ◽  
The Body ◽  
Wave Source ◽  
Method Of Integral Equations ◽  
Infinite Set

The method of integral equations is used here to calculate the virtual mass of a half-immersed cylinder heaving periodically on water of finite constant depth. For general sections this method is more appropriate than the method of multipoles; particular sections that are considered are the circle and the ellipse. Green’s theorem is applied to the potential and to a fundamental solution (wave source) satisfying the conditions at the free surface, at the bottom and at infinity, but not necessarily on the body. An integral equation for the potential on the body only is thus obtained. For the simplest choice of fundamental solution the method breaks down at a discrete infinite set of frequencies, as is well known. When the fundamental solution was modified, however, a different integral equation could be obtained for the same unknown function and this was found not to break down for the circle and ellipse. The present numerical results are in good agreement with those obtained by the method of multipoles which for the circle is more efficient than the method of integral equations but which is not readily applicable to other sections. Much effort now goes into such calculations.

The Role of Coulombic Forces in Quasi-Two Dimensional Electrochemical Deposition

1996 ◽  
Vol 451 ◽  
Author(s):  
G. Marshall ◽  
P. Mocskos ◽  
F. Molina ◽  
S. Dengra
Keyword(s):  
Numerical Modeling ◽  
Pattern Formation ◽  
Electrochemical Deposition ◽  
Growth Pattern ◽  
Stokes Equations ◽  
Fluid Motion ◽  
Navier Stokes ◽  
Experimental Measurements ◽  
Dimensionless Numbers ◽  
Navier Stokes Equations

ABSTRACTRecent work demonstrates the relevant influence of convection during growth pattern formation in thin-layer electrochemical deposition. Convection is driven mainly by coulombic forces due to local charges at the tip of the aggregation and by buoyancy forces due to concentration gradients. Here we study through physical experiments and numerical modeling the regime under which coulombic forces are important. In the experimental measurements fluid motion near the growing tips of the deposit is visualized with neutrally buoyant latex spheres and its speed measured with videomicroscope tracking techniques and image processing software. The numerical modeling consists in the solution of the 2D dimensionless Nernst-Planck equations for ion concentrations, the Poisson equation for the electric field and the Navier-Stokes equations for the fluid flow, and a stochastic growth rule for ion deposition. A new set of dimensionless numbers governing electroconvection dominated flows is introduced. Preliminary experimental measurements and numerical results indicate that in the electroconvection dominated regime coulombic forces increase with the applied voltage, and their influence over growth pattern formation can be assessed with the magnitude of the dimensionless electric Froude number. It is suggested that when this number decreases the deposit morphology changes from fractal to dense branching.

scholarly journals Experimental Measurements of Hydrodynamic Instabilities on Nova of Relevance to Astrophysics

2000 ◽  
Vol 127 (2) ◽  
pp. 325-331
Author(s):  
S. G. Glendinning ◽  
K. S. Budil ◽  
C. Cherfils ◽  
R. P. Drake ◽  
D. Farley ◽  
...  
Keyword(s):  
Experimental Measurements ◽  
Hydrodynamic Instabilities

scholarly journals The Effect of Discharge Depth on Contaminant Dispersion in Turbulent Open Channel Flow

1982 ◽  
Vol 35 (2) ◽  
pp. 107 ◽  
Author(s):  
Albert J Gabric
Keyword(s):  
Total Mass ◽  
Open Channel ◽  
Open Channel Flow ◽  
Finite Depth ◽  
Centre Of Mass ◽  
Contaminant Dispersion ◽  
Transport And Diffusion ◽  
Neutrally Buoyant ◽  
Analytical Expressions ◽  
And Diffusion

The transport and diffusion of neutrally buoyant, conservative contaminants in an open, finite depth channel is analysed at times before uniform mixing over the depth has occurred. Analytical expressions for the total mass at a given depth, the centre of mass and the variance of the contaminant patch are presented.

Wave Kinematics and Pressure Field of Third-Order Theory for Bichromatic Bi-Directional Waves in Water of Finite Depth

2014 ◽  
Vol 580-583 ◽  
pp. 2166-2169
Author(s):  
Hu Huang ◽  
Guo Liang Li
Keyword(s):  
Pressure Field ◽  
State Of The Art ◽  
Finite Depth ◽  
Order Theory ◽  
Offshore Structures ◽  
Structural Members ◽  
Third Order ◽  
Wave Kinematics ◽  
The Third ◽  
Directional Waves

Based on the third-order theory for bichromatic bi-directional waves in water of finite depth, a set of explicit formulas for the state-of-the art quantities of wave kinematics for horizontal and vertical particle displacements, velocities and accelerations, and wave pressure field is developed, and would be much more accurate and realistic in the design of harbor, coastal and offshore structures and their structural members.

scholarly journals Hamiltonian formalism of two-dimensional Vlasov kinetic equation

2014 ◽  
Vol 470 (2172) ◽  
pp. 20140343
Author(s):  
Maxim V. Pavlov
Keyword(s):  
Kinetic Equation ◽  
Hamiltonian Structure ◽  
Bubbly Flow ◽  
Fluid Motion ◽  
Hamiltonian Formalism ◽  
Finite Depth ◽  
Dimensional Case ◽  
Two Dimensional ◽  
The One ◽  
Hydrodynamic Reductions

In this paper, the two-dimensional Benney system describing long wave propagation of a finite depth fluid motion and the multi-dimensional Russo–Smereka kinetic equation describing a bubbly flow are considered. The Hamiltonian approach established by J. Gibbons for the one-dimensional Vlasov kinetic equation is extended to a multi-dimensional case. A local Hamiltonian structure associated with the hydrodynamic lattice of moments derived by D. J. Benney is constructed. A relationship between this hydrodynamic lattice of moments and the two-dimensional Vlasov kinetic equation is found. In the two-dimensional case, a Hamiltonian hydrodynamic lattice for the Russo–Smereka kinetic model is constructed. Simple hydrodynamic reductions are presented.

scholarly journals Scattering Of Internal Waves By Vertical Barrier In A Channel Of Stratified Fluid

2015 ◽  
Vol 20 (3) ◽  
pp. 471-485
Author(s):  
P. Dolai
Keyword(s):  
Internal Wave ◽  
Stream Function ◽  
Wave Train ◽  
Fluid Motion ◽  
Finite Depth ◽  
Boussinesq Approximation ◽  
Scattering Matrix ◽  
Stratified Fluid ◽  
Thin Wall ◽  
Vertical Barrier

Abstract The problem of two dimensional internal wave scattering by a vertical barrier in the form of a submerged plate, or a thin wall with a gap in an exponentially stratified fluid of uniform finite depth bounded by a rigid plane at the top, is considered in this paper. Assuming linear theory and the Boussinesq approximation, the problem is formulated in terms of the stream function. In the regions of the two sides of the vertical barrier, the scattered stream function is represented by appropriate eigen function expansions. By the use of appropriate conditions on the barrier and the gap, a dual series relation involving the unknown elements of the scattering matrix is produced. By defining a function with these unknown elements as its Fourier sine expansion series, it is found that this function satisfies a Carleman type integral equation on the barrier whose solution is immediate. The elements of the scattering matrix are then obtained analytically as well as numerically corresponding to any mode of the incident internal wave train for each barrier configuration. A comparison with earlier results available in the literature shows good agreement. To visualize the effect of the barrier on the fluid motion, the stream lines for an incident internal wave train at the lowest mode are plotted.

Water Waves Over a Channel of Finite Depth With a Submerged Plane Barrier

1950 ◽  
Vol 2 ◽  
pp. 210-222 ◽  
Author(s):  
Albert E. Heins
Keyword(s):  
Surface Waves ◽  
Water Waves ◽  
Finite Depth ◽  
The Third ◽  
Plane Barrier

This is the third in a series of problems in the study of surface waves which have been disturbed by the presence of a plane barrier and to which a solution may be provided. We assume as in part I, that the fluid is incompressible and non-viscous, and that motion is irrotational.

scholarly journals Growth of bioconvection patterns in a suspension of gyrotactic micro-organisms in a layer of finite depth

1989 ◽  
Vol 208 ◽  
pp. 509-543 ◽  
Author(s):  
N. A. Hill ◽  
T. J. Pedley ◽  
J. O. Kessler
Keyword(s):  
Schmidt Number ◽  
Fluid Motion ◽  
Finite Depth ◽  
Layer Depth ◽  
Bulk Fluid ◽  
Parameter Measuring ◽  
Micro Organisms ◽  
Parameter Values ◽  
Negatively Buoyant ◽  
The Continuum

The effect of gyrotaxis on the linear stability of a suspension of swimming, negatively buoyant micro-organisms is examined for a layer of finite depth. In the steady basic state there is no bulk fluid motion, and the upwards swimming of the cells is balanced by diffusion resulting from randomness in their shape, orientation and swimming behaviour. This leads to a bulk density stratification with denser fluid on top. The theory is based on the continuum model of Pedley, Hill & Kessler (1988), and employs both asymptotic and numerical analysis. The suspension is characterized by five dimensionless parameters: a Rayleigh number, a Schmidt number, a layer-depth parameter, a gyrotaxis number G, and a geometrical parameter measuring the ellipticity of the micro-organisms. For small values of G, the most unstable mode has a vanishing wavenumber, but for sufficiently large values of G, the predicted initial wavelength is finite, in agreement with experiments. The suspension becomes less stable as the layer depth is increased. Indeed, if the layer is sufficiently deep an initially homogeneous suspension is unstable, and the equilibrium state does not form. The theory of Pedley, Hill & Kessler (1988) for infinite depth is shown to be appropriate in that case. An unusual feature of the model is the existence of overstable or oscillatory modes which are driven by the gyrotactic response of the micro-organisms to the shear at the rigid boundaries of the layer. These modes occur at parameter values which could be realized in experiments.

Sign in / Sign up

Export Citation Format

Share Document