scholarly journals Settling of Particles beneath Water Waves

2008 ◽  
Vol 38 (12) ◽  
pp. 2846-2853 ◽  
Author(s):  
Ian Eames
Keyword(s):  
Water Waves ◽  
Settling Velocity ◽  
Added Mass ◽  
Stokes Drift ◽  
Inertial Forces ◽  
Leading Order ◽  
Small Particles ◽  
Fall Velocity ◽  
Finite Distance ◽  
The Mean

Abstract Considered here is the motion of small particles beneath irrotational water waves. The added mass and inertial forces are shown to be an important role in the mean transport of particles. To leading order, particles are transported with a mean horizontal Stokes drift velocity and sediment with their terminal fall velocity. The combination of a settling velocity and a mean drift transports particles a finite distance forward from their point of release.

scholarly journals Settling Velocity of Microplastics Exposed to Wave Action

2021 ◽  
Vol 9 (2) ◽  
pp. 142
Author(s):  
Annalisa De Leo ◽  
Laura Cutroneo ◽  
Damien Sous ◽  
Alessandro Stocchino
Keyword(s):  
Laboratory Experiments ◽  
Settling Velocity ◽  
Transport Model ◽  
Stokes Drift ◽  
Inertial Effects ◽  
Sea Waves ◽  
Heavy Particles ◽  
Analytical Formulation ◽  
Simplified Approach ◽  
Remote Areas

Microplastic (MP) debris is recognized to be one of the most serious threats to marine environments. They are found in all seas and oceanic basins worldwide, even in the most remote areas. This is further proof that the transport of MPs is very efficient. In the present study, we focus our attention on MPs’ transport owing to the Stokes drift generated by sea waves. Recent studies have shown that the interaction between heavy particles and Stokes drift leads to unexpected phenomena mostly related to inertial effects. We perform a series of laboratory experiments with the aim to directly measure MPs’ trajectories under different wave conditions. The main objective is to quantify the inertial effect and, ultimately, suggest a new analytical formulation for the net settling velocity. The latter formula might be implemented in a larger scale transport model in order to account for inertial effects in a simplified approach.

The focusing of radiation by a random surface when the source is at a finite distance

1960 ◽  
Vol 56 (1) ◽  
pp. 27-40 ◽  
Author(s):  
M. S. Longuet-Higgins
Keyword(s):  
Mean Curvature ◽  
Joint Distribution ◽  
Total Curvature ◽  
Statistical Distribution ◽  
Constant Parameter ◽  
Random Surface ◽  
Second Derivatives ◽  
Finite Distance ◽  
The Mean ◽  
Image Position

Imagine a nearly horizontal, statistically uniform, random surface ζ(x, y), Gaussian in the sense that the second derivatives , , have a normal joint distribution. The problem considered is the statistical distribution of the quantitywhere J and Ω denote the mean curvature and total curvature of the surface, respectively, and ν is a constant parameter.

scholarly journals Investigation of DNA denaturation from generalized Morse potential

2018 ◽  
Vol 3 (2) ◽  
Author(s):  
R. El Kinani ◽  
H. Kaidi ◽  
M. Benhamou
Keyword(s):  
Morse Potential ◽  
Bound States ◽  
Analytical Study ◽  
Free Energy Density ◽  
Exact Expression ◽  
Dna Denaturation ◽  
Denaturation Temperature ◽  
Finite Distance ◽  
The Mean ◽  
Generalized Morse Potential

In this paper, we present a non-linear model for the study of DNA denaturation transition. To this end, we assume that the double-strands DNA interact via a realistic generalized Morse potential that reproduces well the features of the real interaction. Using the Transfer Matrix Method, based on the resolution of a Schrödinger equation, we first determine exactly their solution, which are found to be bound states. Second, from an exact expression of the ground state, we compute the denaturation temperature and the free energy density, in terms of the parameters of the potential.Then, we calculate the contact probability, which is the probability to find the double-strands at a (finite) distance apart, from which we determine the behaviour of the mean-distance between DNA-strands.The main conclusion is that, the present analytical study reveals that the generalized Morse potential is a good candidate for the study of DNA denaturation

The Vertical Mean Force and Moment of Submerged Bodies Under Waves

1971 ◽  
Vol 15 (03) ◽  
pp. 231-245 ◽  
Author(s):  
C. M. Lee ◽  
J. N. Newman
Keyword(s):  
Free Surface ◽  
Added Mass ◽  
Cross Sectional Area ◽  
The Body ◽  
Slender Body ◽  
Longitudinal Distribution ◽  
Vertical Force ◽  
Sectional Area ◽  
Cross Sectional ◽  
The Mean

A neutrally buoyant slender body of arbitrary sectional form, submerged beneath a free surface, is free to respond to an incident plane progressive wave system. The fluid is assumed inviscid, incompressible, homogeneous and infinitely deep. The first-order oscillatory motion of the body and the second-order time-average vertical force and pitching moment acting on the body are obtained in terms of Kochin's function. By use of slender-body theory for a deeply submerged body, the final expressions for the mean force and the moment are shown to depend on the longitudinal distribution of sectional area and added mass and on the amplitude and the frequency of the ambient surface waves. The magnitude of the mean force for various simple geometric cylinders is compared with that of a circular cylinder of equal cross-sectional area. The mean force on a nonaxisymmetric body is often approximated by replacing the section with circular profiles of equivalent cross-sectional area. A better scheme of approximation is presented, based on a simple way of estimating the two-dimensional added mass. It is expected that the effect of the cross-sectional geometry on mean vertical force and moment will be more significant when the body is very close to the free surface.

The gravitational settling of aerosol particles in homogeneous turbulence and random flow fields

1987 ◽  
Vol 174 ◽  
pp. 441-465 ◽  
Author(s):  
M. R. Maxey
Keyword(s):  
Settling Velocity ◽  
High Strain ◽  
Free Fall ◽  
Terminal Velocity ◽  
Homogeneous Turbulence ◽  
Mean Flow ◽  
Particle Inertia ◽  
The Mean ◽  
Random Flow ◽  
Flow Particle

The average settling velocity in homogeneous turbulence of a small rigid spherical particle, subject to a Stokes drag force, is shown to depend on the particle inertia and the free-fall terminal velocity in still fluid. With no inertia the particle settles on average at the same rate as in still fluid, assuming there is no mean flow. Particle inertia produces a bias in each trajectory towards regions of high strain rate or low vorticity, which affects the mean settling velocity. Results from a Gaussian random velocity field show that this produces an increased settling velocity.

Flows of liquid4He due to oscillating grids

2017 ◽  
Vol 832 ◽  
pp. 578-599 ◽  
Author(s):  
P. Švančara ◽  
M. La Mantia
Keyword(s):  
Turbulent Flows ◽  
Particle Tracking Velocimetry ◽  
Reynolds Numbers ◽  
Quantized Vortices ◽  
Viscous Fluids ◽  
Statistical Distributions ◽  
Small Particles ◽  
Oscillating Grids ◽  
The Mean ◽  
Cryogenic Flows

We investigate cryogenic flows of liquid4He between two grids oscillating in phase, at temperatures ranging from approximately 1.3 to 2.5 K, resulting in suitably defined Reynolds numbers up to$10^{5}$. We specifically study the flow-induced motions of small particles suspended in the fluid by using the particle tracking velocimetry technique. We focus on turbulent flows of superfluid4He that occur below approximately 2.2 K and are known to display, in certain conditions, features different from those observed in flows of classical viscous fluids, such as water. We find that, at large enough length scales, larger than the mean distance between quantized vortices, representing the quantum length scale of the flow, the shapes of the velocity and velocity increment statistical distributions are very similar to those obtained in turbulent flows of viscous fluids. The experimental outcome strongly supports the view that, in the range of investigated parameters, particles probing flows of superfluid4He behave as if they were tracking classical flows.

scholarly journals Sedimentation of finite-size spheres in quiescent and turbulent environments

2016 ◽  
Vol 788 ◽  
pp. 640-669 ◽  
Author(s):  
Walter Fornari ◽  
Francesco Picano ◽  
Luca Brandt
Keyword(s):  
Turbulent Flow ◽  
Settling Velocity ◽  
Solid Phase ◽  
Density Ratio ◽  
Finite Size ◽  
Spherical Particles ◽  
Volume Fractions ◽  
Turbulent Environments ◽  
The Mean ◽  
Quiescent Fluid

Sedimentation of a dispersed solid phase is widely encountered in applications and environmental flows, yet little is known about the behaviour of finite-size particles in homogeneous isotropic turbulence. To fill this gap, we perform direct numerical simulations of sedimentation in quiescent and turbulent environments using an immersed boundary method to account for the dispersed rigid spherical particles. The solid volume fractions considered are ${\it\phi}=0.5{-}1\,\%$, while the solid to fluid density ratio ${\it\rho}_{p}/{\it\rho}_{f}=1.02$. The particle radius is chosen to be approximately six Kolmogorov length scales. The results show that the mean settling velocity is lower in an already turbulent flow than in a quiescent fluid. The reductions with respect to a single particle in quiescent fluid are approximately 12 % and 14 % for the two volume fractions investigated. The probability density function of the particle velocity is almost Gaussian in a turbulent flow, whereas it displays large positive tails in quiescent fluid. These tails are associated with the intermittent fast sedimentation of particle pairs in drafting–kissing–tumbling motions. The particle lateral dispersion is higher in a turbulent flow, whereas the vertical one is, surprisingly, of comparable magnitude as a consequence of the highly intermittent behaviour observed in the quiescent fluid. Using the concept of mean relative velocity we estimate the mean drag coefficient from empirical formulae and show that non-stationary effects, related to vortex shedding, explain the increased reduction in mean settling velocity in a turbulent environment.

Wave-induced mean flows in rotating shallow water with uniform potential vorticity

2018 ◽  
Vol 839 ◽  
pp. 408-429 ◽  
Author(s):  
Jim Thomas ◽  
Oliver Bühler ◽  
K. Shafer Smith
Keyword(s):  
Shallow Water ◽  
Potential Vorticity ◽  
Rotation Rate ◽  
Standing Waves ◽  
Leading Order ◽  
Mean Flow ◽  
Wave Fields ◽  
The Mean ◽  
Rotating Shallow Water ◽  
Wave Induced

Theoretical and numerical computations of the wave-induced mean flow in rotating shallow water with uniform potential vorticity are presented, with an eye towards applications in small-scale oceanography where potential-vorticity anomalies are often weak compared to the waves. The asymptotic computations are based on small-amplitude expansions and time averaging over the fast wave scale to define the mean flow. Importantly, we do not assume that the mean flow is balanced, i.e. we compute the full mean-flow response at leading order. Particular attention is paid to the concept of modified diagnostic relations, which link the leading-order Lagrangian-mean velocity field to certain wave properties known from the linear solution. Both steady and unsteady wave fields are considered, with specific examples that include propagating wavepackets and monochromatic standing waves. Very good agreement between the theoretical predictions and direct numerical simulations of the nonlinear system is demonstrated. In particular, we extend previous studies by considering the impact of unsteady wave fields on the mean flow, and by considering the total kinetic energy of the mean flow as a function of the rotation rate. Notably, monochromatic standing waves provide an explicit counterexample to the often observed tendency of the mean flow to decrease monotonically with the background rotation rate.

Particle paths in nonlinear Schrödinger models in the presence of linear shear currents

2018 ◽  
Vol 855 ◽  
pp. 322-350 ◽  
Author(s):  
C. W. Curtis ◽  
J. D. Carter ◽  
H. Kalisch
Keyword(s):  
Surface Tension ◽  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Stokes Drift ◽  
Carrier Wave ◽  
Nonlinear Schrödinger ◽  
The Mean ◽  
Background Shear

We investigate the effect of constant-vorticity background shear on the properties of wavetrains in deep water. Using the methodology of Fokas (A Unified Approach to Boundary Value Problems, 2008, SIAM), we derive a higher-order nonlinear Schrödinger equation in the presence of shear and surface tension. We show that the presence of shear induces a strong coupling between the carrier wave and the mean-surface displacement. The effects of the background shear on the modulational instability of plane waves is also studied, where it is shown that shear can suppress instability, although not for all carrier wavelengths in the presence of surface tension. These results expand upon the findings of Thomas et al. (Phys. Fluids, vol. 24 (12), 2012, 127102). Using a modification of the generalized Lagrangian mean theory in Andrews & McIntyre (J. Fluid Mech., vol. 89, 1978, pp. 609–646) and approximate formulas for the velocity field in the fluid column, explicit, asymptotic approximations for the Lagrangian and Stokes drift velocities are obtained for plane-wave and Jacobi elliptic function solutions of the nonlinear Schrödinger equation. Numerical approximations to particle trajectories for these solutions are found and the Lagrangian and Stokes drift velocities corresponding to these numerical solutions corroborate the theoretical results. We show that background currents have significant effects on the mean transport properties of waves. In particular, certain combinations of background shear and carrier wave frequency lead to the disappearance of mean-surface mass transport. These results provide a possible explanation for the measurements reported in Smith (J. Phys. Oceanogr., vol. 36, 2006, pp. 1381–1402). Our results also provide further evidence of the viability of the modification of the Stokes drift velocity beyond the standard monochromatic approximation, such as recently proposed in Breivik et al. (J. Phys. Oceanogr., vol. 44, 2014, pp. 2433–2445) in order to obtain a closer match to a range of complex ocean wave spectra.

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