scholarly journals Metachronal Swimming with Rigid Arms near Boundaries

Fluids ◽  
2020 ◽  
Vol 5 (1) ◽  
pp. 24 ◽  
Author(s):  
Rintaro Hayashi ◽  
Daisuke Takagi
Keyword(s):  
Mathematical Model ◽  
Stokes Flow ◽  
Experimental System ◽  
Phase Delay ◽  
Slender Body ◽  
Inertial Effects ◽  
Slender Body Theory ◽  
Measured Displacement ◽  
Body Theory ◽  
Over Time

Various organisms such as crustaceans use their appendages for locomotion. If they are close to a confining boundary then viscous as opposed to inertial effects can play a central role in governing the dynamics. To study the minimal ingredients needed for swimming without inertia, we built an experimental system featuring a robot equipped with a pair of rigid slender arms with negligible inertia. Our results show that directing the arms to oscillate about the same time-averaged orientation produces no net displacement of the robot each cycle, regardless of any phase delay between the oscillating arms. The robot is able to swim if the arms oscillate asynchronously around distinct orientations. The measured displacement over time matches well with a mathematical model based on slender-body theory for Stokes flow. Near a confining boundary, the robot with no net displacement every cycle showed similar behavior, while the swimming robot increased in speed closer to the boundary.

scholarly journals Remarks on Regularized Stokeslets in Slender Body Theory

Fluids ◽  
2021 ◽  
Vol 6 (8) ◽  
pp. 283
Author(s):  
Laurel Ohm
Keyword(s):  
Stokes Flow ◽  
Regularization Parameter ◽  
Slender Body ◽  
Slender Body Theory ◽  
Classical Counterpart ◽  
Regularized Stokeslets ◽  
The Difference ◽  
Body Theory ◽  
Force Data ◽  
Well Posed

We remark on the use of regularized Stokeslets in the slender body theory (SBT) approximation of Stokes flow about a thin fiber of radius ϵ>0. Denoting the regularization parameter by δ, we consider regularized SBT based on the most common regularized Stokeslet plus a regularized doublet correction. Given sufficiently smooth force data along the filament, we derive L∞ bounds for the difference between regularized SBT and its classical counterpart in terms of δ, ϵ, and the force data. We show that the regularized and classical expressions for the velocity of the filament itself differ by a term proportional to log(δ/ϵ); in particular, δ=ϵ is necessary to avoid an O(1) discrepancy between the theories. However, the flow at the surface of the fiber differs by an expression proportional to log(1+δ2/ϵ2), and any choice of δ∝ϵ will result in an O(1) discrepancy as ϵ→0. Consequently, the flow around a slender fiber due to regularized SBT does not converge to the solution of the well-posed slender body PDE which classical SBT is known to approximate. Numerics verify this O(1) discrepancy but also indicate that the difference may have little impact in practice.

Simulation of the Dynamic Behavior of Ships Based on Slender-Body Theory (SBT)

2013 ◽  
Author(s):  
Oscar D. Tascon ◽  
Jaime D. Mora ◽  
Roberto J. Algarin
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Dynamic Performance ◽  
Slender Body ◽  
Computational Time ◽  
Slender Body Theory ◽  
Shipbuilding Industry ◽  
Technology Corporation ◽  
The Mathematical Model ◽  
Body Theory

One of the aims of the Colombian Ministry of Defense in the field of science and technology is to develop and build in-house simulators for training. An important prerequisite in the development of these types of simulators is to have accurate knowledge about the forces that act on the particular type of ship being considered. In the pursuit of this objective, the Science & Technology Corporation for the Development of the Shipbuilding Industry in Colombia — COTECMAR has established a research program for the development of physics-based models to predict the generalized forces acting on maneuvering ships. The following article proposes a mathematical model capable of providing the simulator with calculations for the hydrodynamic forces acting on three types of ships: displacement ships, submarines and planning hulls. Derived from slender-body theory (SBT), the mathematical model presented minimizes computational time and eliminates the need for experimental data, making it possible to use the calculation of hydrodynamics forces at the initial stages of design when the geometry of the ship is constantly revised and the effect of those changes in the dynamic performance of the ship needs to be assessed. The article explains the mathematical model proposed and its modular nature, compares existing numerical and experimental data with results obtained from this study for the three case studies selected: displacement ships, submarines and planing hulls.

A note on the S-transform and slender body theory in Stokes flow

2010 ◽  
Vol 75 (3) ◽  
pp. 343-355 ◽  
Author(s):  
J. R. Blake ◽  
E. O. Tuck ◽  
P. W. Wakeley
Keyword(s):  
Stokes Flow ◽  
Slender Body ◽  
Slender Body Theory ◽  
S Transform ◽  
Body Theory

Stokes flow about a sphere attached to a slender body

1974 ◽  
Vol 64 (4) ◽  
pp. 817-826 ◽  
Author(s):  
N. J. De Mestre ◽  
D. F. Katz
Keyword(s):  
Stokes Flow ◽  
Unit Length ◽  
Interactive Effect ◽  
Slender Body ◽  
Slip Condition ◽  
Image Point ◽  
Image System ◽  
Slender Body Theory ◽  
Spherical Head ◽  
Body Theory

Stokes flow is analysed for a combination body, consisting of a sphere attached to a slender body, translating along its axis in an infinite and otherwise un-disturbed fluid. The cross-section of the after-body, or tail, is circular; the radius, while not necessarily constant, is small compared with the radius of the spherical head. The tail is represented by a distribution of Stokeslets of strength per unit length F(z), located and directed along its axis. The interactive effect of head-tail attachment is manifested by the presence of image singularities located within the sphere. The image system for a single tail Stokeslet must be such that the no-slip condition is satisfied on the surface of the sphere. It is shown that this system consists of a Stokeslet, a Stokes doublet (stresslet only) and a source doublet located a t the image point. The strength F(z) is obtained by applying the no-slip condition to the combination body. The solution follows the lines of traditional slender-body theory, an expansion being performed in ascending powers of the reciprocal of the logarithm of the aspect ratio. The integral force parameters and F(z) are obtained to second order. The interactive effect is assessed, and the results are discussed in the context of a sedimenting micro-organism, such as a spermatozoon. The drag on the combination body is shown to be less by around 10% than the sum of the drags on an isolated sphere and tail. This drag, for a sperm-shaped body, is divided approximately equally between head and tail.

Note on the swimming of slender fish

1960 ◽  
Vol 9 (2) ◽  
pp. 305-317 ◽  
Author(s):  
M. J. Lighthill
Keyword(s):  
Swimming Speed ◽  
Critical Value ◽  
Slender Body ◽  
Vortex Wake ◽  
Frictional Drag ◽  
Slender Body Theory ◽  
Propulsive Efficiency ◽  
Deformable Bodies ◽  
Work Done ◽  
Body Theory

The paper seeks to determine what transverse oscillatory movements a slender fish can make which will give it a high Froude propulsive efficiency, $\frac{\hbox{(forward velocity)} \times \hbox{(thrust available to overcome frictional drag)}} {\hbox {(work done to produce both thrust and vortex wake)}}.$ The recommended procedure is for the fish to pass a wave down its body at a speed of around $\frac {5} {4}$ of the desired swimming speed, the amplitude increasing from zero over the front portion to a maximum at the tail, whose span should exceed a certain critical value, and the waveform including both a positive and a negative phase so that angular recoil is minimized. The Appendix gives a review of slender-body theory for deformable bodies.

Slender-body theory for slow viscous flow

1976 ◽  
Vol 75 (4) ◽  
pp. 705-714 ◽  
Author(s):  
Joseph B. Keller ◽  
Sol I. Rubinow
Keyword(s):  
Integral Equation ◽  
Incompressible Fluid ◽  
Viscous Incompressible Fluid ◽  
Unit Length ◽  
The Body ◽  
Slender Body ◽  
Slow Flow ◽  
Slender Body Theory ◽  
Slow Viscous Flow ◽  
Body Theory

Slow flow of a viscous incompressible fluid past a slender body of circular crosssection is treated by the method of matched asymptotic expansions. The main result is an integral equation for the force per unit length exerted on the body by the fluid. The novelty is that the body is permitted to twist and dilate in addition to undergoing the translating, bending and stretching, which have been considered by others. The method of derivation is relatively simple, and the resulting integral equation does not involve the limiting processes which occur in the previous work.

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