A mathematical model of the dynamics of the inner ear

1982 ◽  
Vol 116 ◽  
pp. 59-75 ◽  
Author(s):  
Mark H. Holmes
Keyword(s):  
Cross Section ◽  
Basilar Membrane ◽  
Three Dimensional ◽  
Low Frequency ◽  
Transverse Cross Section ◽  
Frequency Theory ◽  
Slender Body Theory ◽  
High Frequencies ◽  
Hearing Range ◽  
Body Theory

A three-dimensional hydroelastic model of the dynamical motion in the cochlea is analysed. The fluid is Newtonian and incompressible, and the basilar membrane is modelled as an orthotropic elastic plate. Asymptotic expansions are introduced, based on slender-body theory and the relative high frequencies in the hearing range, which reduce the problem to an eigenvalue problem in the transverse cross-section. After this, an example is worked out and a comparison is made with experiment and the earlier low-frequency theory.

A Numerical Study on Squat of a Wigley Hull

2011 ◽  
Author(s):  
Mahmoud Alidadi ◽  
Sander Calisal
Keyword(s):  
Boundary Element Method ◽  
Cross Section ◽  
Cross Sections ◽  
Numerical Study ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Slender Body Theory ◽  
Flow Potential ◽  
Wigley Hull ◽  
Body Theory

A numerical study is conducted to calculate the squat for a wigley hull. An approach based on slender body theory is used to convert the three dimensional ship problem into a series of two dimensional problems in cross sections from bow to stern (solved sequentially in time). A boundary element method is used to compute the flow potential at every cross section. The ship squat is calculated from the pressure integration over the hull. Numerical results for the Wigley hull is presented and compared with the experimental results.

Boundary-Layer Flow Between the Attachment Lines on a Flat Plate Delta Wing at Incidence

1962 ◽  
Vol 13 (1) ◽  
pp. 1-16
Author(s):  
J. C. Cooke
Keyword(s):  
Boundary Layer ◽  
Delta Wing ◽  
Three Dimensional ◽  
External Flow ◽  
Two Dimensional ◽  
Conical Flow ◽  
Slender Body Theory ◽  
Layer Flow ◽  
Body Theory ◽  
Transition Fronts

SummaryA three-dimensional laminar-boundary-layer calculation is carried out over the area concerned. The external flow is simplified, being calculated by slender-body theory assuming conical flow, with two point vortices above the wing, their positions and strength being determined by experiment. Attempts are made to draw transition fronts both for two-dimensional and sweep instability from this calculation. The combination of these gives fronts similar to those observed in some experiments. Because there is little or no pressure gradient over the area in question it is suggested that it is a region where distributed suction might usefully be applied in order to maintain laminar flow and reduce drag.

Boundary-layer-induced potential flow on an elliptic cylinder

1974 ◽  
Vol 66 (1) ◽  
pp. 145-157 ◽  
Author(s):  
Stanley G. Rubin ◽  
Frank J. Mummolo
Keyword(s):  
Boundary Layer ◽  
Three Dimensional ◽  
Circular Cross Section ◽  
Elliptic Cylinder ◽  
Analytic Form ◽  
Slender Body ◽  
Dimensional Solution ◽  
Slender Body Theory ◽  
Simple Analytic Form ◽  
Body Theory

The application of slender-body theory to the evaluation of the three-dimensional surface velocities induced by a boundary layer on an elliptic cylinder is considered. The method is applicable when the Reynolds number is sufficiently large so that the thin-boundary-layer approximation is valid. The resulting potential problem is reduced to a two-dimensional consideration of the flow over an expanding cylinder with porous boundary conditions. The limiting solutions for a flat plate of finite span and a nearly circular cross-section are obtained in a simple analytic form. In the former case, within the limitations of slender-body theory, the results are in exact agreement with the complete three-dimensional solution for this geometry.

Propulsive Efficiency of the Underwater Dolphin Kick in Humans

2009 ◽  
Vol 131 (5) ◽  
Author(s):  
Alfred von Loebbecke ◽  
Rajat Mittal ◽  
Frank Fish ◽  
Russell Mark
Keyword(s):  
Fluid Dynamic ◽  
Three Dimensional ◽  
Underwater Video ◽  
Dynamic Simulations ◽  
Slender Body Theory ◽  
Propulsive Efficiency ◽  
Video Footage ◽  
Wide Range ◽  
Dolphin Kick ◽  
Body Theory

Three-dimensional fully unsteady computational fluid dynamic simulations of five Olympic-level swimmers performing the underwater dolphin kick are used to estimate the swimmer’s propulsive efficiencies. These estimates are compared with those of a cetacean performing the dolphin kick. The geometries of the swimmers and the cetacean are based on laser and CT scans, respectively, and the stroke kinematics is based on underwater video footage. The simulations indicate that the propulsive efficiency for human swimmers varies over a relatively wide range from about 11% to 29%. The efficiency of the cetacean is found to be about 56%, which is significantly higher than the human swimmers. The computed efficiency is found not to correlate with either the slender body theory or with the Strouhal number.

Numerical Analysis of the Influence of Above-Water Bow Form on Added Resistance Using Nonlinear Slender Body Theory

2005 ◽  
Vol 49 (03) ◽  
pp. 191-206
Author(s):  
Hajime Kihara ◽  
Shigeru Naito ◽  
Makoto Sueyoshi
Keyword(s):  
Three Dimensional ◽  
Wave Force ◽  
Slender Body ◽  
Added Resistance ◽  
Slender Body Theory ◽  
Hull Form ◽  
Nonlinear Properties ◽  
Head Waves ◽  
The Time Domain ◽  
Body Theory

A nonlinear numerical method is presented for the prediction of the hydrodynamic forces that act on an oscillating ship with a forward speed in head waves. A "parabolic" approximation of equations called "2.5D" or "2D+T" theory was used in a three-dimensional ship wave problem, and the computation was carried out in the time domain. The nonlinear properties associated with the hydrostatic, hydrodynamic, and Froude-Krylov forces were taken into account in the framework of the slender body theory. This work is an extension of the previous work of Kihara and Naito (1998). The application of this approach to the unsteady wave-making problem of a ship with a real hull form is described. The focus is on the influence of the above-water hull form on the horizontal mean wave force. Comparison with experimental results demonstrates that the method is valid in predicting added resistance. Prediction of added resistance for blunt ships is also shown by example.

RESEARCH ON THE DISTRIBUTION OF PRESSURE FIELD ON THE BASILAR MEMBRANE IN THE PASSIVE SPIRAL COCHLEA

2014 ◽  
Vol 14 (04) ◽  
pp. 1450061 ◽  
Author(s):  
JIANWEI MA ◽  
WENJUAN YAO
Keyword(s):  
Velocity Potential ◽  
Pressure Field ◽  
Basilar Membrane ◽  
Separation Of Variables ◽  
Three Dimensional ◽  
Low Frequency ◽  
Helical Structure ◽  
Hearing Ability ◽  
Leading Role ◽  
First Case

The cochlea is the important auditory organ of the inner ear. It is responsible for transforming the acoustic signals into neural impulses that travel along the auditory nerve to the brain. The role of, perhaps, the most characteristic feature of the cochlea, its three-dimensional (3D) helical structure, has remained elusive. To address this problem, the present paper develops a 3D spiral cochlea mathematical model using orthogonal coordinate system. Based on the method of separation of variables and conformal transformation, equations of three cases for the velocity potential are derived to solve the steady flow problem of lymph in the cochlea. Then, the distribution of pressure field on the basilar membrane (BM) is obtained. By comparing the analytical results with FE analyses results, the derived formulas are demonstrated to be accurate and reliable. The conclusion can be drawn that the spiral shape and physical dimension of the cochlea have a significant influence on the distribution of pressure field. Interestingly, near the helicotrema, the velocity potential of the first case plays a leading role in pressure distribution on the BM. Therefore, it may enhance the vibration of BM and improve hearing ability in the low-frequency parts of human ears. The proposed model could provide an approach for further investigation of fluid-structure interaction problem in the cochlea.

scholarly journals Experimental verification of an Oseen flow slender body theory

2010 ◽  
Vol 654 ◽  
pp. 271-279 ◽  
Author(s):  
E. CHADWICK ◽  
H. M. KHAN ◽  
M. MOATAMEDI ◽  
M. MAPPIN ◽  
M. PENNEY
Keyword(s):  
Cross Section ◽  
Semimajor Axis ◽  
Major Axis ◽  
The Body ◽  
Slender Body ◽  
Radius Of Curvature ◽  
Slender Body Theory ◽  
Elliptical Cross ◽  
Oseen Flow ◽  
Body Theory

Consider uniform flow past four slender bodies with elliptical cross-section of constant ellipticity along the length of 0, 0.125, 0.25 and 0.375, respectively, for each body. Here, ellipticity is defined as the ratio of the semiminor axis of the ellipse to the semimajor axis. The bodies have a pointed nose which gradually increases in cross-section with a radius of curvature 419 mm to a mid-section which then remains constant up to a blunt end section with semimajor axis diameter 160 mm, the total length of all bodies being 800 mm. The bodies are side-mounted within a low-speed wind tunnel with an operational wind speed of the order 30 m s−1. The side force (or lift) is measured within an angle of attack range of −3° to 3° such that the body is rotated about the major axis of the ellipse cross-section. The lift slope is determined for each body, and how it varies with ellipticity. It is found that this variance follows a straight line which steadily increases with increasing ellipticity. It is shown that this result is predicted by a recently developed Oseen flow slender body theory, and cannot be predicted by either inviscid flow slender body theory or viscous crossflow theories based upon the Allen and Perkins method.

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