The mean drift force and yaw moment on marine structures in waves and current

1993 ◽  
Vol 250 ◽  
pp. 121-142 ◽  
Author(s):  
John Grue ◽  
Enok Palm
Keyword(s):  
Momentum Flux ◽  
Wave Spectrum ◽  
Second Order ◽  
The Body ◽  
Far Field ◽  
Marine Structures ◽  
First Order ◽  
The Mean ◽  
Yaw Moment ◽  
Drift Forces

The effect of the steady second-order velocities on the drift forces and moments acting on marine structures in waves and a (small) current is considered. The second-order velocities are found to arise due to first-order evanescent modes and linear body responses. Their contributions to the horizontal drift forces and yaw moment, obtained by pressure integration at the body, and to the yaw drift moment, obtained by integrating the angular momentum flux in the far field, are expressed entirely in terms of the linear first-order solution. The second-order velocities may considerably increase the forward speed part of the mean yaw moment on realistic marine structures, with the most important contribution occurring where the wave spectrum often has its maximal value. The contribution to the horizontal forces obtained by pressure integration is, however, always found to be small. The horizontal drift forces obtained by the linear momentum flux in the far field are independent of the second-order velocities, provided that there is no velocity circulation in the fluid.

Drift Forces on a Floating Body of Simple Geometry Due to Second Order Interactions Between Pairs of Harmonics With Different Frequencies

2009 ◽  
Author(s):  
Joa˜o Pessoa ◽  
Nuno Fonseca ◽  
C. Guedes Soares
Keyword(s):  
Vertical Cylinder ◽  
Vertical Axis ◽  
Second Order ◽  
The Body ◽  
Floating Body ◽  
Order Problem ◽  
Simple Geometry ◽  
The Mean ◽  
Order Quantities ◽  
Drift Forces

The paper presents an investigation of the slowly varying second order drift forces on a floating body of simple geometry. The body is axis-symmetric about the vertical axis, like a vertical cylinder with a rounded bottom and a ratio of diameter to draft of 3.25. The hydrodynamic problem is solved with a second order boundary element method. The second order problem is due to interactions between pairs of incident harmonic waves with different frequencies, therefore the calculations are carried out for several difference frequencies with the mean frequency covering the whole frequency range of interest. Results include the surge drift force and pitch drift moment. The results are presented in several stages in order to assess the influence of different phenomena contributing to the global second order responses. Firstly the body is restrained and secondly it is free to move at the wave frequency. The second order results include the contribution associated with quadratic products of first order quantities, the total second order force, and the contribution associated to the free surface forcing.

Analysis of the First Order and Slowly Varying Motions of an Axisymmetric Floating Body in Bichromatic Waves

2013 ◽  
Vol 135 (1) ◽  
Author(s):  
João Pessoa ◽  
Nuno Fonseca ◽  
C. Guedes Soares
Keyword(s):  
Vertical Cylinder ◽  
Vertical Axis ◽  
Second Order ◽  
The Body ◽  
Floating Body ◽  
Drift Motion ◽  
First Order ◽  
Motion Responses ◽  
Simple Geometry ◽  
Good Agreement

The paper presents an experimental and numerical investigation on the motions of a floating body of simple geometry subjected to harmonic and biharmonic waves. The experiments were carried out in three different water depths representing shallow and deep water. The body is axisymmetric about the vertical axis, like a vertical cylinder with a rounded bottom, and it is kept in place with a soft mooring system. The experimental results include the first order motion responses, the steady drift motion offset in regular waves and the slowly varying motions due to second order interaction in biharmonic waves. The hydrodynamic problem is solved numerically with a second order boundary element method. The results show a good agreement of the numerical calculations with the experiments.

Second-order recombination in a parallel shear flow

1989 ◽  
Vol 200 ◽  
pp. 389-407 ◽  
Author(s):  
Ronald Smith
Keyword(s):  
Shear Flow ◽  
Concentration Distribution ◽  
Second Order ◽  
Explicit Solutions ◽  
Far Field ◽  
First Order ◽  
Parallel Shear Flow

For a reactive solute, with weak second-order recombination, an investigation is made of the near-source behaviour (where concentrations are high), and of the far field (where the recombination has an accumulative effect). Despite the loss of material and increased spread due to recombination, the far-field concentration distribution is shown to be nearly Gaussian. This permits a simplified (Gaussian) treatment of the chemical nonlinearity. Explicit solutions are given for the total amount of solute, variance and kurtosis for solutes with no first-order reactions.

The Second-Order Master Equation

2019 ◽  
pp. 128-158
Author(s):  
Pierre Cardaliaguet ◽  
François Delarue ◽  
Jean-Michel Lasry ◽  
Pierre-Louis Lions
Keyword(s):  
Master Equation ◽  
Mean Field ◽  
Second Order ◽  
Well Posedness ◽  
Mean Field Game ◽  
First Order ◽  
Common Noise ◽  
System P ◽  
The Mean

This chapter investigates the second-order master equation with common noise, which requires the well-posedness of the mean field game (MFG) system. It also defines and analyzes the solution of the master equation. The chapter explains the forward component of the MFG system that is recognized as the characteristics of the master equation. The regularity of the solution of the master equation is explored through the tangent process that solves the linearized MFG system. It also analyzes first-order differentiability and second-order differentiability in the direction of the measure on the same model as for the first-order derivatives. This chapter concludes with further description of the derivation of the master equation and well-posedness of the stochastic MFG system.

Irregular Frequency Removal and Convergence in Higher-Order BEM for Wave Diffraction/Radiation Analysis

2019 ◽  
Author(s):  
Tomoaki Utsunomiya
Keyword(s):  
Free Surface ◽  
Wave Diffraction ◽  
Higher Order ◽  
The Body ◽  
Diffraction Radiation ◽  
First Order ◽  
Irregular Frequency ◽  
Intersection Line ◽  
Order Quantities ◽  
Drift Forces

Abstract Higher-order boundary element method (HOBEM) for wave diffraction/radiation analysis is a powerful tool for its applicability to a general (curved) geometry. Inspired by the paper which examined the convergence of BIE code with constant panels (Martic, et al., 2018; OMAE2018-77999), the convergence characteristics of HOBEM with quadrilateral panels have been examined. Here, the effect of removal of irregular frequencies is particularly focused as discussed by Martic, et al. (2018). The irregular frequency removal has been made by the rigid-lid method which is applicable to HOBEM, where the intersection line between the body-surface and the free-surface should be carefully handled. The results show that for first order quantities the convergence is quite good for both cases with/without irregular frequency removal (except where the irregular frequencies affect for the case without irregular frequency removal). For mean drift forces, the convergence becomes poor particularly for the case without irregular frequency removal. The convergence characteristics are examined and some discussions are made.

scholarly journals Gain control of synaptic transfer from second- to third-order neurons of cockroach ocelli.

1996 ◽  
Vol 107 (1) ◽  
pp. 121-131 ◽  
Author(s):  
M Mizunami
Keyword(s):  
Synaptic Transmission ◽  
Characteristic Curve ◽  
Gain Control ◽  
Second Order ◽  
The Body ◽  
Intensity Change ◽  
Third Order ◽  
The Mean ◽  
Mean Luminance ◽  
Nonlinear Nature

Synaptic transmission from second- to third-order neurons of cockroach ocelli occurs in an exponentially rising part of the overall sigmoidal characteristic curve relating pre- and postsynaptic voltage. Because of the nonlinear nature of the synapse, linear responses of second-order neurons to changes in ligh intensity are half-wave rectified, i.e., the response to a decrement in light is amplified whereas that to an increment in light is compressed. Here I report that the gain of synaptic transmission from second- to third-order neurons changes by ambient light levels and by wind stimulation applied to the cerci. Transfer characteristics of the synapse were studied by simultaneous intracellular recordings of second- and third-order neurons. Potential changes were evoked in second-order neurons by a sinusoidally modulated light with various mean luminances. With a decrease in the mean luminance (a) the mean membrane potential of second-order neurons was depolarized, (b) the synapse between the second- and third-order neurons operated in a steeper range of the exponential characteristic curve, where the gain to transmit modulatory signals was higher, and (c) the gain of third-order neurons to detect a decrement in light increased. Second-order neurons were depolarized when a wind or tactile stimulus was applied to various parts of the body including the cerci. During a wind-evoked depolarization, the synapse operated in a steeper range of the characteristic curve, which resulted in an increased gain of third-order neurons to detect light decrements. I conclude that the nonlinear nature of the synapse between the second- and third-order neurons provides an opportunity for an adjustment of gain to transmit signals of intensity change. The possibility that a similar gain control occurs in other visual systems and underlies a more advanced visual function, i.e., detection of motion, is discussed.

ORIENTATION OF SYMMETRIC BODIES FALLING IN A SECOND-ORDER LIQUID AT NONZERO REYNOLDS NUMBER

2002 ◽  
Vol 12 (11) ◽  
pp. 1653-1690 ◽  
Author(s):  
GIOVANNI P. GALDI ◽  
ASHWIN VAIDYA ◽  
MILAN POKORNÝ ◽  
DANIEL D. JOSEPH ◽  
JIMMY FENG
Keyword(s):  
Prolate Spheroid ◽  
Critical Value ◽  
Second Order ◽  
The Body ◽  
Body Of Revolution ◽  
Translational Velocity ◽  
Homogeneous Body ◽  
First Order ◽  
The Stability ◽  
Elasticity Number

We study the steady translational fall of a homogeneous body of revolution around an axis a, with fore-and-aft symmetry, in a second-order liquid at nonzero Reynolds (Re) and Weissenberg (We) numbers. We show that, at first order in these parameters, only two orientations are allowed, namely, those with a either parallel or perpendicular to the direction of the gravity g. In both cases the translational velocity is parallel to g. The stability of the orientations can be described in terms of a critical value E c for the elasticity number E = We/Re , where E c depends only on the geometric properties of the body, such as size or shape, and on the quantity (Ψ1 + Ψ2)/Ψ1, where Ψ1 and Ψ2 are the first and second normal stress coefficients. These results are then applied to the case when the body is a prolate spheroid. Our analysis shows, in particular, that there is no tilt-angle phenomenon at first order in Re and We.

Motion Prediction of a Single-Point Moored Tanker Subjected to Current, Wind and Waves

1990 ◽  
Vol 112 (1) ◽  
pp. 83-90 ◽  
Author(s):  
T. Jiang ◽  
T. E. Schellin
Keyword(s):  
Digital Simulation ◽  
Single Point ◽  
Wave Spectrum ◽  
Memory Effects ◽  
Wave Forces ◽  
Restoring Force ◽  
Low Frequencies ◽  
Frequency Wave ◽  
First Order ◽  
Drift Forces

Horizontal motions of a tanker attached to a single-point mooring (SPM) terminal were predicted using digital simulation in the time domain. Excitations from steady current, gusting wind, and irregular seaway were included. Hydrodynamic forces generated by the ship’s motion and the action of its propeller and rudder were calculated in accordance with a previously validated, nonlinear quasi-steady four-quadrant maneuvering model, extended to include linear memory effects due to waves generated by the moving ship. Memory effects were approximated by a vectorial recursive state space model corresponding to a set of higher order differential equations. A nonlinear relationship of the force in the mooring hawser was assumed to represent restoring force characteristics of the SPM system. Wave excitation forces comprised first-order forces at wave frequencies and second-order drift forces at low frequencies. First-order wave forces were obtained by superposition of force components corresponding to regular wave components comprising the wave spectrum. Based on the low-frequency wave envelope, drift forces were calculated using mean drift force coefficients in regular waves. Selected sample simulations are presented to illustrate the use of this digital simulation method.

Real Time Prediction of Second Order Wave Drift Forces for Wave Force Feed Forward in DP

2010 ◽  
Author(s):  
P. Naaijen ◽  
R. H. M. Huijsmans
Keyword(s):  
Wave Field ◽  
Prediction Error ◽  
Wave Force ◽  
Second Order ◽  
First Order ◽  
Wave Drift ◽  
Wave Elevation ◽  
X Band ◽  
Wave Drift Forces ◽  
Drift Forces

The presented research is an extension of the development of an onboard wave and motion estimation system that aims to predict wave elevation and wave frequent vessel motions some 60–120 s ahead, using remote measurements of short crested waves. The main aim is to provide decision support during motion critical offshore operations. As an addition to this, an attempt is made to predict second order wave drift forces. This can be useful for condition monitoring of a Dynamic Positioning (DP) system [18] or for feed forward of wave drift forces into the control of DP systems. The paper describes the techniques used to predict second order wave drift forces real time from remote wave measurements. For validation, measurement data is used from model experiments during which wave elevation in irregular short crested seas was recorded by a large number of probes simultaneously. A method is described to obtain a 3D representation of a wave field in such a way that it can be used to predict both first order waves and motions and second order forces. The second order forces resulting from the wave field description as obtained from remote probe measurements can be compared to those that have been derived from the probes in the proximity of the prediction location, thus providing insight in the sensitivity of the 2nd order wave force prediction error with respect to the first order wave prediction error. In a full scale field situation, remote wave sensing can be provided by X-band radar. Possibilities for application of the developed method with the WAMOS II X-band radar system is considered.

Second Order Difference Frequency Wave-Current Loading Using Kelvin-Newman Approximation

2020 ◽  
Author(s):  
Farid P. Bakti ◽  
Moo-Hyun Kim
Keyword(s):  
Second Order ◽  
The Body ◽  
Difference Frequency ◽  
Computational Time ◽  
Forward Speed ◽  
Frequency Wave ◽  
Order Difference ◽  
First Order ◽  
Current Interaction ◽  
Current Loading

Abstract Kelvin & Newman introduced a linearization method to include the current (or forward speed) effect into the diffraction & radiation wave field for large-slender floating bodies. The K-N method assumes a steady far-field current while disregarding the steady potential field due to the presence of the body. The method is proven to be reliable when the Froude number is relatively small, the body shape is relatively slender (∂∂x≪∂∂y,∂∂z), and the sea condition is mild. This requirement is fulfilled for typical FPSOs and ship-shaped vessels in a typical current (or forward speed) condition. Several studies suggested that the presence of the current might change the first order hydrodynamic coefficients such as the first order diffraction force, added mass, and radiation damping. Currents also contributed to a change in the second-order slowly-varying drift force. However, the effect of current in the second-order difference-frequency force is yet to be investigated. By expanding the Kelvin-Newman approximation up to the second order, and solving the problem in the frequency domain, we can save computational time while expanding the accuracy of the scheme. The second order quadratic force is the main focus of this study, since it is the main contributor to the total second order difference frequency forces especially near the diagonal. By implementing the Kelvin-Newman wave current interaction approach up to the wave’s second order, we can assess the performance of the Kelvin-Newman wave current interaction formulation in various sea conditions.

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