Water Particle Acceleration Research Articles

Acoustic Pressure, Particle Motion, and Induced Ground Motion Signals from a Commercial Seismic Survey Array and Potential Implications for Environmental Monitoring

An experimental marine seismic source survey off the northwest Australian coast operated a 2600 cubic inch (41.6 l) airgun array, every 5.88 s, along six lines at a northern site and eight lines at a southern site. The airgun array was discharged 27,770 times with 128,313 pressure signals, 38,907 three-axis particle motion signals, and 17,832 ground motion signals recorded. Pressure and ground motion were accurately measured at horizontal ranges from 12 m. Particle motion signals saturated out to 1500 m horizontal range (50% of signals saturated at 230 and 590 m at the northern and southern sites, respectively). For unsaturated signals, sound exposure levels (SEL) correlated with measures of sound pressure level and water particle acceleration (r2= 0.88 to 0.95 at northern site and 0.97 at southern) and ground acceleration (r2= 0.60 and 0.87, northern and southern sites, respectively). The effective array source level was modelled at 247 dB re 1µPa m peak-to-peak, 231 dB re 1 µPa2 m mean-square, and 228 dB re 1 µPa2∙m2 s SEL at 15° below the horizontal. Propagation loss ranged from −29 to −30log10 (range) at the northern site and −29 to −38log10(range) at the southern site, for pressure measures. These high propagation losses are due to near-surface limestone in the seabed of the North West Shelf.

NONLINEAR INERTIAL LOADING. PART I: ACCELERATIONS IN STEEP 2-D WATER WAVES

This paper reports on a new series of laboratory observations in which both the unsteady and the convective components of the water particle acceleration arising beneath an extreme two-dimensional transient wave were determined. The waveform investigated was produced by focusing frequency components within an irregular wave train, such that a large number of zero up-crossings arise at one point in space and time. For a given underlying set of frequency components, this produces an extreme event that has the maximum wave slope and therefore also the largest horizontal water particle accelerations. Spectral analysis, based upon the water surface elevation measured at the focal location, confirms that there are significant transfers of energy into the high-frequency components. Neither a linear random wave theory nor a steady nonlinear wave theory, both of which are commonly used in design applications, are able to correctly model these frequency components. As a result, such solutions provide a poor description of the large unsteady accelerations arising close to the water surface. Furthermore, since they are also unable to model the spatial evolution of the wave group, inaccurate predictions of the convective accelerations result. In contrast, a fully nonlinear unsteady wave theory, similar to that originally proposed by Fenton & Rienecker (1980), provides a good description of the laboratory data. To assess the importance of the nonlinear accelerations the inertia forces acting on a vertical, surface-piercing, cylinder are calculated and comparisons made with the nonlinear slender body forces identified by Rainey (1989, 1995). These comparisons confirm the importance of the applied wave model and suggest that the dominant contribution to the high-frequency forcing arises due to the nonlinearity of the wave motion. These results have applications in Offshore Engineering where transient structural deflections, occurring at frequencies well above the wave frequency, have been observed in a number of deep-water structures.

Hydrodynamic forces on fixed submerged cylinders

Wave loads on the cylindrical members of fixed offshore structures are generally calculated by using Morison’s Equation. The inertia force component of this equation is conventionally quoted in a form derived from theoretical calculations for a uniformly accelerating fluid. In this paper the correct form for the inertia force in a general fluid flow is derived from first principles by pressure integration and, independently, from earlier work, by energy arguments. It is shown that, for the thin cylinder limiting case, the transverse force on a circular cylinder is incorrectly given by the conventional approach, in that the product of transverse fluid velocity (in the direction of the required force) with the longitudinal velocity gradient should be added to the water particle acceleration, when computing the added-mass component of the force. Axial divergence, in other words, appears to play the role of a rate-of-change of added mass. It is shown that the mathematical origin of this extra term is the classical three-dimensional flow feature of a ‘zonal harmonic’, which produces a convective fluid acceleration but zero loading. A more elaborate formula is derived for non-circular cylinders, and the nature of point loads occurring at cylinder ends is also discussed.

Application of Morison's Equation to Fixed Offshore Platforms

Four methods for calculating wave forces acting on tubular members affixed offshore platforms are presented and compared under identical design conditions to demonstrate their significant differences. Many wave-crest locations and wave-approach directions are considered. Variation of base shears and overturning moments among these methods is found to exceed 21 percent. percent. Introduction Numerous technical papers, texts, and offshore design codes have used Morison's equation to determine hydrodynamic forces on small, tubular, structural elements. The Morison equation includes terms for both drag and inertial forces. The drag term includes a drag coefficient, CD, and water-particle velocity, while the inertia term includes an inertial coefficient, C1, and water-particle acceleration. This equation applies to small objects (compared with wave length) where wave kinematics do not change appreciably over a distance equal to the width of the structural element. Morison's equation was developed to determine the hydrodynamic force on a small cylindrical body that is at right angles to the water-particle velocity and acceleration vectors. However, when a cylinder is oriented randomly with respect to the mud line, there is considerable question about the application of Morison's equation. Borgman, Ippen, Bursnall et al., Chakrabarti et al., and Morgan et al. have shown how for a vertical cylinder Morison's equation may be applied to a cylindrical member oriented randomly with respect to the mud line. A review of the references reveals that there are many methods for calculating wave forces acting on tubular members of fixed offshore platforms. Four different methods are presented in this study, each within procedures generally used by the industry for computing procedures generally used by the industry for computing wave forces on a randomly oriented cylindrical member. Formulation of the methods considered is based on various interpretations of the application of Morison's equation. The wave-force calculation methods presented here are in the literature. This study compares these various methods with identical design conditions and demonstrates significant differences among the methods. The wave-force equation introduced by Morison et al. is -> -> -> -> F = 1/2 CDpdv x v x + 1/4 Clp d2 a x -> -> F p = ----,...................................(1) d -> -> where vx and ax are the horizontal water-particle velocity and acceleration vectors, respectively, acting on a vertical cylinder of a diameter, d, in water of mass density, p. Both water-particle kinematic vectors are normal to the cylinder and, consequently, the force vector, will be acting in a direction parallel to the mud line. Wave-induced motion, however, includes both horizontal and vertical kinematic components. Furthermore, except for conductors, offshore platforms rarely have cylindrical members that are perfectly vertical. In each wave-force calculation method presented, the total water-particle velocity vector is assumed to be -> -> -> v = v x + v y,...........................(2) and the total acceleration vector is -> -> -> a = a x + a y,...........................(3) P. 447

Extremes of Morison-Type Wave Loading on a Single Pile

A statistical estimate of the extreme wave force per unit length acting on a section of a fixed cylindrical pile in a random sea-state is derived. The random motion of the sea is described by a spectrum of wave heights in conjunction with linear wave theory. The wave force is assumed to depend linearly on the water particle acceleration and non-linearly on the water velocity according to the Morison formula. The interaction of the velocity and acceleration contributions and the contribution of a small steady current are accounted for by an asymptotic approximation valid for large forces. The expected rate of occurrences of extremes based on a simple peak definition agrees satisfactorily with a more elaborate result based on a true maximum definition. The formulas derived here provide a basis for a design-force procedure which could provide an improvement over the design-wave procedure commonly used for the analysis of offshore structures.