Estimating wave heights from pressure data at the bed

2014 ◽  
Vol 743 ◽  
Author(s):  
A. Constantin
Keyword(s):  
Linear Theory ◽  
Wave Height ◽  
Water Wave ◽  
Small Amplitude ◽  
Wave Amplitude ◽  
Pressure Measurements ◽  
Two Dimensional ◽  
Pressure Data ◽  
Hydrostatic Approximation ◽  
Wave Heights

AbstractWe provide some estimates for the wave height of a two-dimensional travelling gravity water wave from pressure measurements at the flat bed. The approach is applicable without limitations on the wave amplitude. It improves the classical estimates available if one relies on the hydrostatic approximation or on the linear theory of waves of small amplitude.

A viscous internal wave in a stratified fluid whose buoyancy frequency varies with altitude

1975 ◽  
Vol 69 (3) ◽  
pp. 615-624 ◽  
Author(s):  
D. Gordon ◽  
U. R. Klement ◽  
T. N. Stevenson
Keyword(s):  
Internal Wave ◽  
Small Amplitude ◽  
Wave Amplitude ◽  
Stratified Fluid ◽  
Similarity Solutions ◽  
Buoyancy Frequency ◽  
Experimental Measurements ◽  
Two Dimensional ◽  
Dimensional Theory ◽  
Curved Paths

A viscous incompressible stably stratified fluid with a buoyancy frequency which varies slowly with altitude is considered. A simple harmonic localized disturbance generates an internal wave in which the energy propagates along curved paths. Small amplitude similarity solutions are obtained for two-dimensional and axisymmetric waves. It is found that under certain conditions the wave amplitude can increase with height. The two-dimensional theory compares quite well with experimental measurements.

On the recovery of solitary wave profiles from pressure measurements

2012 ◽  
Vol 699 ◽  
pp. 376-384 ◽  
Author(s):  
A. Constantin
Keyword(s):  
Solitary Wave ◽  
Explicit Formula ◽  
Large Amplitude ◽  
Water Wave ◽  
Pressure Measurements ◽  
Pressure Data ◽  
Governing Equations ◽  
Wave Profiles

AbstractWe derive an explicit formula that permits the recovery of the profile of an irrotational solitary water wave from pressure data measured at the flat bed of the fluid domain. The formula is valid for the governing equations and applies to waves of small and large amplitude.

Experimental Determination of the Effect of Bow Shape on the Wave Drift Load

2017 ◽  
Author(s):  
Anne Boorsma ◽  
Kees Aalbers ◽  
Riaan van ‘t Veer ◽  
René Huijsmans
Keyword(s):  
Linear Theory ◽  
Wave Height ◽  
Measurement Data ◽  
Ship Motions ◽  
Hull Form ◽  
Small Motion ◽  
Water Line ◽  
Wave Drift ◽  
Wave Heights ◽  
The Mean

In the last forty years wave drift loads have been calculated with methods based on the near-field theory (hull pressure integration, Pinkster [4]) and/or the far field method (linear momentum theory). Both methods use linear theory and through its formulation ignore the ship’s hull form above the mean water line. It is evident that in survival sea-states the small motion assumptions are violated and the hull form above the mean water line can affect the motion characteristics of the ship and the drift loads. In order to get more insight in this effect, SBM has conducted a systematic model test campaign at the TU Delft using an Aframax size tanker. The campaign included tests with two different bow shapes: the original bow with flare, and a wall-sided bow. Horizontal loads on the complete vessel and a section of the bow only were measured accompanied by measurements of the ship motions and relative wave heights. Measurements were performed for various wave heights and periods. Numerous repeat tests were conducted to establish the confidence level of the measurement data. Measurements have shown motions and relative wave heights are dependent on wave height. It was suggested that viscous damping may play a part in this. The relative wave height in high waves is affected by bow shape; namely the finite draft, the flare and the bulb. How this departure from linear theory affects the forces on the vessel should be investigated further.

scholarly journals Global relationships between two-dimensional water wave potentials

1996 ◽  
Vol 312 ◽  
pp. 299-309 ◽  
Author(s):  
M. McIver
Keyword(s):  
Water Wave ◽  
Small Amplitude ◽  
Velocity Potential ◽  
Two Dimensional ◽  
Reciprocity Relations ◽  
Moving Body ◽  
Calm Water ◽  
Exciting Forces ◽  
Scattering Potential ◽  
Scattering And Radiation

When a body interacts with small-amplitude surface waves in an ideal fluid, the resulting velocity potential may be split into a part due to the scattering of waves by the fixed body and a part due to the radiation of waves by the moving body into otherwise calm water. A formula is derived which expresses the two-dimensional scattering potential in terms of the heave and sway radiation potentials at all points in the fluid. This result generalizes known reciprocity relations which express quantities such as the exciting forces in terms of the amplitudes of the radiated waves. To illustrate the use of this formula beyond the reciprocity relations, equations are derived which relate higher-order scattering and radiation forces. In addition, an expression for the scattering potential due to a wave incident from one infinity in terms of the scattering potential due to a wave from the other infinity is obtained.

Forced small-amplitude water waves: a comparison of theory and experiment

1960 ◽  
Vol 7 (1) ◽  
pp. 33-52 ◽  
Author(s):  
F. Ursell ◽  
R. G. Dean ◽  
Y. S. Yu
Keyword(s):  
Wave Height ◽  
Water Waves ◽  
Small Amplitude ◽  
Experimental Error ◽  
Wave Motion ◽  
Wave Theory ◽  
Finite Amplitude ◽  
Uniform Density ◽  
Wave Channel ◽  
Wave Heights

This paper describes an attempt to verify experimentally the wavemaker theory for a piston-type wavemaker. The theory is based upon the usual assumptions of classical hydrodynamics, i.e. that the fluid is inviscid, of uniform density, that motion starts from rest, and that non-linear terms are neglected. If the water depth, wavelength, wave period, and wavemaker stroke (of a harmonically oscillating wavemaker) are known, then the wavemaker theory predicts the wave motion everywhere, and in particular the wave height a few depths away from the wavemaker.The experiments were conducted in a 100 ft. wave channel, and the wave-height envelope was measured with a combination hook-and-point gauge. A plane beach (sloping 1:15) to absorb the wave energy was located at the far end of the channel. The amplitude-reflexion coefficient was usually less than 10%. Unless this reflexion effect is corrected for, it imposes one of the most serious limitations upon experimental accuracy. In the analysis of the present set of measurements, the reflexion effect is taken into account.The first series of tests was concerned with verifying the wavemaker theory for waves of small steepness (0.002 ≤ H/L ≤ 0.03). For this range of wave steepnesses, the measured wave heights were found to be on the average 3.4% below the height predicted by theory. The experimental error, as measured by the scatter about aline 3.4% below the theory, was of the order of 3%. The systematic deviation of 3.4% is believed to be partly due to finite-amplitude effects and possibly to imperfections in the wavemaker motion.The second series of tests was concerned with determining the effects of finite amplitude. For therange of wave steepnesses 0.045 ≤ H/L ≤ 0.048, themeasured wave heights were found to be on the average 10% below the heightspredictedfrom the small-amplitude theory. The experimental error was again of the order of 3%.It is considered that these measurements confirm the validity of the small-amplitude wave theory. No confirmation of this accuracy has hitherto been given for forced motions.

scholarly journals Recovery of steady periodic wave profiles from pressure measurements at the bed

2013 ◽  
Vol 714 ◽  
pp. 463-475 ◽  
Author(s):  
D. Clamond ◽  
A. Constantin
Keyword(s):  
Water Waves ◽  
Water Wave ◽  
Small Amplitude ◽  
Periodic Wave ◽  
Classical Solutions ◽  
Periodic Waves ◽  
Pressure Measurements ◽  
Governing Equations ◽  
Shallow Water Waves ◽  
Wave Profiles

AbstractWe derive an equation relating the pressure at the flat bed and the profile of an irrotational steady water wave, valid for all classical solutions of the governing equations for water waves. This permits the recovery of the surface wave from pressure measurements at the bed. Although we focus on periodic waves, the extension to solitary waves is straightforward. We illustrate the usefulness of the equation beyond the realm of linear theory by investigating the regime of shallow-water waves of small amplitude and by presenting a numerical example.

scholarly journals WAVE SHOALING CALCULATED FROM COKELET'S THEORY

1980 ◽  
Vol 1 (17) ◽  
pp. 6
Author(s):  
T. Sakai ◽  
J.A. Battjes
Keyword(s):  
Experimental Data ◽  
Linear Theory ◽  
Wave Height ◽  
Gravity Waves ◽  
Finite Amplitude ◽  
Experimental Results ◽  
Two Dimensional ◽  
Amplitude Wave ◽  
Non Linear ◽  
Wave Shoaling

Cokelet's numerical non-linear theory for progressive, periodic gravity waves is applied to the two-dimensional shoaling of finite amplitude waves on a beach up to breaking. The shoaling curves so obtained are compared with existing shoaling curves calculated from different finite amplitude wave theories, and with existing experimental data. It was found that the shoaling curves calculated from Cokelet's theory predict higher wave height ratios than other curves. The agreement between the present curves and the experimental results is good except near the breakpoint, where the wave height of the present curves is larger than the experimental wave height.

A note on the uniqueness of small-amplitude water waves travelling in a region of varying depth

1979 ◽  
Vol 86 (3) ◽  
pp. 511-519 ◽  
Author(s):  
G. F. Fitz-Gerald ◽  
R. H. J. Grimshaw
Keyword(s):  
Linear Theory ◽  
Gravity Waves ◽  
Water Waves ◽  
Small Amplitude ◽  
Velocity Potential ◽  
Surface Gravity ◽  
Two Dimensional ◽  
Physical Interest ◽  
Surface Gravity Waves ◽  
Convexity Conditions

The two-dimensional, irrotational, linear theory used in the investigation of the propagation of monochromatic surface gravity waves in a region of varying depth is considered. Uniqueness of the velocity potential is established for bottom profiles satisfying certain convexity conditions. These include the majority of profiles of physical interest.

scholarly journals CRITICAL TRAVEL DISTANCE OF WAVES IN SHALLOW WATER

1974 ◽  
Vol 1 (14) ◽  
pp. 24
Author(s):  
Winfried Siefert
Keyword(s):  
Shallow Water ◽  
Wave Height ◽  
Water Wave ◽  
Characteristic Parameter ◽  
Wave Climate ◽  
Height Distribution ◽  
Shallow Water Wave ◽  
German Coast ◽  
Wave Heights ◽  
The Mean

A new criterion for shallow water wave analysis is evaluated from prototype data off the German coast on the reef and wadden sea areas south of the outer Elbe river. Correlations of mean wave heights H with mean wave peri- - H ods T, and wave height distribution factors C. /•, = —l/3 t-^ respectively show that the mean periods and both complete height and period distributions of waves in shallow water can be expressed as functions of mean height and topography. So the mean wave height H proves to be the characteristic parameter for the description of the complete shallow water wave climate. The upper envelop of the values H = f (meteorology, topography) is defined as the case of fully developed sea, which leads to the function of the highest mean wave heights Hmax.

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