Joint statistical distribution of two-point sea surface elevations in finite water depth

Based on the second-order random wave solutions of water wave equations in finite water depth, a joint statistical distribution of two-point sea surface elevations is derived by using the characteristic function expansion method. It is found that the joint distribution depends on five parameters. These five parameters can all be determined by the water depth, the relative position of two points and the wave-number spectrum of ocean waves. As an illustrative example, for fully developed wind-generated sea, the parameters that appeared in the joint distribution are calculated for various wind speeds, water depths and relative positions of two points by using the Donelan and Pierson spectrum and the nonlinear effects of sea waves on the joint distribution are studied. (C) 2003 Elsevier B.V. All rights reserved.

Statistical distribution of depth-integrated local horizontal momentum for second-order random ocean waves in finite water depth

Based on the second-order random wave solutions of water wave equations in finite water depth, statistical distributions of the depth- integrated local horizontal momentum components are derived by use of the characteristic function expansion method. The parameters involved in the distributions can be all determined by the water depth and the wave-number spectrum of ocean waves. As an illustrative example, a fully developed wind-generated sea is considered and the parameters are calculated for typical wind speeds and water depths by means of the Donelan and Pierson spectrum. The effects of nonlinearity and water depth on the distributions are also investigated.

Statistical distribution of wave-surface elevation for second-order random directional ocean waves in finite water depth

Based on the second-order random wave solutions of water wave equations in finite water depth, a statistical distribution of the wave-surface elevation is derived by using the characteristic function expansion method. It is found that the distribution, after normalization of the wave-surface elevation, depends only on two parameters. One parameter describes the small mean bias of the surface produced by the second-order wave-wave interactions. Another one is approximately proportional to the skewness of the distribution. Both of these two parameters can be determined by the water depth and the wave-number spectrum of ocean waves. As an illustrative example, we consider a fully developed wind-generated sea and the parameters are calculated for various wind speeds and water depths by using Donelan and Pierson spectrum. It is also found that, for deep water, the dimensionless distribution reduces to the third-order Gram-Charlier series obtained by Longuet-Higgins [J. Fluid Mech. 17 (1963) 459]. The newly proposed distribution is compared with the data of Bitner [Appl. Ocean Res. 2 (1980) 63], Gaussian distribution and the fourth-order Gram-Charlier series, and found our distribution gives a more reasonable fit to the data. (C) 2002 Elsevier Science B.V. All rights reserved.

The hydrographic conditions at depth below 1000 m water depth in the region of the Romanche Fracture Zones

During the "Atlantic Expedition" in1965 (IQSY) a comprehensive bathymetric survey and a few hydrographic stations were made by R.V. "Meteor" in the equatorial region of the Mid-Atlantic Ridge. The survey results are shown in a bythymetric chart covering the western parts of the Romanche- and Chain Fracture Zones. West of the original Romanche Trench another deep trench with a medium depth of 6000 m was discovered. The maximum sounding obtained was 7028 m. Both trenches apparently belong to the same fracture zone, but are distinctly separated from each other. The estern boundary of the trench against the Brasil Basin is formed by a sill rising to a depth of about 4400 m. The serial hydrographic observations give some indications of the flow of the cold Westatlantic deep water in the fracture zone area and its influence on the hydrographic conditions in the East-Atlantic Basin. The upper limit of the nearly homogenious Westatlantic bottom water with an Antarctic components lies about 4400 m. The water mass entering the system of trenches of the Romanche Fracture Zone over the western sill originates from the lower part of the discontinuity layer lying above the bottom water. Potential temperatures of 0.6°C were the lowest observed by "Meteor" in the western trench. There seems to be a remarkable tongue of relatively high salinity and a minimum of oxygen in the deep water of this trench. At present we can only speculate upon the origin of this highly saline deep water tongue underneath the eastward moving relatively thin layer of less saline Westatlantic deep water. In the range of the sill separating both trenches a lee wave is indicated by the distribution of salinity and oxygen, which implies a vertical transport of water masses. Caused by this transport it is assumed that relatively cold water may be lifted temporarily to a depth, where it can pass the northbounding ridge, thus getting directly into the Sierra Leone Basin. In the original Romanche Trench the cold Westatlantic deep water seems to fill the whole trough, but its extension remains limited to the trench itself. The water masses found east of the sill separating the trench from the East-Atlantic Basin originate from the lower part of the discontinuity layer. With potential temperatures of about 1.3°C they are much warmer than those observed in the Romanche Trench bottom water.