Deep Water Case Research Articles

Nonlinear Aspects of Subcritical Shallow-Water Flow Past Two-Dimensional Obstructions

Some nonlinear aspects of the two-dimensional problem of a submerged body moving with constant speed in otherwise undisturbed water of uniform depth are considered. It is shown that a theory of Benjamin which predicts a uniform rise of the free surface ahead of the body and the lowering of the mean level of the waves behind it agrees well with experimental data. The local steady-flow problem is solved by a numerical method which satisfies the exact free-surface conditions. Third-order perturbation formulas for the downstream free waves are also presented. It is found that in sufficiently shallow water, the wavelength increases with increasing disturbance strength for fixed values of the free-stream-Froude number. This is opposite to the deepwater case where the wavelength decreases with increasing disturbance strength.

Underwater sound propagation in a range-dependent environment

For an ocean sound channel whose environmental parameters depend not only on depth, but in a gradual fashion also on range, the wave equation may be separated by the adiabatic range variation method of Pierce. For cases of less gradual range dependence, the range equations (and hence the modes) become coupled, and may be solved by diagonalization methods. This approach is used here to calculate underwater sound propagation in a channel with arbitrarily given range dependence, and also with arbitrary depth dependence of the sound velocity profiles, by employing Airy function solutions of segmentwise linearized problems. (For the coupling aspects, the simplification of segmentwise constant problems is made.) Our results are illustrated for a realistic deep water case with profiles from the Western North Atlantic, as well as a shallow water example from the Norwegian Sea, and are compared against the experimental transmission-loss data, and the results of calculations using other methods for the same cases. [Supported in part by NRL Code 8120.]

Paper 5. Directional Stability and Control of a Vessel in Restricted Waters

By way of introduction the paper discusses conflicting observations of stability behaviour of ships in restricted waters. The equations of motion of a ship in a narrow channel are given, leading to stability criteria; differences from the deep water case are highlighted. More qualitatively, the theory also illustrates the asymmetric hydrodynamic force. Criteria are outlined for an automatic control system to improve stability. However, the first-order theory is shown to provide an inadequate description of all experimental results.