Dynamic Problems with Vessels regarding Parametric Resonance and Different Kinds of Sea Loads in Waves in Deep Water

It has been my intention regarding this Main Project, to collect the results of the latest research in the area of avoiding dangerous situations in following and quartering seas. Recent accidents with large container ships have shown that dangerous situations from heavy rolling can also occur in head seas at slow speed, a situation that has traditionally been considered as safe and suitable for riding out a severe storm. Parametric resonance has been found as the explanation for the heavy rolling in this situation.

Excessive stability has become a frequent occurrence on container ships and ro-ro ships designed for large deck loads, when operated in part deck load conditions. This condition makes those ships vulnerable in beam seas due to the risk of harmonic resonance.
A ship sailing in following or stern quartering seas encounters the waves with a longer period than in beam, head or bow waves, and principal dangers caused in such situation are, in addition to parametric resonance, reduction of intact stability when riding a wave crest amidships, and surf-riding and broaching-to. (IMO 2005)

As for the danger of surf-riding and broaching-to, a brief chapter dealing with these phenomena is presented as well.

Furthermore, the freak-wave known as the so-called 100-year wave only ten to twelve years ago, are now recognizeable at least 100 times a year. A lot of research work from all over the world during the last ten years, is about to give us the understanding of why these freaks raise, but not yet how to avoid them. A chapter dealing with this phenomenon is as well presented.

All this information ought to be given to my fellow mates and masters on the bridge, but to make these phenomena understandable, some basic theory is needed.
Elementary transverse ship stability is given a retrospective glance, as well as a brief examination on stability and sea loads on ships at sea. As for the basic wave theory, a comprehensive presentation is given accordingly restricted to waves in deep water.

Freak Waves
Freak waves occupy a special place in nautical lore. They have smashed into cruise ships, sunk oil-drilling platforms, and terrorized seafarers in fictional accounts for 2,000 years. Although freak waves – also called rogue waves or monster waves – are most often encountered during storms or bad weather, they almost always show up with little warning. Scientists once assumed that rogue waves strike any particular patch of ocean only once every several millennia, but oceanographic data now suggest that the waves are much more common.

New mathematical analyses indicate how rogue waves form in some instances and how long these monsters last before they blend back into the surrounding waves. These models suggest that rogue waves build up and dissipate more readily than past research had indicated. The new analyses may enable scientists to better predict where rogue waves will strike – data well worth knowing for the captains of oceangoing vessels.

Scientists do not have many detailed measurements of rogue waves because they tend to appear without warning, and bobbing ships make poor observation platforms. Besides their size, rogue waves differ from the friendly kind in their shape. The larger an ocean wave is, the more its profile diverges from a sine wave. (Perkins 2006)

Parametric Roll
The phenomenon of parametrically excited roll motion has been known to naval architects for almost a half of a century. It is caused by periodic changes of transverse stability in waves, characterized by a decrease of stability when the ship is in the wave crest and an increase in the wave trough.

The problem of parametric roll returned to prominence recently as a result of significant cargo loss and damage sustained by a Post-Panamax container carrier on a voyage from Taiwan to Seattle, Washington. A detailed investigation followed, showing that a large roll motion with up to 35 degrees amplitude accompanied by significant pitch and yaw motion resulted from the periodic change of transverse stability in head seas. The large change of stability in head seas was found to be a direct result of the hull form. Substantial bow flare and stem overhang, now typical of large container carriers, cause a dramatic difference in waterline form – and therefore in transverse stability – between the crest and trough of a large wave.

Despite the fact that the physical nature of parametric roll has been known for many years, several new elements are presented in the past. Now, the concern is for the vulnerability of large container carriers in head seas. The problem is particularly important given the long-standing heavy-weather maritime practice of sailing into head seas at reduced speed. It turns out that this is not necessarily the best practice for large container carriers. (Shin et al. 2004)

Broaching
Ship survivability against capsize in heavy seas has become one of the areas of primary concern among ship researchers, designers and regulators in recent years. When a ship is subjected to the effect of large waves it may capsize according to a number of different scenarios, depending on the size and direction of the rough wave and the ship’s own capability to resist such rough waves. Resonant or breaking waves approaching a ship trom the side have a potential to excite large rolling which could result in capsize, especially if the intensive oscillation of the ship causes shift of cargo or, if a considerable quantity of green water is shipped on the deck.
More dangerous still can be a group of steep and relatively long waves approaching a ship from the stern. Waves of this kind are known to incur significant reductions in roll restoring capability for many types of vessels and they may also instigate dangerous coupled motions. According to a popular classification, in following-seas a ship may capsize in at least three different ways:

Pure-loss of stability is a sudden, non-oscillatory type capsize taking place around a wave crest due to slow passage from a region of the wave where roll restoring has become negative.

Parametric instability is the gradual build-up of excessively large rolling created by a mechanism of internal forcing, the result of a fluctuating restoring that depends on where the ship lies in relation to the wave.

The third distinctively identified, yet until recently not fully understood, type of capsize is broaching. Broaching is an unintentional change in the horizontal-plane kinematics of a ship. Broadly, it may be described as the «loss of heading» by an actively steered ship, that is accompanied by an uncontrollable build-up of large deviation trom the desired course. (Spyrou 1999)

Øystein Johnsen, Master Mariner
Student NAMF, Faculty of Maritime Studies, Vestfold University College