Primer on Naval Architecture- Parametric Roll

Large containerships are particularly susceptible to the physical phenomenon of parametric rolling due to their hull design featuring a wide, flat stern, pronounced bow flare, fine under-water body and relatively light loaded displacement.
Parametric rolling can lead to loss of or damage to cargo containers and possible damage to the ship. Relying on fundamental physics theory to simulate the build up of energy that takes place during a rolling motion, ABS researchers conducted numerical modeling and sequence simulations to illustrate the gravity force effects on ships as they roll, pitch and heave in a seaway. A ship is particularly susceptible to parametric rolling when encountering either head or following seas.

TECHNICAL DISCUSSION
To transport goods efficiently, modern containerships are being designed for high service speeds necessitating a fine underwater body and relatively low block coefficient. To maximize carrying capacity on such a fine body, the deck is extended as far forward and aft as possible, resulting in a somewhat exaggerated bow flare and pronounced stern overhang.
These characteristics are most prominent in large and ultra-large containerships, making these vessels the most susceptible to parametric rolling. Parametric rolling is not a frequent phenomenon because a finely balanced set of circumstances must exist for this physical event to take place. The ship’s geometry must have certain characteristics. The ship’s length must be comparable to the wavelength of the sea conditions through which it is passing. The ship’s speed must bear a certain relationship to both the wavelength and the vessel’s natural rolling frequency.
As a consequence, instead of a balanced pendulum-like rolling momentum occurring, the ship accumulates energy. As the vessel passes through the waves, it encounters a series of wave peaks and troughs. If the ship length is close to the wavelength, it will rapidly change from hogging to sagging configurations. Because of the fine body, pronounced flare and stern
overhang, the ship effectively changes its beam from slim when hogged with the midships
supported, to wide when the midships is in a trough but the bow and stern are supported by wave peaks.
Since stability varies with beam, as the vessel drives through the series of wave fronts its stability changes significantly as the midship moves from crest (maximum) to trough (minimum).
When this pattern occurs together with a wave encounter frequency that is close to twice the ship’s natural roll frequency, the ship enters a condition of cyclically recurring minimum stability.