Rotational turbidity flows and the 1929 Grand Banks earthquake

Abstract

Turbidity currents resulting from underwater earthquakes that cause slumps and bring mud into suspension are common in the ocean. The 1929 Grand Banks earthquake, which generated a large turbidity current, is a particular interest because, as the current advanced, all the submarine telegraph cables situated downslope were broken in sequence. Since the location and breakage times are known, these successive breakages provided a unique set of observations of the current's downhill propagation speed. They show that the current's propagation rate was drastically reduced as it advanced toward the abyssal plain. The dramatic reduction in speed has been previously attributed to (i) the natural reduction in the bottom slope which occurs as one approaches the abyssal plain; (ii) settling of the mud out of suspension, which reduces the density at the current; and (iii) bottom friction. In the present paper, a new and powerful alternative to the above explanations is proposed. It is suggested that, since the observed migration of the current lasts for about 10–15 h, the rotation of the earth could dramatically alter both its path and structure. Using exact solutions of the nonlinear shallow water equations, it is shown that due to the earth's spin, the initial downhill migration is severely altered within hours after the earthquake. The gravity current resulting from the earthquake is modeled as an isolated patch of dense and inviscid fluid situated on a parabolic bottom, which can be either concave or convex. The steep portion of the concave bottom corresponds to the continental rise, whereas the flat portion corresponds to the abyssal plain. This reflects the actual situation corresponding to the 1929 Grand Banks earthquake. (Convex bottoms, on the other hand, correspond to turbidity currents situated on top of the continental shelf.) It turns out that, due to the gravitational pull and the rotation of the earth, the patchy gravity current migrates as a blob (with an anticyclonic circulation) along a cycloid whose mean path is parallel to the isobaths. For a concave (convex) bottom the blob becomes an ellipse which is oriented across (along) the isobaths. The cycloid is composed of inertial oscillations with an amplitude of the order of g′ S 1/ f 2 (where g′ is the “reduced gravity” gΔϱ/ϱ, S 1 is the local bottom slope and f is the Coriolis parameter). For all concave bottoms in mid-latitude, the downhill migration of the patch will be slowed down dramatically within one inertial period (i.e. several hours). Although the comparison of our model to the actual current is qualitative (and not quantitative) in nature, this speed reduction is offered as an alternative explanation for the observations. An additional interesting result, unrelated to the 1929 Grand Banks earthquake, is that the convex bottom has a critical curvature beyond which the blob separates from the bottom and penetrates into the ocean interior. That is, as the curvature of the convex bottom increases, a point is reached when the associated centrifugal force is so large that the blob can no longer cling to the floor and must “fall off”. Furthermore, for strong bottom curvatures (concave and convex) the blob cannot maintain its coherent structure and breaks up into smaller patches.