The rotation of the Ocean‐Solid Earth System

Abstract

It is shown that the long‐period, highly elliptical Markowitz wobble can be viewed as a natural wobble of the coupled mantle‐ocean system. From a rotational point of view, oceanic wobble is possible even if the oceans respond in an equilibrium manner to wobble because the oceans are nonglobal and a thin layer; either of the latter conditions, or an oceanic response which is nonequilibrium, can maintain the separation of rotation and figure axes constituting wobble. Characteristics of the uncoupled bodies are first determined. The inertia tensor of the oceans yields an oceanic body whose free wobble is retrograde and short period under the assumption of an equilibrium fluid response; it also yields an oceanless earth whose precessional constant more nearly equals the hydrostatic rather than the observed whole earth value. The equations governing wobbles of a coupled two‐body system, rigid or deformable, are developed and referred to the same wobbling coordinate system. Solutions are found for various general types of coupling. For a deformable system the retrograde character of the free oceanic wobble leads to coupled motions which are at best undamped and at worst unstably damped. Those types of coupling which avoid unstable rotational behavior and also generate one wobble mode with the characteristics of the Chandler wobble predict a second wobble mode with the period and retrograde (or marginally prograde) sense of the Markowitz wobble. Since those couples are nondissipative, attenuation of the wobbles is presumably achieved by a combination of shallow sea interactions and internal friction within mantle and oceans. Some of the amplitude characteristics predicted for the wobble modes fail to match observations adequately. Resolution of these disparities within the coupled‐system framework may enhance our understanding of wobble excitation and the open ocean pole tide.