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SUMMARY  Dissipative core–mantle coupling is evident in observations of the Earth's nutations, although the source of this coupling is uncertain. Magnetic coupling occurs when conducting materials on either side of the boundary move through a magnetic field. In order to explain the nutation observations with magnetic coupling, we must assume a high (metallic) conductivity on the mantle side of the boundary and a rms radial field of 0.69 mT. Much of this field occurs at short wavelengths, which cannot be observed directly at the surface. High levels of short‐wavelength field impose demands on the power needed to regenerate the field through dynamo action in the core. We use a numerical dynamo model from the study of Christensen &amp; Aubert (2006) to assess whether the required short‐wavelength field is physically plausible. By scaling the numerical solution to a model with sufficient short‐wavelength field, we obtain a total ohmic dissipation of 0.7–1 TW, which is within current uncertainties. Viscous coupling is another possible explanation for the nutation observations, although the effective viscosity required for this is 0.03 m 2  s −1  or higher. Such high viscosities are commonly interpreted as an eddy viscosity. However, physical considerations and laboratory experiments limit the eddy viscosity to 10 −4  m 2  s −1 , which suggests that viscous coupling can only explain a few percent of the dissipative torque between the core and the mantle.

Magnetic and viscous coupling at the core–mantle boundary: inferences from observations of the Earth's nutations