Geophysical and Astrophysical Fluid Dynamics

Abstract:

We examine the consequences of, and apply, the formalism developed in Terquem (2021) for calculating the rate DR at which energy is exchanged between fast tides and convection. In this previous work, DR (which is proportional to the gradient of the convective velocity) was assumed to be positive in order to dissipate the tidal energy. Here we argue that, even if energy is intermittently transferred from convection to the tides, it must ultimately return to the convective flow and transported efficiently to the stellar surface on the convective timescale. This is consistent with, but much less restrictive than, enforcing DR > 0. Our principle result is a calculation of the circularization timescale of late-type binaries, taking into account the full time evolution of the stellar structure. We find that circularization is very efficient during the PMS phase, inefficient during the MS, and once again efficient when the star approaches the RGB. These results are in much better agreement with observations than earlier theories. We also apply our formalism to hot Jupiters, and find that tidal dissipation in a Jupiter mass planet yields a circularization timescale of 1 Gyr for an orbital period of 3 d, also in good overall agreement with observations. The approach here is novel, and the apparent success of the theory in resolving longstanding timescale puzzles is compelling.

Abstract:

We describe the life and scientific accomplishments of Professor Raymond Hide. He was a past President of the Royal Meteorological Society and a supreme example of a geophysicist much honoured in his lifetime. He covered a wide area of geophysics from geomagnetism, meteorology, geodesy, oceanography and related aspects of planetary physics. Raymond Hide was particularly known in meteorology as a founding father of geophysical fluid dynamics, especially for his experiments using a rotating cylindrical annulus to study atmospheric dynamics.

Abstract:

AbstractWhen a fluid system is subject to strong rotation, centrifugal fluid motion is expected, i.e., denser (lighter) fluid moves outward (inward) from (toward) the axis of rotation. Here we demonstrate, both experimentally and numerically, the existence of an unexpected outward motion of warm and lighter vortices in rotating thermal convection. This anomalous vortex motion occurs under rapid rotations when the centrifugal buoyancy is sufficiently strong to induce a symmetry-breaking in the vorticity field, i.e., the vorticity of the cold anticyclones overrides that of the warm cyclones. We show that through hydrodynamic interactions the densely distributed vortices can self-aggregate into coherent clusters and exhibit collective motion in this flow regime. Interestingly, the correlation of the vortex velocity fluctuations within a cluster is scale-free, with the correlation length being proportional ( ≈ 30%) to the cluster length. Such long-range correlation leads to the counterintuitive collective outward motion of warm vortices. Our study brings insights into the vortex dynamics that are widely present in nature.

Abstract:

The tidal evolution of interacting binaries when the orbital period is short compared to the primary star's convective time scale is a problem of long-standing. Terquem (2021) has argued that, when this temporal ordering scheme is obeyed, the rate of energy transfer from tides to convection (denoted $D_R$) is given by the product of the averaged Reynolds stress associated with the tidal velocity and the mean shear associated with the convective flow. In a recent response, Barker and Astoul (2021, hereafter BA21) claim to show that $D_R$ (in this form) cannot contribute to tidal dissipation. Their analysis is based on a study of Boussinesq and anelastic models. Here, we demonstrate that BA21 misidentify the correct term responsible for energy transfer between tides and convection. As a consequence, their anelastic calculations do not prove that the $D_R$ formulation is invalidated as an energy-loss coupling between tides and convection. BA21 also carry out a calculation in the Boussinesq approximation. Here, their claim that $D_R$ once again does not contribute is based on boundary conditions that do not apply to any star or planet that radiates energy from its surface, which is a key dissipational process in the problem we consider.