The thermal phase curve offset on tidally- and non-tidally-locked exoplanets: A shallow water model

Using a shallow water model with time-dependent forcing we show that the peak of an exoplanet thermal phase curve is, in general, offset from secondary eclipse when the planet is rotating. That is, the planetary hot-spot is offset from the point of maximal heating (the substellar point) and may lead or lag the forcing; the extent and sign of the offset is a function of both the rotation rate and orbital period of the planet. We also find that the system reaches a steady-state in the reference frame of the moving forcing. The model is an extension of the well studied Matsuno-Gill model into a full spherical geometry and with a planetary-scale translating forcing representing the insolation received on an exoplanet from a host star. The speed of the gravity waves in the model is shown to be a key metric in evaluating the phase curve offset. If the velocity of the substellar point (relative to the planet's surface) exceeds that of the gravity waves then the hotspot will lag the substellar point, as might be expected by consideration of forced gravity wave dynamics. However, when the substellar point is moving slower than the internal wavespeed of the system the hottest point can lead the passage of the forcing. We provide an interpretation of this result by consideration of the Rossby and Kelvin wave dynamics as well as, in the very slowly rotating case, a one-dimensional model that yields an analytic solution. Finally, we consider the inverse problem of constraining planetary rotation rate from an observed phase curve

Coupling convectively driven atmospheric circulation to surface rotation: Evidence for active methane weather in the observed spin rate drift of Titan

A large drift in the rotation rate of Titan observed by Cassini provided the first evidence of a subsurface ocean isolating the massive core from the icy crust. Seasonal exchange of angular momentum between the surface and atmosphere accounts for the magnitude of the effect, but observations lag the expected signal by a few years. We argue that this time lag is due to the presence of an active methane weather cycle in the atmosphere. An analytic model of the seasonal cycle of atmospheric angular momentum is developed and compared with time-dependent simulations of Titan's atmosphere with and without methane thermodynamics. The disappearance of clouds at the summer pole suggests the drift rate has already switched direction, signaling the change in season from solstice to equinox.Comment: 6 pages, 4 figures, published in Ap

Intra-Firm Human Capital Externalities in Tunisia

In this case-study, we use matched worker-firm Tunisian data to elicit the roles of intra-firm human capital and modern firm features in worker remunerations. We show that the estimated return to education in wage equations is not modified when replacing in the list of regressors the firm dummies, representing observed and unobserved firm heterogeneity, by the first three factors of a Principal Component Analysis of the observed firm characteristics. These factors can be interpreted as: the activity sector, the intra-firm human capital density and the modernity of the firm. These results constitute an interesting argument in favour of the presence of intra-firm human capital externalities. Moreover, the estimated education coefficient does not change when the three factors are replaced by three surrogate variables, respectively: the textile industry dummy, the intra-firm mean education, and the firm’s age.economic development, rate of returns, human capital, wage differentials, intra-firm knowledge externalities, Tunisia.

Ribbon Turbulence

We investigate the non-linear equilibration of a two-layer quasi-geostrophic flow in a channel forced by an imposed unstable zonal mean flow, paying particular attention to the role of bottom friction. In the limit of low bottom friction, classical theory of geostrophic turbulence predicts an inverse cascade of kinetic energy in the horizontal with condensation at the domain scale and barotropization on the vertical. By contrast, in the limit of large bottom friction, the flow is dominated by ribbons of high kinetic energy in the upper layer. These ribbons correspond to meandering jets separating regions of homogenized potential vorticity. We interpret these result by taking advantage of the peculiar conservation laws satisfied by this system: the dynamics can be recast in such a way that the imposed mean flow appears as an initial source of potential vorticity levels in the upper layer. The initial baroclinic instability leads to a turbulent flow that stirs this potential vorticity field while conserving the global distribution of potential vorticity levels. Statistical mechanical theory of the 1-1/2 layer quasi-geostrophic model predict the formation of two regions of homogenized potential vorticity separated by a minimal interface. We show that the dynamics of the ribbons results from a competition between a tendency to reach this equilibrium state, and baroclinic instability that induces meanders of the interface. These meanders intermittently break and induce potential vorticity mixing, but the interface remains sharp throughout the flow evolution. We show that for some parameter regimes, the ribbons act as a mixing barrier which prevent relaxation toward equilibrium, favouring the emergence of multiple zonal jets

Geophysical Fluid Dynamics: Whence, Whither and Why?

This article discusses the role of Geophysical Fluid Dynamics (GFD) in understanding the natural environment, and in particular the dynamics of atmospheres and oceans on Earth and elsewhere. GFD, as usually understood, is a branch of the geosciences that deals with fl uid dynamics and that, by tradition, seeks to extract the bare essence of a phenomenon, omitting detail where possible. The geosciences in general deal with complex interacting systems and in some ways resemble condensed matter physics or aspects of biology, where we seek explanations of phenomena at a higher level than simply directly calculating the interactions of all the constituent parts. That is, we try to develop theories or make simple models of the behaviour of the system as a whole. However, these days in many geophysical systems of interest, we can also obtain information for how the system behaves by almost direct numerical simulation from the governing equations. The numerical model itself then explicitly predicts the emergent phenomena – the Gulf Stream for example – something that is still usually impossible in biology or condensed matter physics. Such simulations, as manifested for example in complicated General Circulation Models, have in some ways been extremely successful and one may reasonably now ask whether understanding a complex geophysical system is necessary for predicting it. In what follows we discuss such issues and the roles that GFD has played in the past and will play in the future.The work was funded by the Royal Society (Wolfson Foundation), NERC, NSF, and the Newton Fund

The catalytic role of beta effect in barotropization processes

The vertical structure of freely evolving, continuously stratified, quasi-geostrophic flow is investigated. We predict the final state organization, and in particular its vertical structure, using statistical mechanics and these predictions are tested against numerical simulations. The key role played by conservation laws in each layer, including the fine-grained enstrophy, is discussed. In general, the conservation laws, and in particular that enstrophy is conserved layer-wise, prevent complete barotropization, i.e., the tendency to reach the gravest vertical mode. The peculiar role of the $\beta$-effect, i.e. of the existence of planetary vorticity gradients, is discussed. In particular, it is shown that increasing $\beta$ increases the tendency toward barotropization through turbulent stirring. The effectiveness of barotropisation may be partly parameterized using the Rhines scale $2\pi E_{0}^{1/4}/\beta^{1/2}$. As this parameter decreases (beta increases) then barotropization can progress further, because the beta term provides enstrophy to each layer

Heaven on Earth

‘Heaven on earth’ is a creative non-fiction piece which juxtaposes life under lockdown in Sydney 2020 with my experience of curfew in Kashmir in the 1990s. The COVID-19 crisis is explored from the resonances and dissonances across place and time. In this hybrid personal essay, I reflect on how a sense of space is constructed from wealth and community, and how a white, middle-class status benefits from lockdown, juxtaposed against the ongoing political and social isolation of Kashmir