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

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

The role of criticality on the horizontal and vertical scales of extratropical eddies in a dry GCM

This paper discusses the sensitivity of the horizontal and vertical scales of extratropical eddies when criticality is varied in a dry, primitive-equation, general circulation model. Criticality is a measure of extratropical isentropic slope and when defined appropriately its value is often close to 1 for Earth's climate. The model is forced by a Newtonian relaxation of temperature to a prescribed temperature profile, and criticality is increased by increasing the thermal relaxation rate on the mean flow. When criticality varies near 1, it is shown that there exists a weakly nonlinear regime in which the eddy scale increases with criticality without involving an inverse cascade, while at the same time the Rossby radius may in fact decrease. The quasigeostrophic instability of the Charney problem is revisited. It is demonstrated that both the horizontal and vertical scales of the most unstable wave depend on criticality, and simple estimates for the two scales are obtained. The authors reconcile the opposite trends of the eddy scale and Rossby radius and obtain an estimate for the eddy scale in terms of the Rossby radius and criticality that is broadly consistent with simulations.NSFNOA

Meridional Rossby Wave Generation and Propagation in the Maintenance of the Wintertime Tropospheric Double Jet

This is the final version of the article. Available from American Meteorological Society via the DOI in this record.The eddy-driven and subtropical jet are two dynamically distinct features of the midlatitude upper troposphere circulation that are often merged into a single zonal wind maxima. Nonetheless, the potential for a distinct double jet state in the atmosphere exists, particularly in the winter hemi-sphere, and presents a unique zonal mean flow with two waveguides and an interjet region with a weakened potential vorticity gradient upon which Rossby waves may be generated, propagate,reflect, and break. We investigate the interaction of two groups of atmospheric waves, those longer or shorter than the deformation radius, with a double jet mean flow in an idealized atmospheric model. Patterns of eddy momentum flux convergence for long and short waves differ greatly. Short waves behave following classic baroclinic instability theory such that their eddy momentum flux convergence is centered at the eddy-driven jet core. Long waves, on the other hand, reveal strong eddy momentum flux convergence along the poleward flank of the eddy-driven jet and within the interjet region. This pattern is enhanced when two jets are present in the zonal mean zonal wind.National Science Foundatio

Emergence of Fofonoff states in inviscid and viscous ocean circulation models

Numerical experiments are performed to directly test the emergence of the Fofonoff solution in an inviscid closed barotropic domain, and to explore its significance to the weakly dissipative system. The Fofonoff solution, characterized by a linear relationship between absolute vorticity and streamfunction, is generally realized as the time mean state of inviscid simulations over a fairly broad parameter range of varying (β-plane) Rossby number and resolution, in different geometrical domains, and with and without topography. The relevance of the Fofonoff solution to the viscous, decaying system is examined by numerical experiments with two different forms of viscosity, namely, biharmonic and harmonic, as well as with various boundary conditions. It is found that the boundary condition is generally more important than the order of the viscosity in determining the time mean fields. All of the frictional forms and boundary conditions prevented the complete realization of the Fofonoff state to a greater or lesser extent. Of the various boundary conditions used, the super-slip condition is most conducive to realizing a Fofonoff state. In this case, at high enough resolution the timescale of energy variability is much longer than a dynamical timescale, and the Fofonoff flow may be considered a ‘minimum enstrophy’ state. At high Reynolds number and high Rossby number an almost linear q — ψ relationship can be achieved. For lower Rossby numbers, absolute vorticity tends to become homogenized, preventing the Fofonoff solution from arising. In the case of a free slip condition, it is still harder to reach a quasi-equilibrium. The time mean fields, after spin-up, generally show a two-gyre structure with homogenization in the absolute vorticity fields. In the no slip case, neither a quasi-equilibrium nor any well formed time mean field can be reached. As a slight generalization of the flow on β-plane, the inviscid topographic experiments also ultimately yield a linear relationship between absolute vorticity and streamfunction

Large-scale circulation with small diapycnal diffusion: The two-thermocline limit

The structure and dynamics of the large-scale circulation of a single-hemisphere, closed-basin ocean with small diapycnal diffusion are studied by numerical and analytical methods. The investigation is motivated in part by recent differing theoretical descriptions of the dynamics that control the stratification of the upper ocean, and in part by recent observational evidence that diapycnal diffusivities due to small-scale turbulence in the ocean thermocline are small (≈0.1 cm2 s−1). Numerical solutions of a computationally efficient, three-dimensional, planetary geostrophic ocean circulation model are obtained in a square basin on a mid-latitude β-plane. The forcing consists of a zonal wind stress (imposed meridional Ekman flow) and a surface heat flux proportional to the difference between surface temperature and an imposed air temperature. For small diapycnal diffusivities (vertical: κv ≈0.1 – 0.5 cm2 s−1, horizontal: κh ≈105 – 5 × 106 cm2 s−1), two distinct thermocline regimes occur. On isopycnals that outcrop in the subtropical gyre, in the region of Ekman downwelling, a ventilated thermocline forms. In this regime, advection dominates diapycnal diffusion, and the heat balance is closed by surface cooling and convection in the northwest part of the subtropical gyre. An ‘advective’ vertical scale describes the depth to which the wind-driven motion penetrates, that is, the thickness of the ventilated thermocline. At the base of the wind-driven fluid layer, a second thermocline forms beneath a layer of vertically homogeneous fluid (‘mode water’). This ‘internal’ thermocline is intrinsically diffusive. An ‘internal boundary layer’ vertical scale (proportional to κv1/2) describes the thickness of this internal thermocline. Two varieties of subtropical mode waters are distinguished. The temperature difference across the ventilated thermocline is determined to first order by the meridional air temperature difference across the subtropical gyre. The temperature difference across the internal thermocline is determined to first order by the temperature difference across the subpolar gyre. The diffusively-driven meridional overturning cell is effectively confined below the ventilated thermocline, and driven to first order by the temperature difference across the internal thermocline, not the basin-wide meridional air temperature difference. Consequently, for small diapycnal diffusion, the abyssal circulation depends to first order only on the wind-forcing and the subpolar gyre air temperatures. The numerical solutions have a qualitative resemblance to the observed structure of the North Atlantic in and above the main thermocline (that is, to a depth of roughly 1500 m). Below the main thermocline, the predicted stratification is much weaker than observed