Geophysical and Astrophysical Fluid Dynamics

Abstract:

Abstract We calculate the dynamical tides raised by a close planetary companion on non–rotating stars of 1 M⊙ and 1.4 M⊙. Using the Henyey method, we solve the fully non–adiabatic equations throughout the star. The horizontal Lagrangian displacement is found to be 10 to 100 times larger than the equilibrium tide value in a thin region near the surface of the star. This is because non–adiabatic effects dominate in a region that extends from below the outer edge of the convection zone up to the stellar surface, and the equilibrium tide approximation is inconsistent with non–adiabaticity. Although this approximation generally applies in the low frequency limit, it also fails in the parts of the convection zone where the forcing frequency is small but larger than the Brunt-Väisälä frequency. We derive analytical estimates which give a good approximation to the numerical values of the magnitude of the ratio of the horizontal and radial displacements at the surface. The relative surface flux perturbation is also significant, on the order of 0.1% for a system modelled on 51 Pegasi b. Observations affected by the horizontal displacement may therefore be more achievable than previously thought, and brightness perturbations may be the result of flux perturbations rather than due to the radial displacement. We discuss the implication of this on the possibility of detecting such tidally excited oscillations, including the prospect of utilising the large horizontal motion for observations of systems such as 51 Pegasi.

Abstract:

Shadowing trajectories are model trajectories consistent with a sequence of observations of a system, given a distribution of observational noise. The existence of such trajectories is a desirable property of any forecast model. Gradient descent of indeterminism is a well-established technique for finding shadowing trajectories in low-dimensional analytical systems. Here we apply it to the thermally-driven rotating annulus, a laboratory experiment intermediate in model complexity and physical idealisation between analytical systems and global, comprehensive atmospheric models. We work in the perfect model scenario using the MORALS model to generate a sequence of noisy observations in a chaotic flow regime. We demonstrate that the gradient descent technique recovers a pseudo-orbit of model states significantly closer to a model trajectory than the initial sequence. Gradient-free descent is used, where the adjoint model is set to $\lambda$I in the absence of a full adjoint model. The indeterminism of the pseudo-orbit falls by two orders of magnitude during the descent, but we find that the distance between the pseudo-orbit and the initial, true, model trajectory reaches a minimum and then diverges from truth. We attribute this to the use of the $\lambda$-adjoint, which is well suited to noise reduction but not to finely-tuned convergence towards a model trajectory. We find that $\lambda=0.25$ gives optimal results, and that candidate model trajectories begun from this pseudo-orbit shadow the observations for up to 80 s, about the length of the longest timescale of the system, and similar to expected shadowing times based on the distance between the pseudo-orbit and the truth. There is great potential for using this method with real laboratory data.

Abstract:

A Martian semiannual oscillation (SAO), similar to that in the Earths tropical stratosphere, is evident in the Mars Analysis Correction Data Assimilation reanalysis dataset (MACDA) version 1.0, not only in the tropics, but also extending to higher latitudes. Unlike on Earth, the Martian SAO is found not always to reverse its zonal wind direction, but only manifests itself as a deceleration of the dominant wind at certain pressure levels and latitudes. Singular System Analysis (SSA) is further applied on the zonal-mean zonal wind in different latitude bands to reveal the characteristics of SAO phenomena at different latitudes. The second pair of principal components (PCs) is usually dominated by a SAO signal, though the SAO signal can be strong enough to manifest itself also in the first pair of PCs. An analysis of terms in the Transformed Eulerian Mean equation (TEM) is applied in the tropics to further elucidate the forcing processes driving the tendency of the zonal-mean zonal wind. The zonal-mean meridional advection is found to correlate strongly with the observed oscillations of zonal-mean zonal wind, and supplies the majority of the westward (retrograde) forcing in the SAO cycle. The forcing due to various non-zonal waves supplies forcing to the zonal-mean zonal wind that is nearly the opposite of the forcing due to meridional advection above ∼3 Pa altitude, but it also partly supports the SAO between 40 Pa and 3 Pa. Some distinctive features occurring during the period of the Mars year (MY) 25 global-scale dust storm (GDS) are also notable in our diagnostic results with substantially stronger values of eastward and westward momentum in the second half of MY 25 and stronger forcing due to vertical advection, transient waves and thermal tides