Nonlinear modal analysis of penetrative convection

Abstract

The modal expansion procedure has been used to analyze penetrative convection that arises when a thin unstable layer is embedded between two stable regions. The Boussinesq approximation is applied in which the effect of compressibility and stratification are neglected. Various calculations have been made, with one and two modes, for Rayleigh numbers ranging from the critical value to more than 10⁵ times critical. The effect of decreasing the Prandtl number has also been investigated.

It is found that in the nonlinear regime, the convective motions penetrate substantially into the stable regions. The flux of kinetic energy plays a crucial role in such penetration, and its existence puts some requirements on the motions: in the single-mode case, they need to be three-dimensional. The extent of penetration amounts to about half of the thickness of the unstable layer on each side of it when the degree of instability and that of stability are comparable in the two domains; it increases as the stability of the outer region is lowered. The penetration depth appears to be independent of all other parameters defining the problem.     

Neogene exhumation and relief evolution in the eastern Betics (SE Spain): Insights from the Sierra de Gador

The Betics are a key area to study an orogenic landscape disrupted by late‐orogenic extension. New low‐temperature thermochronology (LTT) data (AHe and AFT) coupled with geomorphic constraints in the Sierra de Gador (Alpujarride complex) are used to reconstruct the cooling history and evolution of relief during the Neogene. We document three stages: (1) a fast cooling event between 23 and 16 Ma associated with the well‐known extensive tectonic exhumation of the Alpujarride unit, (2) a period of slow cooling between 16 and 7.2 Ma related to a planation event and (3) a post‐7.2 Ma surface uplift associated with the inversion of the Alboran domain undetected by LTT. The planation event followed by this late uplift can explain the occurrence of inherited low‐relief surfaces overlain by Tortonian–Messinian platform deposits at the top of the range. Finally, we propose that the Sierra de Gador is a more transient landscape than the nearby Sierra Nevada.     

Anticipated changes in analysis accuracy with the removal of Ocean Weather Ship P

Abstract

Analysis error patterns have been established for the Pacific Weather Centre Experiment Area, and comparisons made between errors computed for meteorological observing arrays, including Ocean Weather Ship (OWS) P, and errors computed for several alternative arrays which excluded OWS P. These assessments of the impact of replacing the ocean weather ship with alternative observing equipment indicate that, above the 1000‐mb pressure surface, there will be a significant loss of accuracy in the forecast‐minus‐observation analyses regardless of proposed additional report systems. Near the surface, forecast error variances are estimated to decrease slightly with an increase of reports from buoys and ships of opportunity within the region.

The dependence of the assessments on the data selection procedure and on correlation representations for the region suggest that some loss may be compensated by more efficient use of available data. Refinements in the objective analysis scheme are seen to be especially important to analysis accuracy in regions lacking radiosonde coverage.     

Exhumation across the Indus Suture Zone: a record of back sliding of the hanging wall

The Kohistan Arc Complex is an integral part of the NW Himalayan collision system and is bounded by two major suture zones, the Indus Suture Zone (ISZ) and the Northern Suture in the south and north respectively. Fission‐track analyses on samples collected along the Indus River across the arcuated ISZ in the Besham region are presented here. The footwall yields zircon and apatite fission‐track (FT) ages of ∼23 Ma and ∼3.7 Ma respectively; the hanging wall ages range from 24 to 42 Ma for zircon and ∼10 Ma for apatite. Thus, the change in ISZ kinematics from thrusting to normal faulting was not later than Oligocene and normal faulting on this ISZ segment was still active at least into early Pliocene times. At this time normal faulting had already ended at other ISZ segments, but it was still (or again) active across the ISZ in the Besham region most likely as a local phenomenon caused by the growth of the Indus Syntaxis, a transverse antiform parallel to the Nanga Parbat Syntaxis.     

Quantifying the impact of no-till on runoff in southern Brazil at hillslope and catchment scales

No-till (NT) is a conservation system that improves the hydrological regime of agricultural slopes by providing greater surface protection and benefits to the physical and hydrological properties of soils. However, the isolated use of NT is not enough to control runoff and its associated degradation processes. Therefore, this study aimed to evaluate the runoff of agricultural slopes under NT under different runoff control conditions by monitoring 63 rainfall events in two 2.4-ha zero-order catchments and 27 rainfall events in four 0.6-ha macroplots. The catchments are paired and similar in terms of the type of soil and relief, but different regarding the presence of terraces. The macroplots have different soil and crop management systems. By using monitoring techniques, the hyetographs and hydrographs revealed the influence of the different types of management on the catchments and macroplots and allowed rainfall characteristics, runoff volume, runoff coefficients, water infiltration, peak runoff, response times, and curve number to be analysed. The terraces positively affected the NT and controlled runoff and related variables, in addition to infiltration significantly increasing and runoff reducing in the terraced catchment. All the hydrological information assessed pointed to the positive effects provided by the presence of the terraces. The results in the macroplots showed that high amounts of phytomass and/or chiselling do not control runoff and its correlated variables in medium and high magnitude events. The study concludes by underlining the need for additional measures to control runoff (terraces), even in areas under NT and with high phytomass production. Additionally, the study emphasizes the importance of monitoring at the catchment scale to better understand the hydrological behaviour of agricultural areas and provide the necessary parameters to effectively control runoff.     

Modeling branched and intersecting faults in reservoir-geomechanics models with the extended finite element method

Faults are geological entities with thickness several orders of magnitude smaller than the grid blocks typically used to discretize geological formations. On using the extended finite element method (X-FEM), a structured mesh suffices and the faults can arbitrarily cut the elements in the mesh. Modeling branched and intersecting faults is a challenge, in particular when the faults work as internal fluid flow conduits that allow fluid flow in the faults as well as to enter/leave the faults. By appropriately selecting the enrichment function and the nodes to be enriched, we are able to capture the special characteristics of the solution in the vicinity of the fault. We compare different enrichment schemes for strong discontinuities and develop new continuous enrichment functions with discontinuous derivatives to model branched and intersecting weak discontinuities. Symmetric fluid flows within the regions embedded by branched, coplanar intersecting, and noncoplanar intersecting faults are considered to verify the effectiveness of the proposed enrichment scheme. For a complex fault consisting of branched and intersecting faults, the accuracy and efficiency of the X-FEM is compared with the FEM. We also demonstrate different slipping scenarios for branched and intersecting faults with the same friction coefficient. In addition, fault slipping triggered by an injection pressure and three-dimensional fluid flows are modeled to show the versatility of the proposed enrichment scheme for branched and intersecting weak discontinuities.