Nonlinear waves on a coupled density front

Abstract

It is shown that the inclusion of the nonlinear terms in the equations of motion of a coupled density front of zero potential vorticity results in wave solutions which merely propagate with time. The linear theory, on the other hand, predicts an exponential temporal growth. The nonlinear equation admits steady solutions representing standing waves whereas if the nonlinear terms are omitted no steady solutions exist. The general initial value problem is difficult to solve numerically since the linear problem is ill posed.

In addition we prove that the general similarity solution of the nonlinear equation tends to zero for large times, at any point in space, regardless of the initial condition.     

Vegetation changes in the Neotropical Gran Sabana (Venezuela) around the Younger Dryas chron

The occurrence of the Younger Dryas cold reversal in northern South America midlands and lowlands remains controversial. We present a palaeoecological analysis of a Late Glacial lacustrine section from a midland lake (Lake Chonita, 4.6501 °N, 61.0157 °W, 884 m elevation) located in the Venezuelan Gran Sabana, based on physical and biological proxies. The sediments were mostly barren from ～15.3 to 12.7 k cal a BP, probably due to poor preservation. A ligneous community with no clear modern analogues was dominant from 12.7 to 11.7 k cal a BP (Younger Dryas chronozone). At present, similar shrublands are situated around 200 m elevation above the lake, suggesting a cooling‐driven downward shift in vegetation during that period. The interval from 11.7 to 10.6 k cal a BP is marked by a dramatic replacement of the shrubland by savannas and a conspicuous increase in fire incidence. The intensification of local and regional fires at this interval could have played a role in the vegetation shift. A change to wetter, and probably warmer, conditions is deduced after 11.7 k cal a BP, coinciding with the early Holocene warming. These results support the hypothesis of a mixed origin (climate and fire) of the Gran Sabana savannas, and highlight the climatic instability of the Neotropics during the Late Glacial. Copyright © 2011 John Wiley & Sons, Ltd.     

An invariant theory of the linearized shallow water equations with rotation and its application to a sphere and a plane

The system of linearized shallow water equations is formulated in this paper on any rotating and smooth surface M in terms of differential geometry. The system decouples into two separate equations: a scalar one for the height deviation and a vector one for the velocity field. For low and high frequencies these equations yield asymptotic equations whose solutions are the generalizations of the Poincare and Rossby waves to smooth surface. The application of these equations to the β-plane yields both new and previously known equations for the height deviation and for the velocity components. The application of the equations to the rotating spherical Earth shows that the meridional amplitudes of Poincare and Rossby waves are both described by the prolate angular spheroidal wave functions. The asymptotic and the power series expansions of the eigenvalues of these functions yield new approximations for the dispersion relations of these waves on a sphere. The new dispersion relations are very accurate in the physically relevant range of the single nondimensional model parameter – the square of the nondimensional gravity waves’ phase speed. The invariant formulation can also be applied to other surfaces that are of geophysical interest such as an oblate ellipsoid of revolution.     

Anisotropic path modeling to assess pedestrian-evacuation potential from Cascadia-related tsunamis in the US Pacific Northwest

Recent disasters highlight the threat that tsunamis pose to coastal communities. When developing tsunami-education efforts and vertical-evacuation strategies, emergency managers need to understand how much time it could take for a coastal population to reach higher ground before tsunami waves arrive. To improve efforts to model pedestrian evacuations from tsunamis, we examine the sensitivity of least-cost-distance models to variations in modeling approaches, data resolutions, and travel-rate assumptions. We base our observations on the assumption that an anisotropic approach that uses path-distance algorithms and accounts for variations in land cover and directionality in slope is the most realistic of an actual evacuation landscape. We focus our efforts on the Long Beach Peninsula in Washington (USA), where a substantial residential and tourist population is threatened by near-field tsunamis related to a potential Cascadia subduction zone earthquake. Results indicate thousands of people are located in areas where evacuations to higher ground will be difficult before arrival of the first tsunami wave. Deviations from anisotropic modeling assumptions substantially influence the amount of time likely needed to reach higher ground. Across the entire study, changes in resolution of elevation data has a greater impact on calculated travel times than changes in land-cover resolution. In particular areas, land-cover resolution had a substantial impact when travel-inhibiting waterways were not reflected in small-scale data. Changes in travel-speed parameters had a substantial impact also, suggesting the importance of public-health campaigns as a tsunami risk-reduction strategy.     

Community variations in social vulnerability to Cascadia-related tsunamis in the U.S. Pacific Northwest

Tsunamis generated by Cascadia subduction zone earthquakes pose significant threats to coastal communities in the U.S. Pacific Northwest. Impacts of future tsunamis to individuals and communities will likely vary due to pre-event socioeconomic and demographic differences. In order to assess social vulnerability to Cascadia tsunamis, we adjust a social vulnerability index based on principal component analysis first developed by Cutter et al. (2003) to operate at the census-block level of geography and focus on community-level comparisons along the Oregon coast. The number of residents from blocks in tsunami-prone areas considered to have higher social vulnerability varies considerably among 26 Oregon cities and most are concentrated in four cities and two unincorporated areas. Variations in the number of residents from census blocks considered to have higher social vulnerability in each city do not strongly correlate with the number of residents or city assets in tsunami-prone areas. Methods presented here will help emergency managers to identify community sub-groups that are more susceptible to loss and to develop risk-reduction strategies that are tailored to local conditions.     

A fast tour design method using non-tangent v-infinity leveraging transfer

The announced missions to the Saturn and Jupiter systems renewed the space community interest in simple design methods for gravity assist tours at planetary moons. A key element in such trajectories are the V-Infinity Leveraging Transfers (VILT) which link simple impulsive maneuvers with two consecutive gravity assists at the same moon. VILTs typically include a tangent impulsive maneuver close to an apse location, yielding to a desired change in the excess velocity relative to the moon. In this paper we study the VILT solution space and derive a linear approximation which greatly simplifies the computation of the transfers, and is amenable to broad global searches. Using this approximation, Tisserand graphs, and heuristic optimization procedure we introduce a fast design method for multiple-VILT tours. We use this method to design a trajectory from a highly eccentric orbit around Saturn to a 200-km science orbit at Enceladus. The trajectory is then recomputed removing the linear approximation, showing a Δv change of <4%. The trajectory is 2.7 years long and comprises 52 gravity assists at Titan, Rhea, Dione, Tethys, and Enceladus, and several deterministic maneuvers. Total Δv is only 445 m/s, including the Enceladus orbit insertion, almost 10 times better then the 3.9 km/s of the Enceladus orbit insertion from the Titan–Enceladus Hohmann transfer. The new method and demonstrated results enable a new class of missions that tour and ultimately orbit small mass moons. Such missions were previously considered infeasible due to flight time and Δv constraints.     

Positive Relationship between Freshwater Inflow and Oyster Abundance in Galveston Bay,Texas

Analysis of fisheries-independent data for Galveston Bay, Texas, USA, since 1985 shows eastern oysters (Crassostrea virginica) frequently demonstrate increased abundance of market-sized oysters 1 to 2 years after years with increased freshwater inflow and decreased salinity. These analyses are compared to Turner’s (Estuaries and Coasts 29:345–352, 2006) study using 3-year running averages of oyster commercial harvest since 1950 in Galveston Bay. Turner’s results indicated an inverse relationship between freshwater inflow and commercial harvest with low harvest during years of high inflow and increased harvest during low flow years. Oyster populations may experience mass mortalities during extended periods of high inflow when low salinities are sustained. Conversely, oyster populations may be decimated during prolonged episodes of low flow when conditions favor oyster predators, parasites, and diseases with higher salinity optima. Turner’s (Estuaries and Coasts 29:345–352, 2006) analysis was motivated by a proposed project in a basin with abundant freshwater where the goal of the project was to substantially increase freshwater flow to the estuary in order to increase oyster harvest. We have the opposite concern that oysters will be harmed by projects that reduce flow, increase salinity, and increase the duration of higher salinity periods in a basin with increasing demand for limited freshwater. Turner’s study and our analysis reflect different aspects of the complex, important relationships between freshwater inflow, salinity, and oysters.     

Topography and Geologic Characteristics of Aeolian Grooves in the South Polar Layered Deposits of Mars

The topographic and geologic characteristics of grooves and groove-like features in the south polar layered deposits near the Mars Polar Lander/Deep Space 2 landing sites are evaluated using Mariner 9 images and their derived photoclinometry, normalized using Mars Orbiter Laser Altimeter data. Although both Mariner 9 and Viking images of the south polar layered deposits were available at the time of this study, Mariner 9 images of the grooves were selected because they were generally of higher resolution than Viking images. The dimensions and slopes of the grooves, together with orientations that nearly match the strongest winds predicted in the Martian Global Circulation Model and directions inferred from other wind indicators, suggest that they formed by aeolian scour of an easily erodible surface. Most grooves are symmetric and V-shaped in transverse profile, inconsistent with an origin involving extensional brittle deformation. Although the grooves strike along slopes and terraces of the south polar layered deposits, the variable depths and lack of terracing within the grooves themselves indicate that any stratigraphy in the uppermost 100 m of the polar layered deposits is composed of layers of similar, and relatively low, resistance. The grooves do not represent landing hazards at the scale of the Mariner 9 images (72-86 m/pixel) and therefore probably would not have affected Mars Polar Lander and Deep Space 2, had they successfully reached the surface.     

Thermal history analysis by integrated modelling of apatite fission track and vitrinite reflectance data: application to an inverted basin (Buller Coalfield, New Zealand)

Integrated analysis and modelling of apatite fission track with vitrinite reflectance (VR) data allows the timing, magnitude and pattern of Palaeogene subsidence and Neogene inversion to be established for an uplifted and largely denuded basin: the Buller Coalfield, New Zealand. At the time of maximum subsidence in the late Oligocene, the basin consisted of an extensional half graben, bounded to the west by the Kongahu Fault Zone (KFZ), with up to 6 km of upper Eocene to Oligocene section adjacent to it; currently, only a few tens of metres of basal coal measures on basement are preserved on top of a range 800–1000 m above sea level. Integrated modelling of the VR and fission track data show that the deepest parts of the basin were inverted during two Miocene compressional phases (24–19 Ma and 13–8 Ma), and are consistent with a further phase of inversion during the Quaternary that formed the present topography. Palinspastic restoration of the three phases of inversion shows that the basin was not inverted in a simple way: most of the rock uplift/denudation adjacent to the KFZ occurred during the early Miocene phase, and at the same time burial occurred in the south-eastern part of the basin (maximum temperatures were experienced at different times at different places in the basin); during the middle to late Miocene there was broad uplift in the central and eastern parts of the coalfield. Because the timing and magnitude of uplift have been derived from the zone of inversion, they can be compared independently with the timing of unconformity development and rapid subsidence in the adjacent foredeeps, particularly the Westport Trough. For the middle to late Miocene phase of inversion, we show that during the first 1–2 million years of compression, the uplift within the coalfield also involved the margins of the Westport Trough, contributing to unconformity development; subsequently, uplift continued on the inversion structure but the margins of the Westport Trough subsided rapidly. This is explained by a model of stick slip behaviour on the boundary faults, especially for the KFZ. When compression started the fault zone has locked and uplift extends into the basin, whereas subsequently the fault zone unlocks, and the inversion structure overrides the basin margin, thereby loading it and causing subsidence.