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.     

Timing and duration of hydrological transitions in Arctic polygonal ground from stable isotopes

Land surface models and Earth system models that include Arctic landscapes must capture the abrupt hydrological transitions that occur during the annual thaw and deepening of the active layer. In this work, stable water isotopes (δ²H and δ¹⁸O) are used to appraise hydrologically significant transitions during annual landscape thaw at the Barrow Environmental Observatory (Utqiaġvik, Alaska). These hydrologically significant periods are then linked to annual shifts in the landscape energy balance, deduced from meteorological data and described by the microclimatic periods: Winter, Pre-Melt, Melt, Post-Melt, Summer, and Freeze-Up. The tight coupling of the microclimatic periods with the hydrological transitions supports the use of microclimatic periods as a means of linking polygonal surface water hydrology to meteorological datasets, which provides a mechanism for improving the representation of polygonal surface water hydrology in process-based models. Rayleigh process reconstruction of the isotopic changes revealed that 19% of winter precipitation was lost to sublimation prior to melting and that 23% of surface water was lost to evaporation during the first 10 days post-melt. This agrees with evaporation rates reported in a separate study using an eddy covariance flux tower located nearby. An additional 17% was lost to evaporation during the next 33 days. Stable water isotopes are also used to identify the dominant sources of surface water to various hydrogeomorphological features prevalent in polygonal terrain (a lake, a low centre polygon centre, troughs within the rims of low centre polygons, flat centre polygon troughs, a high centre polygon trough, and drainages). Hydrogeomorphologies that retained significant old water or acted as snow drifts are isotopically distinct during the Melt Period and therefore are easily distinguished. Biogeochemical changes related to the annual thaw are also reported and coupled to the hydrological transitions, which provides insight into the sources and sinks of these ions to and from the landscape.     

Mechanisms of melt extraction during lower crustal partial melting

Progressive vapour‐absent partial melting of a closed rock system increases melt pressure due to an expansion in the volume of the mineral plus melt assemblage. For a locally closed system, we quantify the melt pressure increase per increment of partial melting of a metapelite using phase equilibria modelling and combine it with Mohr–Coulomb theory to examine the interplay between melt pressure and fracture behaviour. It is shown that very small increments of vapour‐absent partial melting (<1%) increase melt pore pressure by tens of MPa leading to inevitable brittle failure of locally closed systems. Fracturing will affect these systems, even if initially limited to the scale of a few grains, and a connected microfracture network will enhance permeability as partial melting progresses. This will lead to a conditionally open system, potentially limiting accumulation of melt in the source. Repeated and cyclic fracture as temperature progressively increases will drive migration of the melt into sites of low fluid pressure at all scales. Crystal‐plastic creep processes create deformation‐induced dilatancy gradients that dominate over buoyancy forces at all scales in the melt source. Brittle and ductile deformation therefore cooperate in the extraction of melt. Enhanced porosity and permeability in ductile shear zones result in lower fluid pressure, providing a potentially important driving force for melt migration and drainage ‘up’ shear zones and along larger scale fluid pressure gradients in the crust.     

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.