Planetons: An example of large amplitude solitary waves

Abstract

The term ‘‘solitary wave'’ is usually used to denote a steadily propagating permanent form solution of a nonlinear wave equation, with the permanency arising from a balance between steepening and dispersive tendencies. It is known that large-scale thermal anomalies in the ocean are subject to a steepening mechanism driven by the beta effect, while at the smaller deformation scale, such phenomena are highly dispersive. It is shown here that the evolution of a physical system subject to both effects is governed by the ‘‘frontal semi-geostrophic equation'’ (FSGE), which is valid for large amplitude thermocline disturbances. Solitary wave solutions of the FSGE (here named planetons) are calculated and their properties are described with a view towards examining the behavior of finite amplitude solitary waves. In contrast, most known solitary wave solutions belong to weakly nonlinear wave equations (e.g., the Korteweg—deVries (KdV) equation).

The FSGE is shown to reduce to the KdV equation at small amplitudes. Classical sech² solitons thus represent a limiting class of solutions to the FSGE. The primary new effect on planetons at finite amplitudes is nonlinear dispersion. It is argued that due to this effect the propagation rates of finite amplitude planetons differ significantly from the ‘‘weak planeton'', or KdV, dispersion relation. Planeton structure is found to be simple and reminiscent of KdV solitons. Numerical evidence is presented which suggests that collisions between finite amplitude solitary waves are weakly inelastic, indicating the loss of true soliton behavior of the FSGE at moderate amplitudes. Lastly, the sensitivity of solitary waves to the existence of a nontrivial far field is demonstrated and the role of this analysis in the interpretation of lab experiments and the evolution of the thermocline is discussed.     

Characterization of seafloor pockmark seepage of hydrocarbons employing fractal: A case study from the western continental margin of India

Here we apply quantitative technique to describe the seafloor seepages based on the multi-beam backscatter and bathymetric investigations to characterize the pockmark morphology. The variable seafloor backscatter strength for coarser seafloor sediments are related to the diagenesis derived from biodegraded seepages. In this regard, box counting method is used to estimate ‘fractal dimension’ for backscatter imagery data of 398 blocks. These blocks are further sub-grouped into six classes depending on the spread of pockmark related seepages. The study area lies 102 km west off Marmagao along the central west coast of India which contains pre-dominantly (70%) gas-charged sediments. Comparison between the estimated self-similar fractals reveals that there is approximately 97% correlation between the box (D_box) and information (D_info) dimensions. Box dimension–derived fractal dimension values, suggest that the seepages are more along the fault trace in deeper waters, in comparison to sparsely distributed shallow water seepages. Besides, this poor seepage is confined within the smooth to moderately rough seafloor. It is established that the high backscatter strength along the upper slope of the pockmark region having higher fractal dimensions reflects multifractal behavior of seepage distribution. Entire area indicates patchy seepage patterns as supported by estimated fractal values showing intermittent fluctuations, which emphasizes non-linear behavior. Estimated self organizing criticality (SOC) parameters for six representative blocks reveal that the nature of pockmark, fault trace, sediment nature coupled with slumping of pockmark’s wall, sediment movement due to bottom currents are controlling the dynamic balance in the area seepage system. Further, our study emphasizing the multifractal behavior of seepage blocks, clearly depicts the drift in the seepage pattern.     

Detrital zircon geochronology of Palaeozoic Novaya Zemlya – a key to understanding the basement of the Barents Shelf

The Novaya Zemlya fold‐and‐thrust‐belt is the northern continuation of the late Palaeozoic Uralide Orogen. Little is known about its deeper structure and the basement history of the adjacent Barents and Kara shelves. Based on geological evidence and detrital zircon analysis of 28 samples from the northeastern and stratigraphically deepest part of the archipelago, we demonstrate that Cambro‐Ordovician turbidite‐dominated deposition was almost exclusively sourced from rocks consolidated during the Timanian orogeny (Timanian basement). A profound change in provenance occurred near the end of the Ordovician. Over 90% of the zircons from Silurian and about 80% from Devonian strata have ages characteristic of the Sveconorwegian Orogen, implying uplift of these rocks in the vicinity of Novaya Zemlya. The presence of Sveconorwegian and Grenvillian rocks in the high Arctic suggests revision of recent reconstructions of the Rodinia supercontinent, its break‐up and subsequent Caledonian orogeny.     

Salinity stratification in a river-dominated estuary

Analysis of salinity data from Mobile Bay indicates that stratification-destratification events within this broad, shallow estuary are not uncommon. These events are related to the strength of the winds, through their influence on wave generation and subsequent bottom drag coefficient increases, and to the strength of river discharge. They do not appear to be due to the strength of tidal currents, as has been observed elsewhere. Furthermore, river flow appears to be the dominant control, the winds being important only in the absence of large freshwater discharges. The annual spring freshet can flush most of the salt from the bay. During other times of the year the relative strengths of river discharge and wind stress change the bay from highly stratified to nearly homogeneous and back on a variety of time scales ranging from daily to seasonal.     

Nutrient exchanges between the water column and a subtidal benthic microalgal community

Exchanges of nutrients between a shallow (ca. 1 m) nodiment and the water column were measured in the York River, Virginia, during 1983, using transparent and opaque plexiglass hemispheres. Exchanges of nitrate and phosphate were not significantly different between dome treatments, but ammonium release was significantly reduced within the transparent domes. Within the dark domes, ranges of hourly rates of ammonium and phosphate exchange were 21 to 364 μmol N m² and 3 to 76 μmol P m² while those in the transparent domes were ?162 to 244 and 6 to 80, respectively. Negative values denote uptake by the sediment. Nitrate 1 nitrite exchanges averaged only 15% and 17% of the total dissolved luorganle nitrogen exchange in the dark and transparent domes, respectively.     

The use of7LiOH-impregnated filters for the collection of acidic gases and analysis by instrumental neutron activation analysis

A simple system was designed using⁷LiOH-impregnated filters to collect acidic gases from ambient air and from highly concentrated volcanic plumes or gas streams. These filters were developed for analysis using instrumental neutron activation analysis, but other analytical techniques could be used as well. The sampling system was designed to use a series of 1–3 M⁷LiOH-impregnated filters to collect high concentrations of acidic gases found in gas plumes of active volcanoes. The filters are quantitative for SO₂ and the halide acids when sufficient base is present to neutralize the acidic species. Extremely high concentrations of SO₂ may not be collected quantitatively since SO₂ is a relatively weak Lewis acid compared to the halide acids. The acidic oxides of Sb, As, and Se were also collected quantitatively. A particle filter preceded the impregnated filters in order to remove particles from the fumes. This system has proven effective under difficult sampling conditions and, since it is portable and light weight, it could be used for many volcanological applications where high levels of acidic gaseous phase species need to be collected.     

The surface of labradorite feldspar after acid hydrolysis

After reaction with a pH < 4, the surface of labradorite is extensively enriched in Si and H, and depleted in Al, Ca and Na relative to an unreacted crystal. However, the amount of hydrogen measured in the reacted surface is less than that predicted on the basis of exchange of hydrogen (or hydronium) ions for cations in the feldspar. By analogy with studies of silicate glass, this low concentration of hydrogen suggests that some silanol groups in the reacted surface repolymerize subsequent to ion-exchange and depolymerization reactions. The net result is a relatively porous, Si-rich leached layer which is amorphous to electron diffraction, and which allows rapid diffusion of unreactive solutes.

Both the surface area of the reacted feldspar and the porosity increase with acid hydrolysis. Modeling of nitrogen sorption onto the surface suggests that the pores have a nominal radius of 20–80 Å or less. This distribution of pore sizes resembles other acid-reacted silicate materials, such as glass, chrysotile and kaolinite. Although the mineral surface clearly becomes more porous during acid hydrolysis, the increase in powder area also does not coincide with an increase in the flux of dissolved Si from the powder. We thus attribute most of this increase in area to spallation of the silica-rich surface from the feldspar upon drying.     

31P solid-state nuclear magnetic resonance spectroscopy of aluminum phosphate minerals

This study examines the links between ³¹P solidstate NMR studies of aluminum phosphate minerals and their crystallographic structures. We found that ³¹P isotropic chemical shift values, _iso, carry little information about mineral structures. There seems to be no relation between the chemical shift anisotropy, =₃₃–₁₁ (₃₃>₂₂> ₁₁), and indicies of phosphate-tetrahedra distortion. ³¹P¹H heteronuclear magnetic dipole interactions, on the other hand, carry important information about hydrous phosphate mineral structures, information that should prove to be quite valuable in studies of phosphate adsorbed on mineral surfaces. This interaction can be measured through a variety of qualitative and quantitative experiments. It appears that spin diffusion is so rapid that subtle differences in hydrogen-bonding environments cannot be resolved.     

One-dimensional baroclinically unstable waves on the Gulf Stream potential vorticity gradient near Cape Hatteras

Application of linear baroclinic instability theory to the observed distributions of velocity, stratification, and potential vorticity in the Gulf Stream near 74° W is successful in predicting the time and length scales of the most rapidly growing disturbances. A continuously-stratified, one-dimensional model with realistic bottom slope predicts propagation speeds of 10–50 cm s⁻¹ associated with two regimes of rapid temporal growth centered at periods of 28 days and 5–7 days. This prediction is consistent with observations of the propagation and growth of Gulf Stream meanders derived from inverted echo sounder measurements in this region. The instability model also predicts that for realistic bottom slopes the baroclinic energy transfer should be weakly negative (eddy-to-mean) in deep water, but for low-frequency waves should change to significant positive (mean-to-eddy) transfer above depths of 1500 m, consistent with observations.