Nonlinear dynamics of long-wave perturbations of the Kolmogorov flow for large Reynolds numbers

The nonlinear dynamics of long-wave perturbations of the inviscid Kolmogorov flow, which models periodically varying in the horizontal direction oceanic currents, is studied. To describe this dynamics, the Galerkin method with basis functions representing the first three terms in the expansion of spatially periodic perturbations in the trigonometric series is used. The orthogonality conditions for these functions formulate a nonlinear system of partial differential equations for the expansion coefficients. Based on the asymptotic solutions of this system, a linear, quasilinear, and nonlinear stage of perturbation dynamics is identified. It is shown that the time-dependent growth of perturbations during the first two stages is succeeded by the stage of stable nonlinear oscillations. The corresponding oscillations are described by the oscillator equation containing a cubic nonlinearity, which is integrated in terms of elliptic functions. An analytical formula for the period of oscillations is obtained, which determines its dependence on the amplitude of the initial perturbation. Structural features of the field of the stream function of the perturbed flow are described, associated with the formation of closed vortex cells and meandering flow between them. As a supplement, an asymptotic analysis of nonlinear dynamics of long-wave perturbations superimposed on a damped by small viscosity Kolmogorov flow (very large, but finite Reynolds numbers) is made. It is strictly shown that all velocity components of the perturbed flow remain bounded in this case.     

A weakly nonlinear stability of centrally symmetric magnetohydrodynamic systems to perturbations involving large scales

The problem of weakly nonlinear stability of 3-D centrally symmetric magnetohydrodynamic systems to perturbations involving large scales is considered. It is assumed that large space-time scales are absent in the magnetohydrodynamic state under study, which is stable with respect to perturbations whose scales are as small as those of the state itself. Equations derived by asymptotic methods for average fields of perturbations generalize the Navier-Stokes and magnetic induction equations. They include a combined eddy diffusion operator, generally anisotropic and not necessarily negative definite, and additional quadratic terms. An effective method is proposed for the calculation of coefficients of eddy diffusion and advection in equations governing average fields.     

Stalagmite growth perturbations from the Kumaun Himalaya as potential earthquake recorders

The central part of the Himalaya (Kumaun and Garhwal Provinces of India) is noted for its prolonged seismic quiescence, and therefore, developing a longer-term time series of past earthquakes to understand their recurrence pattern in this segment assumes importance. In addition to direct observations of offsets in stratigraphic exposures or other proxies like paleoliquefaction, deformation preserved within stalagmites (speleothems) in karst system can be analyzed to obtain continuous millennial scale time series of earthquakes. The Central Indian Himalaya hosts natural caves between major active thrusts forming potential storehouses for paleoseismological records. Here, we present results from the limestone caves in the Kumaun Himalaya and discuss the implications of growth perturbations identified in the stalagmites as possible earthquake recorders. This article focuses on three stalagmites from the Dharamjali Cave located in the eastern Kumaun Himalaya, although two other caves, one of them located in the foothills, were also examined for their suitability. The growth anomalies in stalagmites include abrupt tilting or rotation of growth axes, growth termination, and breakage followed by regrowth. The U-Th age data from three specimens allow us to constrain the intervals of growth anomalies, and these were dated at 4273?±?410 years BP (2673–1853 BC), 2782?±?79 years BP (851–693 BC), 2498?±?117 years BP (605–371 BC), 1503?±?245 years BP (262–752 AD), 1346?±?101 years BP (563–765 AD), and 687?±?147 years BP (1176–1470 AD). The dates may correspond to the timings of major/great earthquakes in the region and the youngest event (1176–1470 AD) shows chronological correspondence with either one of the great medieval earthquakes (1050–1250 and 1259–1433 AD) evident from trench excavations across the Himalayan Frontal Thrust.     

Impact-induced perturbations of atmospheric sulfur

Asteroids and comets that are vaporized during hypervelocity impact events can inject large masses of S into the stratosphere where it can potentially affect the radiation budget of the Earth, alter the chemistry of the ozone layer, and eventually be converted to sulfuric acid rain. Relatively small carbonaceous asteroids, 0.3 km in diameter, contain 5 times more S than the entire modern stratosphere and these objects hit the Earth at an average rate of 1 per 10,000 years. Larger impact events, capable of injecting 10¹⁵ g of S into the stratosphere, occur at an average rate of 1 per 1 million years. Calculations indicate there is sufficient O and H in the vapor plumes of most impact events to convert the S to sulfuric acid aerosols. If this conversion occurs, then the larger impact events could depress mean surface temperatures by more than 2°C for 3 years or longer.     

A determination of the hydromagnetic waves polarization from their perturbations on the terminator

The influence of the homogeneous and inhomogeneous ionosphere on the orientation angle of the horizontal magnetic vectors of the long-time geomagnetic pulsations is under consideration in this study. It was realized that this angle is small in the case of the homogeneous ionosphere for both the Alfvén and magnetosonic types of oscillations. An increase in the ionospheric electric field was discovered as the ionospheric conductivity changes during the switch from day to night conditions. It is valid only for the initial Alfvén wave. The ionospheric equivalent current systems excited by the initial magnetospheric waves of Alfvén and magnetosonic types as well as their behavior near the terminator were studied for different seasons. For the Alfvén source, seasonal variations of the orientation angle close to sunrise at the equator depend on the type of source: odd or even modes of Alfvén oscillations excite observable pulsations. It was found that the ionospheric two-vortex equivalent current system of the long-period pulsations arising in high-latitudes in the equatorial region alters not only its direction, but its intensity too. The largest anomaly (\sim25% of the source value) would be expected near the terminator. A new experimental method was suggested to recognize the type of incident magnetospheric waves by implementing observations either at a single observatory or at a couple of observatories. In the case of a single observatory it is proposed to study the frequency dependence of the orientation angle of their magnetic components close to sunrise. If the initial wave is magnetosonic, this angle must not be changed as a function of the local time within the wide frequency range of pulsations. When pulsations have an orientation angle sensitive to the presence of the terminator, they may be classified as both Alfvén and magnetosonic. For the Alfvén waves no frequency dependence of the orientational angle is peculiar. On the contrary, magnetosonic waves should be determined as oscillations with an orientational angle proportional to the frequency. These oscillations may be revealed at observatories located on the high-resistance cross sections. The example of the spectral-temporal analysis of pulsation at the equatorial observatory in Huancayo was demonstrated to confirm the proposed experimental technique. A weak dependence of the orientation angle anomaly on the frequency near the terminator was found. The latter is evidence for the dominant contribution of the Alfvén waves to low-latitude and equatorial oscillations.     

Using data-derived perturbations to incorporate uncertainty in generating stochastic areal rainfall from point rainfall

Abstract

Raingauge measurements are commonly used to estimate daily areal rainfall for catchment modelling. The variation of rainfall between the gauges is usually inadequately captured and areal rainfall estimates are therefore very uncertain. A method of quantifying these uncertainties and incorporating them into ensembles of areal rainfall is demonstrated and tested. The uncertainties are imposed as perturbations based on the differences in areal rainfall that result when half of the raingauges are alternately omitted. Also included is a method of: (a) estimating the proportion rainfall that falls on areas where no gauges are located that are consequently computed as having zero rain, and (b) replacing them with plausible non-zero rainfalls. The model is tested using daily rainfall from two South African catchments and is found to exhibit the expected behaviour. One of the two parameters of the model is obtained from the rainfall data, while the other has direct physical interpretation.

Editor D. Koutsoyiannis; Associate editor C. Onof

Citation Ndiritu, J., 2013. Using data-derived perturbations to incorporate uncertainty in generating stochastic areal rainfall from point rainfall. Hydrological Sciences Journal, 58 (8), 1704–1717.     

Diurnal and seasonal occurrence of polar patches

Analysis of the diurnal and seasonal variation of polar patches, as identified in two years of HF-radar data from Halley, Antarctica during a period near sunspot maximum, shows that there is a broad maximum in occurrence centred about magnetic noon, not local noon. There are minima in occurrence near midsummer and midwinter, with maxima in occurrence between equinox and winter. There are no significant correlations between the occurrence of polar patches and the corresponding hourly averages of the solar wind and IMF parameters, except that patches usually occur when the interplanetary magnetic field has a southward component. The results can be understood in terms of UT and seasonal differences in the plasma concentration being convected from the dayside ionosphere into the polar cap. In summer and winter the electron concentrations in the polar cap are high and low, respectively, but relatively unstructured. About equinox, a tongue of enhanced ionisation is convected into the polar cap; this tongue is then structured by the effects of the interplanetary magnetic field, but these Halley data cannot be used to separate the various competing mechanisms for patch formation. The observed diurnal and seasonal variation in the occurrence of polar patches are largely consistent with predictions of Sojka et al. (1994) when their results are translated into the southern hemisphere. However, the ionospheric effects of flux transfer events are still considered essential in their formation, a feature not yet included in the Sojka et al. model.     

Magnetic perturbations before the strong earthquakes

The search for the magnetic precursors of earthquakes by the method of synchronous detection is described. The data of the Guam Observatory (13.6°N, 144.9°E) located in a seismically active region and the USGS/NEIC catalogue of the National Earthquake Information Center of the U.S. Geological Survey for the period from 1991 to 2009 are used. Earthquakes with magnitudes M ≥ 7 in the range of longitudes from 100° to 170°E are analyzed. The intervals of accumulation cover 40 hours before and 40 hours after an earthquake. The preliminary result reveals an enhancement of fluctuations in the Z-component within 12 hours before the earthquake.     

Velocity analysis from large offset seismic records

One of the most important problems in applied geophysics is to extract velocities of compressional and shear waves, using the observed data collected at the Earth's surface or in boreholes. Unfortunately, in a typical seismic experiment, we do not have enough information to uniquely recover seismic velocities as functions ofx, y, andz. Thus, in the paper, a simplified model of the Earth (a stack of horizontal homogeneous layers) is considered and a critical discussion of modern techniques for processing reflection arrivals is presented.     

Evidence of tidal perturbations in the middle atmosphere over Southern Tropics as deduced from LIDAR data analyses

Systematic measurements of the middle-atmosphere temperature by a RAYLEIGH LIDAR located at La Réunion Island (20.8°S–55.5°E) has led to a preliminary study of the tidal effects in the height range of 30–70 km. Two analysis methods able to estimate the mean nighttime evolution of the temperature have been compared. Method 1 consists in averaging the temperature deviations from the nightly mean over several successive nights of measurement for given local solar times (LST); method 2 consists in averaging the raw data over the period of observation for given LST and in deriving afterwards the mean nighttime evolution of the temperature profiles. Some consistent LST-related structures have been observed with both methods, though better results have been obtained with method 1. One possible explanation for the differences between the two methods is the use of a series of data ranging from 4 to 8 h/night, depending on the meteorological conditions. In contrast to method 2, method 1 allows to correct the mean temperature for a given night, when the measurement window is different from night to night. Method 1 has been applied to two time series recorded in October and November 1995. The results clearly show the presence of tidal components with a downward phase propagation, specifically a warmer early night and a colder midnight in the stratosphere and the lower mesosphere. This behaviour is consistent with other LIDAR measurements made at similar latitudes in the Northern Hemisphere. In addition, a close comparison with the Global-Scale Wave Model (GSWM) tidal model predictions has also pointed out some similarities. Yet, large discrepancies in magnitude are also observed: as already reported in previous studies, the amplitudes predicted by GSWM are more than two times smaller compared to the corresponding values observed with the LIDAR.     

Mesospheric bore formation from large-scale gravity wave perturbations observed by collocated all-sky OH imager and sodium lidar

On 9 October 2007, long-horizontal-wavelength gravity waves were observed for the first time to steepen and form mesospheric bores at the altitude of ～87 km, by an all-sky OH imager located at Fort Collins (41°N, 105°W), Colorado. The collocated sodium lidar simultaneously observed the presence of a temperature inversion layer as the ducting region. One mesospheric bore uniquely later evolved into a large-amplitude soliton-like perturbation. When the gravity wave and the associated soliton-like perturbation passed through the lidar beams, the lidar detected strong vertical disturbance at 90 km, indicating convective instability. A large cold front system recorded several hours before in the troposphere was aligned to phase fronts of these large gravity waves. For all of the 7 mesospheric bores observed over a 5 year period, we found a similar alignment with a cold front 1000–1500 km away as the likely source of these large-scale gravity waves.     

Physical basis of earthquake magnitudes: an extreme value of seismic amplitudes from incoherent fracture of random fault patches

A relation between surface-wave magnitude M_s and fault area S for great earthquakes has been proposed

log S 2M_{s − 11.5 (}M_{s > 7.5)}

A similar formula has been also derived for body-wave magnitude m_b^* redetermined from maximum amplitudes of short-period P-wavetrains

log S ∝ 1.7 m_b^*

These are quite different from a theoretical relation expected on the basis of long-wave approximation. Because wavelengths of seismic waves used for the above magnitudes are very short compared to the size of earthquake sources, these relations represent the short-period nature of the earthquake process. The statistical theory of extreme values has been applied to understand the relations considering that the component waves which constitute the wavetrains for m_b^* and M_s determinations originate from the random fracture of fault heterogeneities.     

Magnitudes of large shallow earthquakes from 1904 to 1980

In order to obtain a uniform magnitude catalogue, surface-wave magnitudes M_s and broad-band body-wave magnitudes m_B have been determined for large shallow earthquakes from 1904 to 1980. In making the catalogue homogeneous, the author consistently adheres to the original definitions of M_s and m_B given by Gutenberg (1945) and Gutenberg and Richter (1956). The determinations of M_s and m_B are all based on the amplitude and period data listed in Gutenberg and Richter's unpublished notes, bulletins from stations worldwide, and other basic information. m_B is measured on broad-band instruments in periods of ～8 s. Consistency of the magnitude determinations from these different sources is carefully checked in detail. More than 900 shallow shocks of magnitude 7 and over are catalogued. The meaning of the magnitude scales in various catalogues is examined in terms of M_s and m_B. Most of the magnitudes listed by Gutenberg and Richter (1954) in their “Seismicity of the Earth” are basically M_s for large shocks shallower than 40 km, but are basically m_B for large shocks at depths of 40–60 km. The surface-wave magnitudes given by “Earthquake Data Reports” are higher than M_s by 0.2 unit whether the combined horizontal amplitude or the vertical amplitude is used. m_B and the currently used 1 s body-wave magnitude are measured at different periods and should not be directly compared.     

Length of phytoplankton species patches on the Southern California Shelf

Study of a longshore transect off Southern California suggests that the length scales (22 to 27 km) of phytoplankton species patches may be related to those of low-frequency currents. The patch boundaries were independent of shelf width but they were probably not independent of changes in chlorophyll fluorescence, temperature, and bottom topography.     

Fate of pioneering vegetation patches in a dynamic meandering river

Fluvial biomorphodynamics in actively meandering rivers entail interactions between hydromorphodynamics and pioneering tree species that have eco-engineering effects. Here we study spatiotemporal patterns of vegetation patches smaller than 150 m² in a 4 km reach of the river Allier in France in order to unravel causes for tree persistence and mortality and identify spatial trends across the river valley. To this end we analysed aerial photographs by object-based image analysis over a period of 56 years and tracked individual patches through time. Furthermore the cover and surface age of the study reach were classified. The large-scale shifts of channels, bars and vegetation are consistent with the meandering process and chute cutoffs. However, the spatiotemporal patterns of the vegetation patches are surprising in that they are ubiquitous and have ages up to decades on the highly dynamic meander belt, but hardly expand into larger vegetation patches. Patches disappear exponentially as a function of their age, and faster so in the last decades. Causes are amalgamation into the riparian forest flanking the meander belt and mortality likely due to desiccation or erosion. Patches have a higher probability of survival when further away from the active channel and closer to high vegetation patches and valley boundary. The window of opportunity of vegetation settlement widens towards the valley boundaries and in floodplain lows of former channels and chutes. These results imply a gradual cross-valley gradient of riparian vegetation settling, survival and succession. © 2019 The Authors. Earth Surface Processes and Landforms Published by John Wiley & Sons Ltd.     

Runoff response to multiple land-use changes and climate perturbations

Runoff response to multiple land-use changes and climate perturbations is distinct, and the main influencing factors vary significantly in different regions. However, few have simultaneously considered the effects of multiple land use changes (vegetation cover changes, terraces and check-dams construction, and urban expansion) and climatic perturbations (precipitation, potential evapotranspiration, and temperature) on runoff and constructed separate expressions for distinct study areas. This article attempted to determine the main influencing factors of runoff according to the fitting function in the eight subregions of the middle Yellow River (MYR), construct the expressions between the controlling parameter in the Budyko framework and the main factors, and quantify the contribution of climate factors and land use changes to runoff by combining the elasticity coefficient in each subregion. The results indicated that climate factors and land use changes could significantly impact controlling parameters, and there were differences between regions. Climate change promoted an increase in runoff, while land use change promoted its reduction, and the reduction value outweighed its increase. In terms of land use changes, increasing vegetation coverage could suppress runoff reduction, while constructing terraces and check-dams could promote its reduction. The urban expansion benefited runoff collection and, therefore, could suppress runoff reduction. Its absolute contribution rate exceeded 200% in apparent urban expansion areas. In addition, the contribution rates of land use to runoff changes in the northern arid and semi-arid regions were significantly higher than those in the southern, and they were more sensitive to land use changes. The research results can provide a reference for analysing the runoff response to different land-use changes and can further advance people's understanding of the water cycle.