Layers Of Constant Density Research Articles

Extent and Magnitude of Subsurface Anomalies During the Northeast Pacific Blob as Measured by Animal‐Borne Sensors

AbstractMarine heatwaves (MHWs) are prolonged warm water events that are increasing in frequency and magnitude due to rising global temperatures. The Northeast Pacific Blob was an unusually widespread MHW that affected ecosystems across the Northeast Pacific, from producers to top predators. Temperature and salinity data collected by northern elephant seals (Mirounga angustirostris) from 2014 to 2017 show significant (>2 sd) warm anomalies throughout the top 1,000 m of the water column, with peak warming in late 2015. Using temperature and salinity as a tracer of layers of constant density, we looked at how lateral advection may have contributed to the development of the Blob. Temperature and salinity anomalies and the expansion of the water column at the base of the pycnocline both indicate that northward advection of warm, salty water played an important role in the observed accumulation of warm water, in addition to surface warming. These findings contribute to our understanding of the physical dynamics of the Blob, especially the thermal content and structure of the water column, and offer mechanisms for its formation and maintenance, which are crucial to assessing the ecological effects of MHWs now and in the future.

Regularized gradient algorithms for solving the nonlinear gravimetry problem for the multilayered medium

We present new numerical algorithms for solving the structural inverse gravimetry problem for the case of multiple surfaces. The inverse problem of finding the multiple surfaces that divide the constant density layers is an ill‐posed one described by a nonlinear integral equation of the first kind. To solve it, it is necessary to apply the regularization ideas. The new regularized variants of the gradient type methods with the weighting factors are constructed, namely, the steepest descent and conjugate gradient method. We suggest the empirical rule for choosing the regularization parameters. On the basis of the constructed methods, we elaborate the parallel algorithms and implement them in the multicore CPU using the OpenMP technology. A set of experiments with the disturbed data is performed to test the gradient algorithms and study performance of the developed code. For the test problems with quasi‐real data, these new regularized algorithms increase the accuracy and speed up computation in comparison with the unregularized ones. By using the 8‐core CPU, we achieve the speedup of 8 times.

Formation, Detection, and Modeling of Submerged Oil: A Review

Submerged oil, oil in the water column (neither at the surface nor on the bottom), was found in the form of oil droplet layers in the mid depths between 900–1300 m in the Gulf of Mexico during and following the Deepwater Horizon oil spill. The subsurface peeling layers of submerged oil droplets were released from the well blowout plume and moved along constant density layers (also known as isopycnals) in the ocean. The submerged oil layers were a challenge to locate during the oil spill response. To better understand and find submerged oil layers, we review the mechanisms of submerged oil formation, along with detection methods and modeling techniques. The principle formation mechanisms under stratified and cross-current conditions and the concepts for determining the depths of the submerged oil layers are reviewed. Real-time in situ detection methods and various sensors were used to reveal submerged oil characteristics, e.g., colored dissolved organic matter and dissolved oxygen levels. Models are used to locate and to predict the trajectories and concentrations of submerged oil. These include deterministic models based on hydrodynamical theory, and probabilistic models exploiting statistical theory. The theoretical foundations, model inputs and the applicability of these models during the Deepwater Horizon oil spill are reviewed, including the pros and cons of these two types of models. Deterministic models provide a comprehensive prediction on the concentrations of the submerged oil and may be calibrated using the field data. Probabilistic models utilize the field observations but only provide the relative concentrations of the submerged oil and potential future locations. We find that the combination of a probabilistic integration of real-time detection with trajectory model output appears to be a promising approach to support emergency response efforts in locating and tracking submerged oil in the field.

Application of the transfer matrix approximation for wave propagation in a metafluid representing an acoustic black hole duct termination

The transfer matrix method has been proposed to analyze the acoustic black hole effect in duct terminations. The latter is achieved by placing a retarding waveguide structure inside the duct, which consists in a set of rings whose inner radii decrease to zero following a power law. The rings are separated by thin air cavities. If the number of ring-cavity ensembles is large enough, wave propagation inside the waveguide can be treated as a continuous problem. A governing differential equation can be derived for the acoustic black hole which intrinsically relies on assumptions from transfer matrix theory. However, no formal demonstration exists showing that the transfer matrix solution is consistent and formally tends to the solution of the continuous problem. Proving such consistency is the main goal of the paper and an original option has been adopted to this purpose. First, we prove the differential equation for the acoustic black hole is identical to the wave equation for a metafluid with a power-law varying density. Transfer matrices are then applied to solve wave propagation in a discretization of the metafluid into layers of constant density. It is shown that when the number of layers tends to infinity and their thicknesses to zero, the transfer matrix solution satisfies the metafluid equation and therefore the acoustic black hole one. The transfer matrices for the metafluid discrete layers take a particularly simple form, which is a great advantage. This work allows one to interpret the retarding waveguide structure as a particular realization of the metafluid.

Decoherence in neutrino propagation through matter, and bounds from IceCube/DeepCore

We revisit neutrino oscillations in matter considering the open quantum system framework, which allows to introduce possible decoherence effects generated by New Physics in a phenomenological manner. We assume that the decoherence parameters gamma _{ij} may depend on the neutrino energy, as gamma _{ij}=gamma _{ij}^{0}(E/text {GeV})^n (n = 0,pm 1,pm 2) . The case of non-uniform matter is studied in detail and, in particular, we develop a consistent formalism to study the non-adiabatic case dividing the matter profile into an arbitrary number of layers of constant densities. This formalism is then applied to explore the sensitivity of IceCube and DeepCore to this type of effects. Our study is the first atmospheric neutrino analysis where a consistent treatment of the matter effects in the three-neutrino case is performed in presence of decoherence. We show that matter effects are indeed extremely relevant in this context. We find that IceCube is able to considerably improve over current bounds in the solar sector (gamma _{21}) and in the atmospheric sector (gamma _{31} and gamma _{32}) for n=0,1,2 and, in particular, by several orders of magnitude (between 3 and 9) for the n=1,2 cases. For n=0 we find gamma _{32},gamma _{31}< 4.0times 10^{-24}, (1.3times 10^{-24}) hbox {GeV} and gamma _{21}<1.3times 10^{-24}, (4.1times 10^{-24}) hbox {GeV} at the 95% CL, for normal (inverted) mass ordering.

Comments on avalanche flow models based on the concept of random kinetic energy

ABSTRACTIn a series of papers, Bartelt and co-workers developed novel snow-avalanche models in which random kinetic energy (RKE) RK (a.k.a. granular temperature) is a key concept. The earliest models were for a single, constant density layer, using a Voellmy model but with RK-dependent friction parameters. This was then extended to variable density, and finally a suspension layer (powder-snow cloud) was added. The physical basis and mathematical formulation of these models are critically reviewed here, with the following main findings: (i) Key assumptions in the original RKE model differ substantially from established results on dense granular flows; in particular, the effective friction coefficient decreases to zero with velocity in the RKE model. (ii) In the variable-density model, non-canonical interpretation of the energy balance leads to a third-order evolution equation for the flow depth or density, whereas the stated assumptions imply a first-order equation. (iii) The model for the suspension layer neglects gravity and disregards well-established theoretical and experimental results on particulate gravity currents. Some options for improving these aspects are discussed.

Propagation of converging spherical deformation waves in a heteromodular elastic medium

The unsteady one-dimensional boundary-value problem of shock deformation of a medium bounded by a sphere is solved. The propagation of converging deformation wave fronts in an elastic material with different tensile and compressive strengths is studied. A boundary condition is obtained that provides the formation of a converging spherical shock wave with constant velocity. The impact conditions on the boundary of the heteromodular sphere are determined that can lead to the formation of a transition zone (a spherical layer of constant density) between the compression and tension regions.

The existence and stability of generalized planar central configurations of the trapezoidal type with a non-spherical body at their centre

The existence of trapezoidal planar central configurations (CCs) without a central body and with a spherical central body (the classic case), and also with a central body in the form of an ellipsoid, either homogeneous or inhomogeneous but consisting of ellipsoidal layers of constant density (generalized cases), is demonstrated. It is shown that such CCs exist in a heliocentric system of coordinates with mutually perpendicular diagonals of the trapezia, at the vertices of which the remaining bodies are positioned. The stability of the generalized trapezoidal planar CCs is investigated. It is established that most versions of such CCs do not possess Lyapunov stability.

Tropical cyclone footprint in the ocean mixed layer observed by Argo in the Northwest Pacific

This study systematically investigated the ocean mixed layer responses to tropical cyclone (TC) using available Argo profiles during the period of 1998–2011 in the northwest Pacific. Results reveal that isothermal layer (IL) deepening and isothermal layer (IL) cooling with evident rightward biases induced by strong TCs are clearer compared to the weak TCs. Likewise, the rightward biases of IL deepening and cooling induced by fast TCs are more obvious than that induced by slow TCs. The upwelling within TC's eye is much stronger for the strong (slow) TCs than weak (fast) TCs. For the strong and slow TCs, the TC-induced rainfall reduces deepening of constant density layer (with its depth called the mixed layer depth, MLD), and in turn increases the barrier layer thickness (BLT). The initial BL prior to TC can restrict IL cooling more markedly under the weak and fast TCs than under the strong and slow TCs. The inertial oscillation is stronger induced by the strong (fast) TCs than by the weak (slow) TCs. In addition, the most pronounced TC-induced mixed layer deepening and IL cooling in July to October climatology occur in the subtropical gyre of the northwest Pacific with enhanced vertical diffusivity. The maximum increase of isothermal layer depth (ILD) and MLD is up to 5 m, with IL cooling up to 0.4°C.

Numerical study of interfacial solitary waves propagating under an elastic sheet.

Steady solitary and generalized solitary waves of a two-fluid problem where the upper layer is under a flexible elastic sheet are considered as a model for internal waves under an ice-covered ocean. The fluid consists of two layers of constant densities, separated by an interface. The elastic sheet resists bending forces and is mathematically described by a fully nonlinear thin shell model. Fully localized solitary waves are computed via a boundary integral method. Progression along the various branches of solutions shows that barotropic (i.e. surface modes) wave-packet solitary wave branches end with the free surface approaching the interface. On the other hand, the limiting configurations of long baroclinic (i.e. internal) solitary waves are characterized by an infinite broadening in the horizontal direction. Baroclinic wave-packet modes also exist for a large range of amplitudes and generalized solitary waves are computed in a case of a long internal mode in resonance with surface modes. In contrast to the pure gravity case (i.e without an elastic cover), these generalized solitary waves exhibit new Wilton-ripple-like periodic trains in the far field.

The collocation approach to Moho estimate

&lt;p&gt;In this paper, the collocation approach to Moho estimate is presented. This method is applied to the inversion of gravity data that can be complemented by Moho depth information coming from e.g. seismic information. In this context, a two layers model is considered and discussed in order to give a general theoretical framework for the inversion method. A body with two inner constant density layers and an inner separation surface between is considered and a uniqueness theorem is proved for the estimability of the separation surface given the gravity outside the body itself. Based on this result, a discussion is given on the estimation of the Moho depths based on terrestrial gravity observations. The observation equation is presented and its local planar approximation is derived. The application of the collocation method to the estimate of Moho depths is then studied and discussed in relationship to the planar observation equation. Also, numerical tests are presented. To this aim, the collocation inversion algorithm is implemented and tested on simulated data to prove its effectiveness. The results show that the proposed method is reliable provided that proper data reductions for model discrepancies are taken into account.&lt;/p&gt;

Evaluation of an improved intermediate complexity snow scheme in the ORCHIDEE land surface model

Snow plays an important role in land surface models (LSM) for climate and model applied over Fran studies, but its current treatment as a single layer of constant density and thermal conductivity in ORCHIDEE (Organizing Carbon and Hydrology in Dynamic Ecosystems) induces significant deficiencies. The intermediate complexity snow scheme ISBA‐ES (Interaction between Soil, Biosphere and Atmosphere‐Explicit Snow) that includes key snow processes has been adapted and implemented into ORCHIDEE, referred to here as ORCHIDEE‐ES. In this study, the adapted scheme is evaluated against the observations from the alpine site Col de Porte (CDP) with a continuous 18 year data set and from sites distributed in northern Eurasia. At CDP, the comparisons of snow depth, snow water equivalent, surface temperature, snow albedo, and snowmelt runoff reveal that the improved scheme in ORCHIDEE is capable of simulating the internal snow processes better than the original one. Preliminary sensitivity tests indicate that snow albedo parameterization is the main cause for the large difference in snow‐related variables but not for soil temperature simulated by the two models. The ability of the ORCHIDEE‐ES to better simulate snow thermal conductivity mainly results in differences in soil temperatures. These are confirmed by performing sensitivity analysis of ORCHIDEE‐ES parameters using the Morris method. These features can enable us to more realistically investigate interactions between snow and soil thermal regimes (and related soil carbon decomposition). When the two models are compared over sites located in northern Eurasia from 1979 to 1993, snow‐related variables and 20 cm soil temperature are better reproduced by ORCHIDEE‐ES than ORCHIDEE, revealing a more accurate representation of spatio‐temporal variability.

Maximum angle method for determining mixed layer depth from seaglider data

A new maximum angle method has been developed to determine surface mixed-layer (a general name for isothermal/constant-density layer) depth from profile data. It has three steps: (1) fitting the profile data with a first vector (pointing downward) from an upper level to a depth and a second vector (pointing downward) from that depth to a deeper level; (2) identifying the angle (varying with depth) between the two vectors; (3) after fitting and calculating angle all depths, and then selecting the depth with maximum angle as the mixed layer depth (MLD). Temperature and potential density profiles collected from two seagliders in the Gulf Stream near the Florida coast during 14 November–5 December 2007 were used to demonstrate the method’s capability. The quality index (1.0 for perfect identification of the MLD) of the maximum angle method is about 0.96. The isothermal layer depth is generally larger than the constant-density layer depth, i.e., the barrier layer occurs during the study period. Comparison with the existing difference, gradient, and curvature criteria shows the advantage of using the maximum angle method. Uncertainty in determining MLD because of varying threshold using the difference method is also presented.

A numerical model for simulation of fluid mud with different rheological behaviors

In this paper, a three-dimensional isopycnal approach is presented to simulate the dynamics of fluid mud covering the formation, development, transport, and disappearance of fluid mud. The basic assumption is the assignment of the fluid’s density as the indicating parameter for the rheological behavior. Considering stable stratification, as is usually the case for fluid mud, layers of constant density discretize the vertical domain. The non-Newtonian dynamics of fluid mud is simulated by solving the Cauchy equations for general continuum dynamics. Instead of using a turbulent viscosity approach, the viscosity is allowed to vary according to the rheological behavior of mud suspensions. This apparent viscosity can be determined for different rheological formulations in dependence of the volume solid fraction and the shear rate. An existing three-dimensional isopycnal hydrodynamic model was extended for vertical mass transport processes and was applied on a schematic system with hindered settling. For including the rheological behavior of fluid mud, the Worrall–Tuliani approach was parameterized and implemented. The resulting flow behavior is shown on a model application of fluid mud layers moving down an inclined plane. With these changes, it is demonstrated that the isopycnal model is capable of simulating fluid mud dynamics.

Steady flow of a buoyant plume into a constant-density layer

The upward flow of a buoyant plume emanating from a horizontal fissure into a two-layered fluid region is considered. Solutions are computed numerically for a range of fissure widths and water depths. It is shown that for a given fluid depth and fissure size there is a minimum flow rate beneath which no steady solutions exist. At this limiting flow, the fluid detaches from the wall of the fissure via a stagnation point. Solutions exist for all values of flow rate above this minimum. Exact solutions are presented for very large flow rates.

Static and flowing regions in granular collapses down channels: Insights from a sedimenting shallow water model

A two layer model for the collapse and spreading of a granular column is presented. This model builds upon that of Larrieu et al. [J. Fluid Mech. 554, 669 (2006)] where the free fall collapse of the column and subsequent flow of material onto a plane is represented by a “raining” mass source term into a thin flowing layer of constant density. These modified shallow water equations with Coulomb friction capture the free surface of the flows and key scaling laws for initial sand columns of aspect ratios up to a&amp;lt;10. However, unrealistically high coefficients of friction of μ=0.9 are required to reproduce run-outs observed. Key scaling laws for high aspect ratio columns are also not captured. We thus extend the model of Larrieu (2006) to include an estimation for the interface between the static and flowing regions observed within granular collapses in the laboratory by Lube et al. [Phys. Fluids 19, 043301 (2007)]. An empirical sedimentation term Ls and the instantaneous removal of a static deposit wedge, seen in the laboratory, are incorporated into the “raining” shallow water model. The growing static deposit surface provides a basal topography for the flowing layer. For a constant empirical sedimentation rate of Ls=0.20m∕s, a coefficient of friction of μ=0.4 simulates comparable run-outs to laboratory observations. The correct run-out dependence of a2∕3 for columns of aspect ratio a&amp;gt;3 is also captured. Simulating this behavior for values of a above 10 has not been possible with previous continuum models. In addition, this model captures the correct dependence of final run-out time upon a0.5. The application of this extends beyond observed and simulated collapses, to sedimenting highly concentrated debris flows, useful in the development of large mechanistic numerical models utilized in hazard assessment.

Guided modes in a plane elastic layer with gradually continuous acoustic properties

A theoretical study of wave propagation through an inhomogeneous plane infinite elastic layer of constant density whose velocities vary continuously with the depth is presented. If the shear speed gradient effects are to be modelled, then the simple Helmholtz representation of the displacement field cannot be used; however, for high frequencies, the longitudinal and transversal wave equations are decoupled. The study is conducted for two symmetrical velocity profiles for which the wave equations have exact solutions. The effect of the relative amplitude of gradients on the position of cutoff-frequencies of guided modes existing in the structure is examined. The numerical results show a shift of cutoff-frequencies compared to those of the homogeneous layer.

A simple analytic three-flavour description of the day-night effect in the solar neutrino flux

In the 3-flavour framework we derive a simple approximate analytic expression for the day-night difference of the flux of solar $\nu_e$ at terrestrial detectors which is valid for an arbitrary Earth density profile. Our formula has the accuracy of a few per cent and reproduces all the known analytic expressions for the Earth matter effects on the solar neutrino oscillations obtained under simplifying assumptions about the Earth's density profile (matter of constant density, 3 layers of constant densities, and adiabatic approximation). It can also be used for studying the Earth matter effects on the oscillations of supernova neutrinos. We also discuss the possibility of probing the leptonic mixing angle $\theta_{13}$ through day--night asymmetry measurements at future water Cherenkov solar neutrino detectors. We show that, depending on the measured value of the asymmetry, the current upper bound on $\theta_{13}$ may be improved, or even a lower bound on this mixing parameter may be obtained.

Sediment thickness and crustal structure of offshore western New Zealand from 3D gravity modelling

3D modelling of satellite gravity data covering the offshore area west of New Zealand has been used to predict the depth to the seafloor, basement, and Moho. The models assume constant densities for each layer, with no lateral changes of rock properties. The modelling was done on a 2.5 km grid. Depths to the seafloor, basement, and Moho were interpreted from seismic data or taken from published sources, and were used to constrain the solutions. Where control points are available, the models generally match the interpreted depths to within the expected level of accuracy. Basement depth is underestimated in the deeper parts of the basin. This is due to the assumption of constant density layers. Use of a more appropriate density/depth function would have resulted in a better match with the interpreted depths. The modelling highlights Cretaceous rift structures along the margins of the Challenger Plateau, Lord Howe Rise, and West Norfolk Ridge. Horsts and graben oriented parallel to the Challenger Plateau and Lord Howe Rise margin formed prior to seafloor spreading in the Tasman Sea. They are typically 10–20 km across and 1–2 km deep. The northwest‐southeast trend is interrupted by north‐south‐trending faults associated with a later phase of subsidence in the Bellona Trough. The basement structure of the West Norfolk Ridge extends to the southwest as a buried series of horsts and graben which separate sedimentary basins in Northland and the New Caledonia Basin. The sediment thickness predicted by the models in the New Caledonia Basin is thinner than that interpreted on seismic sections, emphasising the importance of using density gradients in models of deep sedimentary basins. The modelled depth to Moho is c. 13 km in the Tasman Sea and 25 km beneath the Challenger Plateau. Crustal thinning of c. 30% is predicted for the Bellona Trough, New Caledonia Basin, and Lord Howe Basin.

Neutrinooscillations in matter of varying density

We consider two-family neutrino oscillations in a mediumof continuously varying density as a limit of the processin a series of constant-density layers. We find a formfor the transition amplitudes that could provide newanalytic solutions or could serve asnumerical solutions. We test our approach withconstructive analytic expressions for the conversionamplitude at high energies within a medium with a densityprofile that is piecewise linear. We also shed somelight on effects that depend on the order of the materialtraversed by a neutrino beam.