Nonhydrostatic Components Research Articles

Pressure-induced optical anisotropy of HfS2

The effect of pressure on Raman scattering (RS) in bulk HfS2 is investigated under hydrostatic and non-hydrostatic pressure conditions. The RS line shape does not change significantly in the hydrostatic regime up to P = 9.6 GPa, showing a systematic blueshift of the spectral features. In a non-hydrostatic environment, seven peaks appear in the spectrum at P = 7 GPa, which dominate the RS line shape up to P = 10.5 GPa. The change in the RS line shape manifests a pressure-induced phase transition in HfS2. The simultaneous observation of both low-pressure (LP) and high-pressure (HP) related RS peaks suggests the coexistence of two different phases over a wide pressure range. It is found that the HP-related phase is metastable and persists during the decompression cycle down to P = 1.2 GPa, while the LP-related features eventually recover at even lower pressure. The angle-resolved polarized RS performed under P = 7.4 GPa revealed a strong in-plane anisotropy of both the LP-related A1g mode and the HP peaks. The anisotropy is related to the possible distortion of the structure induced by the non-hydrostatic component of the pressure. The results are explained in terms of a distorted Pnma phase as a possible pressure-induced phase of HfS2.

Numerical Investigation into the Performance of an OWC Device under Regular and Irregular Waves

A numerical investigation into the hydrodynamic efficiency of an oscillating water column (OWC) device for the production of energy from sea waves under the conditions of regular and irregular waves is proposed. The numerical simulations were carried out using a two-dimensional version of a recently published three-dimensional free-surface nonhydrostatic numerical model, which is based on a conservative form of the contravariant Navier–Stokes equations written for a moving co-ordinate system. The governing equations are spatially discretized by a finite volume shock-capturing scheme based on high-order wave-targeted essentially nonoscillatory reconstructions and an exact Riemann solver. Time discretization was performed by a predictor-corrector method that took into account the nonhydrostatic pressure component. The proposed numerical model allowed us to highlight the significant differences between the hydrodynamic efficiency obtained under irregular waves and those obtained under regular monochromatic waves and provides more realistic evaluations of the OWC device performances. The results of the above comparison showed a reduction in the hydrodynamic efficiency of the OWC from 0.78 to about 0.54 when passing from regular waves to the corresponding irregular ones. The model was applied to assess the potential energy production obtainable by a set of OWCs at the Cetraro harbor (southern Italy). The numerical results show that, by adopting the optimal dimensions of the OWC, the estimated mean annual energy production obtainable at the Cetraro harbor is equal to 1540.52 MWh, which corresponds to the energy production of about 10 wind turbines with a nominal power of 60 KW.

A nonhydrostatic oceanic regional model, ORCTM v1, for internal solitary wave simulation

Abstract. The Oceanic Regional Circulation and Tide Model (ORCTM), including a nonhydrostatic dynamics module which can numerically reproduce internal solitary wave (ISW) dynamics, is presented in this paper. The performance of a baroclinic tidal simulation is also examined in regional modeling with open boundary conditions. The model control equations are characterized by three-dimensional and fully nonlinear forms considering incompressible Boussinesq fluid in Z coordinates. The pressure field is decomposed into the surface, hydrostatic, and nonhydrostatic components on the orthogonal curvilinear Arakawa-C grid. The nonhydrostatic pressure determined by the intermediate velocity divergence field is obtained via solving a three-dimensional Poisson equation based on a pressure correction method. Model validation experiments for ISW simulations with the topographic change in the two-layer and continuously stratified ocean demonstrate that ORCTM has a considerable capacity for reproducing the life cycle of internal solitary wave evolution and tide–topography interactions.

Experimental and numerical investigation of breaking bores in straight and meandering channels with different Froude numbers

ABSTRACT This study investigates the propagation characteristics of breaking bore in meandering channels focusing on the effects of Froude number (F) on the breaking bore. The experiments are conducted with different Froude number conditions of F = 3.99 for high F and F = 1.53 for low F in a straight and meandering channel. The experimental results are compared with calculated results by Shallow Water Equation (SWE) model and three-dimensional calculation model. In the low F condition, the oscillation of water level like a soliton fission was observed and it was amplified along both banks in the meandering channel. This was explained using the temporal variation of the transverse water surface gradient calculated by SWE model, that is not related with non-hydrostatic pressure component and vertical distribution of the velocity. The high F condition is characterized by the longitudinal gradient of bore head caused by large energy loss. In the meandering channel, the SWE model overestimated the wave height near the bore front along both banks. This is because the secondary flow in the meandering channel increases the velocity near the bed and the flow resistance compared with low F condition and reduces the wave height.

A depth-integrated non-hydrostatic model for nearshore wave modelling based on the discontinuous Galerkin method

In this study, a convergent two-dimensional depth-integrated non-hydrostatic shallow water model is discretized using the discontinuous Galerkin (DG) method. This model can account for the dispersive effects by including a non-hydrostatic pressure component and can be used for the simulation of weakly dispersive water waves. Additionally, this model is based on the fractional step method. In the first step, the traditional nonlinear shallow water model plus a transport equation for vertical momentum is discretized by the DG method, and the resulting semi-discrete system is evolved in time by the explicit third-order strong-stability-preserving Runge-Kutta (SSPRK3) method to obtain the provisional solution. In the second step, the provisional solution is corrected by satisfying a divergence constraint for the velocity. The latter step is conducted after application of the DG discretization to an elliptic equation regarding the non-hydrostatic pressure. Both theoretical and experimental tests are carried out to validate the proposed model. The results indicate that for smooth problems, our model can arrive at a given error tolerance by using a mesh with fewer degrees of freedom (DOFs) at the cost of a smaller CPU time when a higher approximation order is adopted and can properly simulate wave run-up, diffraction, refraction, and focusing.

Dynamical Tides in Jupiter as Revealed by Juno

Abstract The Juno orbiter has continued to collect data on Jupiter's gravity field with unprecedented precision since 2016, recently reporting a nonhydrostatic component in the tidal response of the planet. At the mid-mission perijove 17, Juno registered a Love number k 2 = 0.565 ± 0.006 that is −4% ± 1% (1σ) from the theoretical hydrostatic k 2 ( hs ) = 0.590 . Here we assess whether the aforementioned departure of tides from hydrostatic equilibrium represents the neglected gravitational contribution of dynamical tides. We employ perturbation theory and simple tidal models to calculate a fractional dynamical correction Δk 2 to the well-known hydrostatic k 2. Exploiting the analytical simplicity of a toy uniform-density model, we show how the Coriolis acceleration motivates the negative sign in the Δk 2 observed by Juno. By simplifying Jupiter’s interior into a coreless, fully convective, and chemically homogeneous body, we calculate Δk 2 in a model following an n = 1 polytrope equation of state. Our numerical results for the n = 1 polytrope qualitatively follow the behavior of the uniform-density model, mostly because the main component of the tidal flow is similar in each case. Our results indicate that the gravitational effect of the Io-induced dynamical tide leads to Δk 2 = − 4% ± 1%, in agreement with the nonhydrostatic component reported by Juno. Consequently, our results suggest that Juno obtained the first unambiguous detection of the gravitational effect of dynamical tides in a gas giant planet. These results facilitate a future interpretation of Juno tidal gravity data with the purpose of elucidating the existence of a dilute core in Jupiter.

Hard, transparent, sp3-containing 2D phase formed from few-layer graphene under compression

Despite several theoretically proposed two-dimensional (2D) diamond structures, experimental efforts to obtain such structures are in initial stage. Recent high-pressure experiments provided significant advancements in the field, however, expected properties of a 2D-like diamond such as sp3 content, transparency and hardness, have not been observed together in a compressed graphene system. Here, we compress few-layer graphene samples on SiO2/Si substrate in water and provide experimental evidence for the formation of a quenchable hard, transparent, sp3-containing 2D phase. Our Raman spectroscopy data indicates phase transition and a surprisingly similar critical pressure for two-, five-layer graphene and graphite in the 4–6 GPa range, as evidenced by changes in several Raman features, combined with a lack of evidence of significant pressure gradients or local non-hydrostatic stress components of the pressure medium up to ≈ 8 GPa. The new phase is transparent and hard, as evidenced from indentation marks on the SiO2 substrate, a material considerably harder than graphene systems. Furthermore, we report the lowest critical pressure (≈ 4 GPa) in graphite, which we attribute to the role of water in facilitating the phase transition. Theoretical calculations and experimental data indicate a novel, surface-to-bulk phase transition mechanism that gives hint of diamondene formation.

Modeling of Nonhydrostatic Dynamics and Hydrology of the Lombok Strait

The long-wave dynamics of the Lombok Strait, which is the most important link of the West Indonesian throughflow connecting the Pacific and Indian Ocean waters, was simulated and analyzed. A feature of the strait is its extremely complex relief, on which water transport creates a field of pronounced vertical velocities, which requires consideration of the nonhydrostatic component of pressure. The work presents a 3-D nonhydrostatic model in curvilinear coordinates, which is verified on a test problem. Particular attention is paid to the method of solving the 3-D elliptical solver for a nonhydrostatic problem in boundary-matched coordinates and a vertical σ level. The difference in transport through the Lombok Strait is determined by the difference in atmospheric pressure over the Pacific and Indian Oceans. Based on the results of the global simulation, the role of these factors in terms of their variability is analyzed, and the value of nonhydrostatic pressure in the dynamics of the Lombok Strait is revealed and evaluated. The vertical dynamics of the Lombok Strait are considered in detail based on hydrostatic and nonhydrostatic approaches.

Mechanical control of crystal symmetry and superconductivity in Weyl semimetal MoTe2.

The noncentrosymmetric Weyl semimetal candidate MoTe2 was investigated through neutron-diffraction and transport measurements at pressures up to 1.5 GPa and at temperatures down to 40 mK. Centrosymmetric and noncentrosymmetric structural phases were found to coexist in the superconducting state. Density functional theory (DFT) calculations reveal that the strength of the electron-phonon coupling is similar for both crystal structures. Furthermore, it was found that by controlling nonhydrostatic components of stress, it is possible to mechanically control the ground-state crystal structure. This allows for the tuning of crystal symmetry in the superconducting phase from centrosymmetric to noncentrosymmetric. DFT calculations support this strain control of crystal structure. This mechanical control of crystal symmetry gives a route to tuning the band topology of MoTe2 and possibly the topology of the superconducting state.

A non-hydrostatic pressure distribution solver for the nonlinear shallow water equations over irregular topography

We extend a recently proposed 2D depth-integrated Finite Volume solver for the nonlinear shallow water equations with non-hydrostatic pressure distribution. The proposed model is aimed at simulating both nonlinear and dispersive shallow water processes. We split the total pressure into its hydrostatic and dynamic components and solve a hydrostatic problem and a non-hydrostatic problem sequentially, in the framework of a fractional time step procedure. The dispersive properties are achieved by incorporating the non-hydrostatic pressure component in the governing equations. The governing equations are the depth-integrated continuity equation and the depth-integrated momentum equations along the x, y and z directions. Unlike the previous non-hydrostatic shallow water solver, in the z momentum equation, we retain both the vertical local and convective acceleration terms. In the former solver, we keep only the local vertical acceleration term. In this paper, we investigate the effects of these convective terms and the possible improvements of the computed solution when these terms are not neglected in the governing equations, especially in strongly nonlinear processes. The presence of the convective terms in the vertical momentum equation leads to a numerical solution procedure, which is quite different from the one of the previous solver, in both the hydrostatic and dynamic steps. We discretize the spatial domain using unstructured triangular meshes satisfying the Generalized Delaunay property. The numerical solver is shock capturing and easily addresses wetting/drying problems, without any additional equation to solve at wet/dry interfaces. We present several numerical applications for challenging flooding processes encountered in practical aspects over irregular topography, including a new set of experiments carried out at the Hydraulics Laboratory of the University of Palermo.

Development of a Godunov-type model for the accurate simulation of dispersion dominated waves

A new numerical model based on the Navier–Stokes equations is presented for the simulation of dispersion dominated waves. The equations are solved by splitting the pressure into hydrostatic and non-hydrostatic components. The Godunov approach is utilized to solve the hydrostatic flow equations and the resulting velocity field is then corrected to be divergence free. Alternative techniques for the time integration of the non-hydrostatic pressure gradients are presented and investigated in order to improve the accuracy of dispersion dominated wave simulations. Numerical predictions are compared with analytical solutions and experimental data for test cases involving standing, shoaling, refracting, and breaking waves.

A Lagrange-Galerkin hp-Finite Element Method for a 3D Nonhydrostatic Ocean Model

We introduce in this paper a Lagrange-Galerkin hp-finite element method to calculate the numerical solution of a nonhydrostatic ocean model. The Lagrange-Galerkin method yields a Stokes-like problem the solution of which is computed by a second-order rotational splitting scheme that separates the calculation of the velocity and pressure, the latter is decomposed into hydrostatic and nonhydrostatic components. We have tested the method in flows where the nonhydrostatic effects are important. The results are very encouraging.

A mode split, Godunov‐type model for nonhydrostatic, free surface flow

SUMMARYA previously developed model for nonhydrostatic, free surface flow is redesigned to improve computational efficiency without sacrificing accuracy. Both models solve the Reynolds averaged Navier–Stokes equations in a fractional step manner with the pressure split into hydrostatic and nonhydrostatic components. The hydrostatic equations are first solved with an approximate Riemann solver. The hydrostatic solution is then corrected by including the nonhydrostatic pressure and requiring the velocity field to obey the incompressibility constraint.The original model requires the solution of a Riemann problem at every cell face for each vertical layer of cells, which is computationally expensive. The redesigned model instead solves the shallow water (long wave) equations for the hydrostatic solution. Vertical shear is computed by subtracting the shallow water equations from the full three dimensional equations, which removes the hydrostatic thrust terms. Therefore, the required fluxes may be more efficiently computed with velocity based upwind differencing rather than solving a Riemann problem in each vertical layer of cells. This approach is termed mode splitting and has been used in hydrostatic coastal and ocean circulation models, but not surf zone models. Numerical predictions are compared with analytical solutions and experimental data to show that the mode split model is as accurate as the original model, but requires significantly less computational effort especially for large numbers of cell layers. Published 2014. This article is a U.S. Government work and is in the public domain in the USA.

Design of a Dynamical Core Based on the Nonhydrostatic “Unified System” of Equations*

Abstract This paper presents the design of a dry dynamical core based on the nonhydrostatic “unified system” of equations. The unified system filters vertically propagating acoustic waves. The dynamical core predicts the potential temperature and horizontal momentum. It uses the predicted potential temperature to determine the quasi-hydrostatic components of the Exner pressure and density. The continuity equation is diagnostic (and used to determine the vertical mass flux) because the time derivative of the quasi-hydrostatic density is obtained from the predicted potential temperature. The nonhydrostatic component of the Exner pressure is obtained from an elliptic equation. The main focus of this paper is on the integration procedure used with this unique dynamical core. In the implementation described in this paper, height is used as the vertical coordinate, and the equations are vertically discretized on a Lorenz-type grid. Cartesian horizontal coordinates are used along with an Arakawa C grid. A detailed description of the discrete equations is presented in the supplementary material, along with the rationale behind the decisions made during the discretization process. Only a short description is given here. To demonstrate that the model is capable of simulating a wide range of dynamical scales, the results from cyclone- and cloud-scale simulations are presented. The solutions obtained for the selected cloud-scale simulations are compared to those from a fully compressible, anelastic, and pseudo-incompressible models that (as far as possible) uses the same schemes used in the unified dynamical core. The results show that the unified dynamical core performs reasonably well in all these experiments.

Evaluation of Symmetric Neutral-Atmosphere Mapping Functions Using Ray-Tracing Through Radiosonde Observations

Abstract The aim of this paper is to compare the validity of six recent symmetric mapping functions. The mapping function models the elevation angle dependence of the tropospheric delay. Niell Mapping Function (NMF), Vienna Mapping Function (VMF1), University of New Brunswick- VMF1 (UNB-VMF1) mapping functions, Global Mapping Function (GMF) and Global Pressure and Temperature (GPT2)/GMF are evaluated by using ray tracing through 25 radiosonde stations covering different climatic regions in one year. The ray-traced measurements are regarded as “ground truth”. The ray-tracing approach is performed for diverse elevation angle starting at 5° to 15°. The results for both hydrostatic and non-hydrostatic components of mapping functions support the efficiency of online-mapping functions. The latitudinal dependence of standard deviation for 5° is also demonstrated. Although all the tested mapping functions can provide satisfactory results when used for elevation angles above 15°, for high precision geodetic measurements, it is highly recommended that the online-mapping functions (UNBs and VMF1) be used.The results suggest that UNB models, like VMF have strengths and weaknesses and do not stand out as being consistently better or worse than the VMF1. The GPT2/GMF provided better accuracy than GMF and NMF. Since all of them do not require site specific data; therefore GPT2/GMF can be useful as regards its ease of use.

An enigma in estimates of the Earth's dynamic ellipticity

The precession and obliquity frequencies of the Earth's rotational motion are functions of the dynamic ellipticity of the Earth's gravitational figure, and this connection has provided a novel bridge between studies of palaeoclimate and geodynamics. In particular, analyses of tuned climate proxy records have yielded bounds on the mean relative perturbation in dynamic ellipticity over both the last 3 Myr and 25 Myr that are less than ∼3 per cent of the non-hydrostatic component of the ellipticity. We demonstrate that this apparent consistency actually defines an important geophysical enigma. Over the last 3 Myr, changes in the Earth's figure are likely dominated by ice age forcings—in this case, a small perturbation to dynamic ellipticity implies significant isostatic compensation of the ice-ocean surface mass loads and, hence, a relatively low mantle viscosity. In contrast, over the last 25 Myr, changes in the Earth's long-wavelength gravitational form are likely dominated by mantle convective flow, and in this case, the small perturbation to dynamic ellipticity implies sluggish convection and a relatively high mantle viscosity. There are at least four possible routes to resolving this enigma: The viscosity in the Earth's mantle is transient (i.e. dependent on the timescale of the applied forcing), tidal dissipation changed in a manner between the last 3 Myr and 25 Myr that was sufficient to resolve the issue, the observationally inferred bounds are unrealistically restrictive, or earth models exist in which the ice age and convection effects approximately cancel leading to no net perturbation. In this paper, we compute a suite of numerical predictions of ice age and convection-induced perturbations to the dynamic ellipticity to illustrate the enigma described above.

Improving the efficiency and accuracy of a nonhydrostatic surf zone model

A previously developed model for simulating breaking surf zone waves is improved to yield more accurate and computationally efficient predictions. The model employs a sigma coordinate transformation in the vertical direction and solves the Reynolds averaged Navier–Stokes equations in a fractional step manner with the pressure split into hydrostatic and nonhydrostatic components. The hydrostatic equations are first solved with an approximate Riemann solver and the velocity field is then corrected to be divergence free by including the nonhydrostatic pressure. The previous model required a cumbersome modification to accurately predict surf zone wave heights. In this paper, a simpler alteration is presented that is shown to also yield accurate surf zone wave height predictions. In addition, other opportunities for improving model accuracy, robustness, and computational efficiency are also investigated including the discretization of advection terms and the selective neglect of potentially insignificant lateral viscous terms in the governing equations.

Effect of nonhydrostatic stresses on solid-fluid equilibrium. I. Bulk thermodynamics

We present a thermodynamic analysis of the effect of nonhydrostatic stresses on solid-fluid equilibrium in single-component systems. The solid is treated in the small-strain approximation and anisotropic linear elasticity. If the latent heat of the solid-fluid transformation is nonzero and pressure in the fluid is fixed, the shift of the equilibrium temperature relative to hydrostatic equilibrium is shown to be quadratic in nonhydrostatic components of the stress. If atomic volumes of the phases are different and temperature is fixed, the shift of the equilibrium liquid pressure relative to a hydrostatic state is quadratic in nonhydrostatic components of the stress in the solid. The stress effects at special points, at which either the latent heat or the volume difference turn to zero, have also been analyzed. Our theoretical predictions for the temperature and pressure shifts are quantitatively verified by atomistic computer simulations of solid-liquid equilibrium in copper using molecular dynamics with an embedded-atom potential. The simulations also demonstrate spontaneous crystallization of liquid on the surface of a stressed solid with the formation of solid-solid interfaces with the same crystallographic orientation of the solid layers. The lattice mismatch between the stressed and unstressed regions is accommodated by misfit dislocations dissociated in a zigzag pattern.

Nonhydrostatic Model for Surf Zone Simulation

A previously developed model for nonhydrostatic free surface flow is adapted to simulate breaking waves in the surf zone. The model solves the Reynolds-averaged Navier-Stokes equations in a fraction step manner with the pressure split into hydrostatic and nonhydrostatic components. The hydrostatic equations are first solved with an approximate Riemann solver. This approach is particularly well suited for simulating discontinuous flow associated with breaking waves because the model prediction converges to the classical solution for a turbulent bore, which closely resembles breaking waves in the surf zone. The hydrostatic solution is then corrected by including the nonhydrostatic pressure. The model uses a sigma coordinate discretization in the vertical direction, which has been previously demonstrated to yield significant truncation errors with highly skewed grids over large bottom slopes. This potential problem is investigated in the context of highly skewed (but transient) grids that occur with steep br...

Effect of pressure on transport and magnetotransport properties inCaFe2As2single crystals

The effects of pressure generated in a liquid-medium clamp pressure cell on the in-plane and $c$-axis resistance, temperature-dependent Hall coefficient, and low-temperature magnetoresistance in ${\text{CaFe}}_{2}{\text{As}}_{2}$ are presented. The $T\ensuremath{-}P$ phase diagram, including the observation of a complete superconducting transition in resistivity delineated in earlier studies is found to be highly reproducible. The Hall resistivity and low-temperature magnetoresistance are sensitive to different states/phases observed in ${\text{CaFe}}_{2}{\text{As}}_{2}$. Auxiliary measurements under uniaxial $c$-axis pressure are in general agreement with the liquid-medium clamp cell results with some difference in critical pressure values and pressure derivatives. The data may be viewed as supporting the potential importance of nonhydrostatic components of pressure in inducing superconductivity in ${\text{CaFe}}_{2}{\text{As}}_{2}$.