Nonhydrostatic Pressure Gradient Research Articles

Evolution characteristics and mechanism of meso-γ-scale vortex in an atypical bow echo in the North China Plain

On June 25, 2020, an atypical bow echo (ATBE) accompanied by a meso-γ-scale vortex (MV) incurred the strongest gust (41.4 m s−1) recorded since 1957 in the North China Plain. In this article, we investigate the evolution characteristics of MV and its mechanism for the extreme wind by using the observation data of Doppler weather radar and automatic weather stations as well as the four-dimensional Variational Doppler Radar Analysis System (VDRAS). The results show that the MV in this process was initially born at a height of 0.9–2.4 km, and the contracting and stretching vertical vortex rapidly descended to surface from the 2.0 km height with the rotation speed increasing rapidly. Six minutes later, the extreme wind occurred. The generation mechanism of the MV is that, under the strong vertical wind shear and downdraft in the lower troposphere, the vertical vortex tube of MV was transformed from the horizontal vortex tube generated in the zone of perturbation temperature gradient. The influence mechanism of MV on the extreme wind is that, as the MV continued to intensify and extend downward, a negative perturbation low-pressure center formed in the lower troposphere near the MV. Meanwhile, the descending rear-inflow jet (RIJ) was blocked by the prefrontal upward motion and a positive perturbation high-pressure center formed at around 1 km height. The violent positive-negative couplets of perturbation pressure gradient produced a downward nonhydrostatic perturbation pressure gradient force (NPPGF) that further intensified the vertical downward velocity. In addition to the strong downdraft velocity, the Coriolis force also enhanced the formation of the extreme wind through the action of ageostrophic winds. Besides, this paper also compares the mechanism of this process with that of a typical bow echo MV and the extreme wind it affected.

Simulation of Ocean Circulation of Dongsha Water Using Non-Hydrostatic Shallow-Water Model

A two-dimensional non-hydrostatic shallow-water model for weakly dispersive waves is developed using the least-squares finite-element method. The model is based on the depth-averaged, nonlinear and non-hydrostatic shallow-water equations. The non-hydrostatic shallow-water equations are solved with the semi-implicit (predictor-corrector) method and least-squares finite-element method. In the predictor step, hydrostatic pressure at the previous step is used as an initial guess and an intermediate velocity field is calculated. In the corrector step, a Poisson equation for the non-hydrostatic pressure is solved and the final velocity and free-surface elevation is corrected for the new time step. The non-hydrostatic shallow-water model is verified and applied to both wave and flow driven fluid flows, including solitary wave propagation in a channel, progressive sinusoidal waves propagation over a submerged bar, von Karmann vortex street, and ocean circulations of Dongsha Atolls. It is found hydrostatic shallow-water model is efficient and accurate for shallow water flows. Non-hydrostatic shallow-water model requires 1.5 to 3.0 more cpu time than hydrostatic shallow-water model for the same simulation. Model simulations reveal that non-hydrostatic pressure gradients could affect the velocity field and free-surface significantly in case where nonlinearity and dispersion are important during the course of wave propagation.

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.

X-ray induced mobility of molecular oxygen at extreme conditions

We report an in situ Raman study of KClO4 irradiated with x-rays in a diamond anvil cell. Decomposition via KClO4 + hv → KCl + 2O2 was monitored via the O2 vibron at 2 GPa, 6 GPa, and 9 GPa. For all pressures, the vibron grew in intensity and then diminished after successive irradiation suggesting that O2 was diffusing away from the irradiated region. Surprisingly, the diffusion rate accelerated with pressure increase, indicating that the nonhydrostatic pressure gradient was likely driving molecular diffusion of oxygen. At 9 GPa, the vibron bifurcated suggesting that O2 exists as two forms: interstitial and bulk solid. This method can be employed to study molecular diffusion under extreme conditions.

Correcting Fast-Mode Pressure Errors in Storm-Scale Ensemble Kalman Filter Analyses

A typical storm-scale ensemble Kalman filter (EnKF) analysis/forecast system is shown to introduce imbalances into the ensemble posteriors that generate acoustic waves in subsequent integrations. When the EnKF is used to research storm-scale dynamics, the resulting spurious pressure oscillations are large enough to impact investigation of processes driven by nonhydrostatic pressure gradient forces. Fortunately, thermodynamic retrieval techniques traditionally applied to dual-Doppler wind analyses can be adapted to diagnose the balanced portion of an EnKF pressure analysis, thereby eliminating the fast-mode pressure oscillations. The efficacy of this approach is demonstrated using a high-resolution supercell thunderstorm simulation as well as EnKF analyses of a simulated and a real supercell.

Numerical studies of wind forced internal waves with a nonhydrostatic model

The nonhydrostatic pressure effects on the generation and propagation of wind-forced internal waves are studied with a two-dimensional numerical ocean model. A one-way directed wind pulse over a stratified ocean initiates surface and internal waves in a closed basin. The studies are performed with horizontal grid sizes in the range from 1 km to 62.5 m. The experiments are performed with both a hydrostatic and a nonhydrostatic model, facilitating systematic studies of the sensitivity of the numerical model results to the grid size and to the nonhydrostatic pressure adjustments. The results show that the nonhydrostatic pressure effects are highly dependent on the grid size and grow with increased resolution. In the internal depression wave, the horizontal nonhydrostatic pressure gradients reach the same order of magnitude as the hydrostatic gradients in the high-resolution nonhydrostatic studies. In these studies, the nonhydrostatic pressure gradients approximately balance the corresponding hydrostatic pressure gradients in the internal depression wave, and the wave degenerates into a train of soliton waves. The time for the soliton form to develop agrees with the steepening timescale calculated from Korteweg-de Vries theory. In the high-resolution hydrostatic model, the internal depression wave takes the form of a single wave front. When the internal waves are generated in the boundary layers, the nonhydrostatic pressure gradients are much smaller than the hydrostatic gradients and the generation processes are not effected by the nonhydrostatic pressure with the present range of grid sizes.

Evolution of Low-Level Angular Momentum in the 2 June 1995 Dimmitt, Texas, Tornado Cyclone

Abstract The life cycle of the 2 June 1995 Dimmitt, Texas, tornado cyclone, observed during the Verification of the Origins of Rotation in Tornadoes Experiment (VORTEX), is described. The tornado cyclone here is defined as a significantly axisymmetric flow larger than the visible tornado and characterized by increasing angular momentum with increasing radius. Its life cycle included three phases with somewhat differing evolution of angular momentum, herein called intensifying, transition, and weakening. During the intensifying stage, the funnel and debris cloud gradually increased in size. The azimuthally averaged secondary circulation of the larger-scale tornado cyclone, as determined using high-resolution single-Doppler data obtained by a mobile radar, was primarily inward and upward, consistent with the presence of a wall cloud outside the tornado. The azimuthally averaged angular momentum increased monotonically away from the tornado, so inward advection allowed the angular momentum to increase slowly with time in part of the tornado cyclone. During the transition phase, downdrafts began to occur within the tornado cyclone. The transport of angular momentum by the secondary circulation nearly was offset by eddy flux convergence of angular momentum so that the azimuthally averaged angular momentum tendency was only weakly negative at most radii. The tornado was visually impressive during this stage, featuring a 400-m diameter debris cloud extending to cloud base, while the surrounding wall cloud shrank and eroded. During the weakening phase, the funnel and debris cloud gradually shrank, and the funnel went through a rope stage prior to disappearing. The weakening phase was characterized by extensive downdrafts at all radii outside the tornado, and large-scale near-ground outflow as observed by mobile mesonet systems in a portion of the tornado cyclone. The secondary circulation acted to transport smaller angular momentum downward from aloft, and outward along the ground. All terms of the angular momentum budget became negative throughout most of the low-level (0–800-m AGL) tornado cyclone during the weakening phase. Several hypotheses for this evolution are evaluated, including changes in water loading in the tornado cyclone, cooling of the near-ground air, and the distribution of tangential velocity with height with its concomitant influence on the nonhydrostatic vertical pressure gradient force.

Air transport in chute flows

The air bubble rise velocity in still water depends mainly on the bubble size and is basically influenced by buoyancy, viscosity and surface tension. In high-speed flows the number of forces acting on air bubbles increases with turbulence, non-hydrostatic pressure gradient, shear forces, bubble clouds and free-surface entrainment. Air bubbles in these flows are used for cavitation protection of hydraulic structures such as chutes, spillways and bottom outlets. Here, air is normally added by means of aerators upstream of regions where the cavitation number falls below a critical value mainly to reduce the sonic velocity of the fluid and cushion the cavitation bubble collapse process. The distance between successive aerators depends basically on the bubble rise velocity. Until today, the bubble rise velocity in high-speed flows was not thoroughly investigated because of limited laboratory instrumentation. The present project focused on the streamwise development of air concentrations in high-speed flows along a 14 m long model chute. The bubble rise velocity was indirectly derived from the air detrainment gradient of the air concentration contour lines downstream of an aeration device. It accounts for the main hydraulic parameters chute slope, Froude number and air concentration. It is demonstrated that the bubble rise velocity in high-speed flow and stagnant water differ significantly due to fracturing processes, turbulence, and the ambient air concentration.

Observations of natural-state fluid pressures and temperatures in young oceanic crust and inferences regarding hydrothermal circulation

Four boreholes, drilled a few tens of meters into igneous basement on the eastern flank of the Juan de Fuca Ridge during ODP Leg 168, were sealed and instrumented for long-term monitoring to observe the hydrologic state of young sediment-sealed oceanic crust. The thermal regime is dominated by the effects of rapid fluid circulation in uppermost igneous basement driven by very small non-hydrostatic pressure gradients. Upper basement temperatures are uniform laterally between pairs of holes over distances of hundreds of meters to kilometers. In the case of two holes drilled into a sediment-buried basement ridge and adjacent valley, basement temperatures differ by less than 2 K despite the 2.2 km lateral separation of the sites and the 2.5:1 contrast in sediment cover thickness. Under conductive conditions, upper basement temperatures would differ by roughly 50 K. By comparison with modeling results, the observed degree of isothermality suggests a fluid flux of at least 10 −6 m s −1 (30 m yr −1), and an effective permeability in the range of 10 −10–10 −9 m 2 in the uppermost igneous crust. The pressure difference available to drive this rapid flux between the ridge and valley, estimated by comparing the observed pressures via the isothermal upper basement hydrostat that is inferred to connect the two sites, is small (≈2 kPa) and also suggests high permeability. Relative to the hydrostats defined by the local conductive sediment geotherms, substantial super-hydrostatic pressure (+18 kPa) is present within the buried basement ridge, and sub-hydrostatic pressure is present in the adjacent valley (−26 kPa). Such pressure differentials are the direct consequence of the advection-dominated thermal regime and small pressure losses in high-permeability basement, and are available to drive fluid seepage through sediment sections vertically up above and horizontally away from buried ridges, and down above valleys. No constraints are provided by any of the observations on the depth in the crust to which thermally or chemically significant flow might extend, although just as in the overlying sediments, the pattern of deep flow may be affected by the near-isothermal and near-hydrostatic conditions present in the permeable uppermost crustal section.

Fourth- and Fifth-Order Finite-Difference Methods Applied to a Control-Volume Ocean Model

Abstract A semi-implicit, control-volume, nonhydrostatic model is presented. Advection is fifth order with respect to space. Boundary conditions and molecular fluxes are also formulated at fourth order with respect to space. Computational cost is strictly proportional to the number of grid points. Barotropic and nonhydrostatic pressure gradients are calculated using fourth-order explicit calculation followed by a second-order implicit correction for the incremental pressure gradient updates. This strategy is used in the DieCAST model in order to ensure accurate treatment of geostrophy with minimal computational cost, and here it is diagnosed to be advantageous for both small- and large-scale convective flows. Anisotropic grids can result in the vertical Courant number being much larger than the horizontal Courant number, in which case it may be advantageous to use a time step–limited horizontal advection scheme with a more computationally expensive but time step–unlimited vertical advection scheme. An ani...

Mobile Mesonet Observations on 3 May 1999

Abstract Two long-lived tornadic supercells were sampled by an automobile-borne observing system on 3 May 1999. The “mobile mesonet” observed relatively warm and moist air, weak baroclinity, and small pressure excess at the surface within the rear-flank downdrafts of the storms. Furthermore, the downdraft air parcels, which have been shown to enter the tornado in past observational and modeling studies, were associated with substantial convective available potential energy and small convective inhibition. The detection of only small equivalent potential temperature deficits (1–4 K) within the downdrafts may imply that the downdrafts were driven primarily by nonhydrostatic pressure gradients and/or precipitation drag, rather than by the entrainment of potentially cold environmental air at midlevels.

A Convective Cloud Model for Use in a Cumulus Parameterization Scheme

Abstract A quasi-one-dimensional steady-state cloud model that is based on integrating the two-dimensional equation for the azimuthal vorticity over the cloud radius is described. The equations are reduced to one dimension in the vertical direction by assuming that the streamfunction is oscillatory and a function of r only allowing this model to incorporate the nonhydrostatic pressure gradient force. It also includes an empirical buoyancy correction to account for vertical wind shear; the correction is based on application of the Klemp-Wilhelmson convective cloud model to a variety of buoyancy and wind-shear environments. In addition, the model includes consideration of rainwater, freezing of condensate, and a moist penetrative downdraft. The downdraft includes consideration of the nonhydrostatic pressure gradient, rainwater loading, and buoyancy; below cloud base, it is unsaturated. The results from the model for cases with and without vertical wind shear are compared to the Schlesinger three-dimensional...

Vertical structure of the head of a cylindrical mantle plume from a model of two-phase flow with melting

SUMMARY Within the mushroom-shaped head of a cylindrical mantle plume melting occurs, the melt segregates from the matrix, and the matrix deforms and spreads laterally. These processes have been studied with a model of two-phase flow with melting. After characteristics of the solution near the axis of symmetry of the plume were found, a set of asymptotic relations for the variables along the symmetry axis was derived from McKenzie's equations for conservation of mass, momentum and energy of a two-phase system. The distribution of porosity along the plume axis and the vertical and radial segregation velocity of the melt in the vicinity of the axis of symmetry were obtained as functions of depth. Our analytic results show that within the head of a cylindrical mantle plume the contribution of the deformation of the matrix to the total non-hydrostatic pressure gradient cannot be neglected, and melt convergence or divergence is controlled by the radial scale of the upward velocity profile at the depth of the beginning of melting.

A study of nonhydrostatic effects in idealized sea breeze systems

Nonhydrostatic effects in two-dimensional mesoscale sea breeze systems are investigated by numerical simulations. It is shown that nonhydrostatic effects are directly contributed by the vertical gradients of the vertical velocity variance as well as by the vertical accelerations. It is also shown that a K-type turbulence closure is not suitable in a nonhydrostatic primitive equation model, and a higher-order closure scheme should therefore be used. Results from hydrostatic and fully-nonhydrostatic models are compared for various surface and atmospheric background conditions, such as scale and strength of surface heating, geostrophic wind, stability, surface roughness contrast, Coriolis effect, etc. It is found that for strongly developed sea breeze cases, vertical gradients of vertical velocity variance contribute most to nonhydrostatic forcing in the lower layers, and that the resultant nonhydrostatic pressure gradient acts against the hydrostatic pressure gradient, so that nonhydrostatic simulations produce weaker systems than hydrostatic ones. For weak sea breeze systems, the difference between the two models tends to be small.

Theory of melt segregation — A review

Abstract The processes by which melt is extracted from partially molten source regions at depth are collectively known as melt segregation. During the past three years, a dynamical theory has been developed which provides a unified description of the mechanical, thermodynamical and chemical aspects of melt segregation. In this theory, a partially molten region is regarded as a deformable porous medium or “matrix” saturated with melt. Migration of melt relative to the matrix can be driven either by the buoyancy of the melt or by nonhydrostatic pressure gradients associated with the deformation of the matrix. This paper reviews the basic governing equations of the theory and the solutions which have been obtained during the past three years.

A stagnation point flow model for melt extraction from a mantle plume

We present a two‐dimensional dynamical model for melt extraction from a mantle plume. Mantle material rises at constant velocity Wo until it reaches a depth at which melting begins. The flow in the melt zone above this depth has the form of a stagnation point flow. Melt migrates through the unmelted matrix in response to the total nonhydrostatic pressure gradient, which is the sum of contributions from the deformation of the matrix and the buoyancy of the melt. Melt extraction is modeled as a melt flux through the upper surface of the melt zone. Our main conclusions are as follows: (1) The nonhydrostatic pressure gradient associated with the deformation of the matrix is small relative to the buoyancy of the melt everywhere within the melt zone, and the melt migration within the plume obeys Darcy's law. The rate of melt extraction from a mantle plume is therefore controlled by the buoyancy and viscosity of the melt itself, and not by the viscosity of the matrix. (2) Melt extraction from a plume occurs over an area comparable to that of the plume itself, and about 60–80% of the melt generated within the plume is extracted. Both the geometry and rate of extraction predicted by the model are consistent with observations in the Hawaiian Islands. (3) Layers of segregated melt (magma chambers) are likely to form at the the base of the lithosphere under intraplate volcanoes.

Convection in a compressible fluid with infinite Prandtl number

An approximate set of equations is derived for a compressible liquid of infinite Prandtl number. These are referred to as the anelastic-liquid equations. The approximation requires the product of absolute temperature and volume coefficient of thermal expansion to be small compared to one. A single parameter defined as the ratio of the depth of the convecting layer,d, to the temperature scale height of the liquid,HT, governs the importance of the non-Boussinesq effects of compressibility, viscous dissipation, variable adiabatic temperature gradients and non-hydrostatic pressure gradients. Whend/HT[Lt ] 1 the Boussinesq equations result, but whend/HTisO(1) the non-Boussinesq terms become important. Using a time-dependent numerical model, the anelastic-liquid equations are solved in two dimensions and a systematic investigation of compressible convection is presented in whichd/HTis varied from 0·1 to 1·5. Both marginal stability and finite-amplitude convection are studied. Ford/HT[les ] 1·0 the effect of density variations is primarily geometric; descending parcels of liquid contract and ascending parcels expand, resulting in an increase in vorticity with depth. Whend/HT> 1·0 the density stratification significantly stabilizes the lower regions of the marginal state solutions. At all values ofd/HT[ges ] 0·25, an adiabatic temperature gradient proportional to temperature has a noticeable stabilizing effect on the lower regions. Ford/HT[ges ] 0·5, marginal solutions are completely stabilized at the bottom of the layer and penetrative convection occurs for a finite range of supercritical Rayleigh numbers. In the finite-amplitude solutions adiabatic heating and cooling produces an isentropic central region. Viscous dissipation acts to redistribute buoyancy sources and intense frictional heating influences flow solutions locally in a time-dependent manner. The ratio of the total viscous heating in the convecting system, ϕ, to the heat flux across the upper surface,Fu, has an upper limit equal tod/HT. This limit is achieved at high Rayleigh numbers, when heating is entirely from below, and, for sufficiently large values ofd/HT, Φ/Fuis greater than 1·00.

Dynamics of a Falling Particle Zone

Abstract A numerical experiment on falling particles arranged in zones, with slab symmetry, constant air density, and initially still air is performed whereby single-shed particles are treated by a Lagrangian method and the air motion by an Eulerian method. The results of this study of the zone's dynamics indicate that the zones fall considerably faster than their respective terminal velocity. This additional or convective velocity depends on loading and terminal speed. The spreading velocities, away from the axis of symmetry, appear to be dependent on terminal velocity such that a maximum occurs near the terminal velocity of 4 m sec−1. In all cases considered, the magnitude of the perturbation nonhydrostatic pressure gradient in the vertical is found to be an order of magnitude smaller than the perturbation hydrostatic pressure gradient.