On open boundary conditions for three dimensional primitive equation ocean circulation models

Abstract

An open boundary condition is constructed for three dimensional primitive equation ocean circulation models. The boundary condition utilises dominant balances in the governing equations to assist calculations of variables at the boundary. The boundary condition can be used in two forms. Firstly as a passive one in which there is no forcing at the boundary and phenomena generated within the domain of interest can propagate outwards without distorting the interior. Secondly as an active condition where a model is forced by the boundary condition. Three simple idealised tests are performed to verify the open boundary condition, (1) a passive condition to test the outflow of free Kelvin waves, (2) an active condition during the spin up phase of an ocean, (3) finally an example of the use of the condition in a tropical ocean.     

A three-dimensional,iterative mapping procedure for the implementation of an ionosphere-magnetosphere anisotropic Ohm’s law boundary condition in global magnetohydrodynamic simulations

The mathematical formulation of an iterative procedure for the numerical implementation of an ionosphere-magnetosphere (IM) anisotropic Ohm’s law boundary condition is presented. The procedure may be used in global magnetohydrodynamic (MHD) simulations of the magnetosphere. The basic form of the boundary condition is well known, but a well-defined, simple, explicit method for implementing it in an MHD code has not been presented previously. The boundary condition relates the ionospheric electric field to the magnetic field-aligned current density driven through the ionosphere by the magnetospheric convection electric field, which is orthogonal to the magnetic field B, and maps down into the ionosphere along equipotential magnetic field lines. The source of this electric field is the flow of the solar wind orthogonal to B. The electric field and current density in the ionosphere are connected through an anisotropic conductivity tensor which involves the Hall, Pedersen, and parallel conductivities. Only the height-integrated Hall and Pedersen conductivities (conductances) appear in the final form of the boundary condition, and are assumed to be known functions of position on the spherical surface R=R₁ representing the boundary between the ionosphere and magnetosphere. The implementation presented consists of an iterative mapping of the electrostatic potential , the gradient of which gives the electric field, and the field-aligned current density between the IM boundary at R=R₁ and the inner boundary of an MHD code which is taken to be at R₂>R₁. Given the field-aligned current density on R=R₂, as computed by the MHD simulation, it is mapped down to R=R₁ where it is used to compute by solving the equation that is the IM Ohm’s law boundary condition. Then is mapped out to R=R₂, where it is used to update the electric field and the component of velocity perpendicular to B. The updated electric field and perpendicular velocity serve as new boundary conditions for the MHD simulation which is then used to compute a new field-aligned current density. This process is iterated at each time step. The required Hall and Pedersen conductances may be determined by any method of choice, and may be specified anew at each time step. In this sense the coupling between the ionosphere and magnetosphere may be taken into account in a self-consistent manner.     

The study and analysis of floating datum selection for rugged terrain

We analyze the characteristics of different floating datums for static corrections and discuss the methods for determining them. The effect of different floating datum corrections was studied using theoretical model experiments, resulting in the conclusion that the velocity obtained after the floating datum correction with the minimum static correction errors depends on the velocity of the layer below the low velocity layer （LVL） lower boundary and is not related to topographic relief and LVL structure. For the real data processing case, wave equation numerical model experiments were conducted which resulted in a new method for calculating objective functions based on the waveform and modifications to the calculation equation for minimum static correction errors to make the method suitable for real data static correction processing using inhomogeneous velocity models with lower velocity boundary relief. Real data processing results demonstrate the method＇s superiority.     

Numerical simulation of internal solitary wave—induced reverse flow and associated vortices in a shallow,two-layer fluid benthic boundary layer

The wave-induced velocity and pressure fields beneath a large amplitude internal solitary wave of depression propagating over a smooth, flat, horizontal, and rigid boundary in a shallow two-layer fluid are computed numerically. A numerical ocean model is utilised, the set-up of which is designed and tuned to replicate the previously published experimental results of Carr and Davies (Phys Fluids 18(1):016,601–1–016,601–10, 2006). Excellent agreement is found between the two data sets and, in particular, the numerical simulation replicates the finding of a reverse flow along the bed aft of the wave. The numerically computed velocity and pressure gradients confirm that the occurrence of the reverse flow is a consequence of boundary layer separation in the adverse pressure gradient region. In addition, vortices associated with the reverse flow are seen to form near the bed.     

Upon boundary conditions imposed by a stratified fluid

Abstract

It is shown that in the limit of slow steady linearized flow and infinite stratification a stratified region lying above or below a layer of destabilized fluid produces zero velocity and zero stress boundary conditions. These novel boundary conditions constrain flow more fully than the more common rigid or free conditions, and arise because the penetrative flow in the stabilized region must pump only a finite amount of heat.     

Some effects of the air-water interface on gravity waves

Abstract

New rates of decay are presented for temporally-attenuated gravity waves in deep water, allowance being made for the energy dissipated in the Stokes interfacial boundary layer in the air. This decay-rate, involving air drag, may then be used to deduce a new “free-surface” boundary condition for the problem of the mass transport velocity due to progressive waves; for shallow-water waves, two specific velocity profiles are calculated, and indicate large differences in comparison with the corresponding profiles of Longuet-Higgins (1953) for a vacuum-water interface.     

Experimental methods for river discharge measurements: comparison among tracers and current meter

Abstract

Discharge measurements in natural watercourses are performed in order to determine the value of the surface outflow of a basin, its temporal variability, and the outflow characteristics. The methods conventionally used for these measurements utilize an immersed current meter in different points of a river section, which acquires the mean flow velocity. Using this measurement, the discharge can be calculated. Some experimental problems arise, however, when there is a very high discharge. An important method, valid in such cases, is the artificial tracing method. In particular, the use of chemical tracers for small watercourses is very convenient because they are low cost, easily handled, low impact and provide satisfactory results. In the past, radioactive tracers such as tritium have been used in large rivers, while fluorescent tracers have been commonly exploited in the USA and now elsewhere. However, if the water is turbid, the suspended sediments may easily absorb some tracers. In this paper, the preliminary results of a comparison between current meter and artificial tracer measurements are reported. In particular, field tests in a small tributary have been performed, in order to investigate the behaviour of different tracers.

Citation Tazioli, A. (2011) Experimental methods for river discharge measurements: comparison among tracers and current meter. Hydrol. Sci. J. 56(7), 1314–1324.     

A study on 3-D velocity structure of crust and upper mantle in Sichuan-Yunan region, China

Based on the first arrival P and S data of 4 625 regional earthquakes recorded at 174 stations dispersed in the Yunnan and Sichuan Provinces, the 3-D velocity structure of crust and upper mantle in the region is determined, incorporating with previous deep geophysical data. In the upper crust, a positive anomaly velocity zone exists in the Sichuan basin, whereas a negative anomaly velocity zone exists in the western Sichuan plateau. The boundary between the positive and negative anomaly zones is the Longmenshan fault zone. The images of lower crust and upper mantle in the Longmenshan fault, Xianshuihe fault, Honghe fault and others show the characteristic of tectonic boundary, indicating that the faults likely penetrate the Moho discontinuity. The negative velocity anomalies at the depth of 50 km in the Tengchong volcanic area and the Panxi tectonic zone appear to be associated with the temperature and composition variations in the upper mantle. The overall features of the crustal and the upper mantle structures in the Sichuan-Yunnan region are the lower average velocity in both crust and uppermost mantle, the large crustal thickness variations, and the existence of high conductivity layer in the crust or/and upper mantle, and higher geothermal value. All these features are closely related to the collision between the India and the Asia plates. The crustal velocity in the Sichuan-Yunnan rhombic block generally shows normal value or positive anomaly, while the negative anomaly exists in the area along the large strike-slip faults as the block boundary. It is conducive to the crustal block side-pressing out along the faults. In the major seismic zones, the seismicity is relative to the negative anomaly velocity. Most strong earthquakes occurred in the upper-mid crust with positive anomaly or normal velocity, where the negative anomaly zone generally exists below. Foundation item: National Scientific and Technological Development Program (95-973-02-02), the Climb Program (95-S-05-01) of National Scientific and Technological Ministry of China, and the State Natural Sciences Foundation of China (49874021). Contribution No. 02FE2004, Institute of Geophysics, China Seismological Bureau.     

The Influence of the Prandtl Number on the Style of Vigorous Thermal Convection

The effect of the Prandtl number on convection in a planar three-dimensional geometry is investigated in this study. We have employed a numerical scheme to integrate the governing equations. Differently from previous studies we have chosen stress-free boundaries. Experiments have been performed at a Rayleigh number of Ra = 10 6 for Prandtl numbers (Pr) ranging from 0.025 to 100. We have further conducted one experiment in the limiting case of infinite Prandtl number. Despite the differences in the geometry and the boundary conditions, as compared to other studies, we find a similar transition in the dynamics of the flow when the Prandtl number is increased. While the velocity and the temperature structure show diffusive character at low Pr, sharp thermal boundary layers form at high Pr. The heat transport efficiency increases with Pr until a transition value is reached, from there on Nu behaves almost asymptotically. The transition can not be caused by a change in hierarchies between velocity and thermal boundary layers, as suggested in other studies. Due to the stress-free boundaries, a velocity boundary layer does not exist. We observe that the toroidal part of the flow is strong at low Pr and looses its strength with increasing Pr, thus it is likely to be responsible for the transition. In a further chapter we demonstrate that due to the neglect of the toroidal part in two-dimensional calculations at low Pr results are obtained which are misleading, even in a qualitative sense. Infinite Pr results from 2D calculations closely resemble the dynamics of fully 3D flows.     

On the possibility of using an electromagnetic ionosphere in global MHD simulations

Global magnetohydrodynamic (MHD) simulations of the Earths magnetosphere must be coupled with a dynamical ionospheric module in order to give realistic results. The usual approach is to compute the Reld-aligned current (FAC) from the magnetospheric MHD variables at the ionospheric boundary. The ionospheric potential is solved from an elliptic equation using the FAC as a source term. The plasma velocity at the boundary is the E × B velocity associated with the ionospheric potential. Contemporary global MHD simulations which include a serious ionospheric model use this method, which we call the electrostatic approach in this paper. We study the possibility of reversing the flow of information through the ionosphere: the magnetosphere gives the electric Reld to the ionosphere. The Reld is not necessarily electrostatic, thus we will call this scheme electromagnetic. The electric Reld determines the horizontal ionospheric current. The divergence of the horizontal current gives the FAC, which is used as a boundary condition for MHD equations. We derive the necessary formulas and discuss the validity of the approximations necessarily involved. It is concluded that the electromagnetic ionosphere-magnetosphere coupling scheme is a serious candidate for future global MHD simulators, although a few problem areas still remain. At minimum, it should be investigated further to discover whether there are any differences in the simulation using the electrostatic or the electromagnetic ionospheric coupling.     

Numerical simulations of thermal convection in a rapidly rotating spherical shell cooled inhomogeneously from above

Abstract

Numerical simulations of thermal convection in a rapidly rotating spherical fluid shell with and without inhomogeneous temperature anomalies on the top boundary have been carried out using a three-dimensional, time-dependent, spectral-transform code. The spherical shell of Boussinesq fluid has inner and outer radii the same as those of the Earth's liquid outer core. The Taylor number is 10⁷, the Prandtl number is 1, and the Rayleigh number R is 5R_c (R_c is the critical value of R for the onset of convection when the top boundary is isothermal and R is based on the spherically averaged temperature difference across the shell). The shell is heated from below and cooled from above; there is no internal heating. The lower boundary of the shell is isothermal and both boundaries are rigid and impermeable. Three cases are considered. In one, the upper boundary is isothermal while in the others, temperature anomalies with (l,m) = (3,2) and (6,4) are imposed on the top boundary. The spherically averaged temperature difference across the shell is the same in all three cases. The amplitudes of the imposed temperature anomalies are equal to one-half of the spherically averaged temperature difference across the shell. Convective structures are strongly controlled by both rotation and the imposed temperature anomalies suggesting that thermal inhomogeneities imposed by the mantle on the core have a significant influence on the motions inside the core. The imposed temperature anomaly locks the thermal perturbation structure in the outer part of the spherical shell onto the upper boundary and significantly modifies the velocity structure in the same region. However, the radial velocity structure in the outer part of the shell is different from the temperature perturbation structure. The influence of the imposed temperature anomaly decreases with depth in the shell. Thermal structure and velocity structure are similar and convective rolls are more columnar in the inner part of the shell where the effects of rotation are most dominant.     

Galactic dynamo models without sharp boundaries

Abstract

A new numerical approach is introduced which allows investigation into the conditions for dynamogeneration of axisymmetric and non-axisymmetric large-scale magnetic field modes in galaxy models which are defined by axisymmetric distributions of the α-parameter, the angular velocity and the electrical conductivity. The velocity field is assumed to be localized, however, the common assumption of a sharp boundary of the conducting region is dropped.

The possible anisotropy of the α-tensor is taken into account. The critical dynamo numbers (excitation conditions) for different modes are obtained by a direct method. The required steady states are attained by the use of an artificial non-linearity.

Initial test calculations demonstrate the efficacy of this new concept.     

Buoyant boundary layer flows- an analogy to the Ekman spiral

Abstract

Flow details inside the buoyant boundary layer in the heat-up process of a contained, stably stratified, fluid are presented. Numerical solutions were obtained for the heatup problem in a cylinder considered by Sakurai and Matsuda (1972). By plotting the scaled vertical velocity W versus the scaled temperature θ as functions of the normal distance from the sidewall, the precise shape of the buoyant layer spiral is constructed. The analogy between this spiral and the Ekman spiral in rotating fluids is apparent. As the Rayleigh number Ra increases, the magnitude of the scaled vertical velocity increases substantially, but the scaled temperature does not vary appreciably. The buoyant layer thickness is determined by measuring the zero-crossing normal distance for the vertical velocity. The buoyant layer suction increases significantly as Ra increases. The effects of vertical level and of time on the qualitative behavior of buoyant layer flows are found to be small. The buoyant layer flows decay over the heat-up time scale t _n ; t _h characterizes the time span over which the overall adjustment process in the inviscid interior region is accomplished. This work clarifies that the analogy between heat-up and spin-up, which has been known to exist in the main body of inviscid fluid, applies equally well to the boundary layer regions.     

Variations of heat flow and Pn - velocity in the continental area of China

Temperature is an important factor affecting seismic velocity, and terrestrial heat flow is the most direct indication of temperature distribution of the lithosphere. Some authors therefore suggested that Pn velocity should be inversely related with heat flow. The average heat flow values (q) and Pn velocities (V _Pn) in 22 areas have been calculated and collected from published literatures to investigate the possible correlation between these two parameters for the continental area of China. However, the results show that the variations ofq andV _Pn in the studied areas are far away from the expected inverse relation. The effects of pressure of seismic velocity and contribution of crustal radiogenic heat on heat flow have been taken into consideration in regressions respectively and simultaneously. However, all the corrections are of little help for the improvement of the expected inverse relation. The conclusion deduced from the present study is that in a large scale region with complex tectonic evolution history and complex deep structure framework such as the continental area of China, temperature at the Moho boundary is not the most important factor affecting Pn velocity. The conceptual inverse correlation between heat flow and Pn velocity might be masked by various “noises”. The Chinese version of this paper appeared in the Chinese edition ofActa Seismologica Sinica,14, 42–50, 1992.     

The complexity feature of crust-mantle boundary in Zhangbei seismic region and its tectonic implication

The ProP waveform data obtained from a deep seismic sounding profile, which ran through Zhangbei seismic region, were processed by means of both seismic wave complexity coefficient and frequency spectrum analysis methods, and the complexity characteristics of crest-mantle boundary beneath the studied area and its adjacent region were determined. The results show that the place below epicenter can be taken as boundary, the northern side of which is Inner Mongolia axis with small complexity coefficient and the southern side of which is Huai＇an basin with large complexity coefficient. The different spectrum patterns at the two sides of the epicenter were inferred from spectrum analysis. In the epicentral area, there have been multi-period magmatic eruptions since Meso-Cenozoic and craters exist at the surface. From the velocity imaging of middle and upper crust in Zhangbei seismic region it can be found that there are crustal low velocity bodies around the craters and also there are low velocity zones, which went into deep crust. It is suggested that the distinct zones of crust-mantle boundary complexity may be the margin, where the magma had intruded due to magma activity in Meso-Cenozoic. The southern side with large complexity coefficient is deep magmatic activity area and the northern side with small complexity coefficient is stable crust-mantle tectonics. The difference of crust-mantle complexity provides deep background for the development of strong earthquake.     

On the steady mass transport induced by wave motions in a viscous rotating fluid

Abstract

The steady second-order motion induced by a first-order wave motion in a homogeneous, viscous and rotating fluid is examined. If the wave motion produces a steady Ekman layer suction by non-linear interactions, this suction must induce a steady component of interior, relative vorticity parallel to the axis of rotation in order to conserve mass. A boundary value problem for the determination of the induced, steady interior mass transport velocity is presented. The mass transport induced by a Kelvin wave is examined as an illustration and possible application of the theory.     

A) A. I. H. S. / A) I. A. S. H.

SUMMARY

Basing their studies on an extended Reynolds principle of similarity, the authors present in this paper a thorough theoretical investigation of the turbulent flow in pipes.

Making appropriate assumptions regarding the distribution of the turbulent apparent viscosity over the entire pipe diameter, the well-known discharge formulas, i. e. the resistance laws, of Prandtl-V. Kármán for the hydraulically smooth and the hydraulically rough region, and of Colebrook for the transition region—the accuracy of these being well established by measurements—can be clearly shown to be correct.

Thus it is also possible to determine the velocity distribution in the region near the wall for the hydraulically smooth region and the transition region, as well as for the hydraulically rough region.

The concept, that the flow with a fully developed roughness effect begins when the laminar boundary layer at the wall disappears can be seen to be in close agreement with the asssumptions made. The limits which were established for the hydraulically rough region and the transition region correspond well with the curve plotted by PRANDTL and the boundary curve of Rouse.     

An experimental study of the effects of the upper boundary condition on the thermal convection in a rotating,differentially heated cylindrical annulus of water

Abstract

The effects of the upper boundary condition on the regime diagram and certain characteristics of the convection within a rotating, differentially heated cylindrical anulus of water were studied in the laboratory. It was found that the regime diagram was not substantially affected by the upper boundary condition. However, the thermal amplitude of the baroclinic waves, as a function of parameter space, and, as expected from previous work, the angular drift velocity of those waves were found to be strongly affected by the upper boundary condition. When the upper surface was free, the amplitude changes were explosive and highly non-linear (as discovered earlier by Kaiser, 1970). When the upper surface was rigid, they were smooth and quite linear. The baroclinic wave patterns drifted round the annulus at rates which were in direct response to the imposed “thermal wind”. However, (as previously observed by Koschmieder, 1972), when the upper surface was rigid they drifted approximately ten times more slowly than when it was free.     

Rain-induced outflow from deep snowpacks in the central Sierra Nevada,California

Abstract

In many mountainous areas of the Pacific coast of North America, rainfall onto snowpacks causes massive floods, probably the single greatest cause of changes in channel morphology and lotie habitats. To understand and model this hydrometeorological phenomenon better, process-response hypotheses were developed for snowpack outflow amount, duration and rate and the time lags from the beginning of rainfall to initial and peak outflow. The hypotheses were evaluated by correlation and regression analyses based on measurements of 20 rainon-snow events monitored between 1984 and 1990 at forested and open plots near Lake Tahoe, California. Outflow amount correlated significantly with precipitation amount, duration and rate, snow depth and melt potential. Many of these variables also correlated significantly with outflow duration and rate and lag time to peak outlfow. Regression models expalined 80–90% of the variation in outflow amount and duration. Significant differences were not identified between the forest and open plots for any of the outflow attributes.     

The ionospheric response to flux transfer events: the first few minutes

We utilise high-time resolution measurements from the PACE HF radar at Halley, Antarctica to explore the evolution of the ionospheric response during the first few minutes after enhanced reconnection occurs at the magnetopause. We show that the plasma velocity increases associated with flux transfer events (FTEs) occur first 100–200 km equatorward of the region to which magnetosheath (cusp) precipitation maps to the ionosphere. We suggest that these velocity variations start near the ionospheric footprint of the boundary between open and closed magnetic field lines. We show that these velocity variations have rise times 100 s and fall times of 10 s. When these velocity transients reach the latitude of the cusp precipitation, sometimes the equatorward boundary of the precipitation begins to move equatorward, the expected and previously reported ionospheric signature of enhanced reconnection. A hypothesis is proposed to explain the velocity variations. It involves the rapid outflow of magnetospheric electrons into the magnetosheath along the most recently reconnected field lines. Several predictions are made arising from the proposed explanation which could be tested with ground-based and space-based observations.