VARIATIONS OF WATER SURFACE GRADIENT AND VELOCITY DISTRIBUTION CAUSED BY WATER JETS

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An elasto-visco-plastic model using the finite element method for crustal and lithospheric deformation

A novel numerical model based on solid deformation is presented in this paper. This thermo-mechanical model can simulate the tectonic evolution of crust and (lithospheric and asthenospheric) mantle under different conditions. Our implementation uses the finite element method (FEM) in order to solve the equations. As a Lagrangian approach is employed, remeshing techniques are implemented to avoid distortion problems when a certain deformation threshold is reached. The translation of the state between the old and new mesh is achieved by means of the information stored on Lagrangian particles, which minimizes the diffusion. The model is able to represent elastic, viscous and plastic behaviour inside the studied domain. Three types of creep mechanism (diffusion, dislocation and Peierls) are included. Two different quadrilateral isoparametric elements were implemented and can be employed to perform the calculations. The first one is an element with 4 nodes, selective reduced integration and a stabilization operator to diminish hourglass modes, which reduces the computational time needed. The second one has 8 nodes located in standard positions, uses full integration scheme and has no hourglass modes as it satisfies the Inf-Sup condition. Several test cases with known solutions were run to validate the different aspects of the implementation.     

Geostrophic vs magneto-geostrophic adjustment and nonlinear magneto-inertia-gravity waves in rotating shallow water magnetohydrodynamics

The evolution of localised jets and periodic nonlinear waves in rotating shallow water magnetohydrodynamics (rotating SWMHD) and standard rotating shallow water model (RSW) is compared within the framework of translationally-invariant 1.5-dimensional configurations, which are traditionally used in geophysical fluid dynamics for studying geostrophic adjustment and frontogenesis. Such configurations also allow for exact nonlinear wave solutions in both models. A theory of the magneto-geostrophic adjustment, i.e. adjustment of an arbitrary initial configuration to a state of magneto-geostrophic equilibrium in RSWMHD, is developed and confirmed by numerical simulations with a finite-volume well-balanced code. The code is resolving all kinds of waves in the model and corresponding weak solutions equally well. It is benchmarked by reproducing exact solutions – steady essentially nonlinear Alfvèn and mixed magneto-inertia-gravity waves – and used to demonstrate robustness of these solutions with respect to localised along-wave perturbations. It is also shown how the results on adjustment can be extended to the fully 2-dimensional case.     

Comparison of methods for modelling the behaviour of bubbles produced by marine seismic airguns

Three models for the dynamics of seismic airgun‐generated bubbles and their associated far‐field signals are developed and compared with geophysical data. The first model of an airgun‐generated bubble uses a spherical approximation, the second is an approximate Lagrangian model which allows for small deformations from a spherical shape, whilst the final model is an axisymmetric boundary‐integral method which permits the bubble to evolve into highly non‐spherical geometries. The boundary‐integral method also allows both geometric interference and strong dynamic interactions in multi‐bubble studies. When comparing the spherical model to experimental data there are three apparent, significant differences: the magnitude of the primary pressure peak, which is greater in the model; the subsequent decay of the pressure peaks and motion – the experimental data demonstrating greater decay and a slower rise rate; and the frequency of oscillation, which is slower in the experimental data. It is believed that the first discrepancy is due to the initial stages of expansion where the compressed air is forced to sparge through the airgun ports. The other differences indicate that there is some other energy‐loss mechanism which is not accounted for in the spherical bubble model. Non‐spherical bubble behaviour is investigated through the use of two different deformable many‐bubble codes and their predictions are compared with the spherical model and experimental data. The Lagrangian model predicts the formation of a buoyancy‐driven liquid jet on the first collapse of a typical airgun bubble; however, the model breaks down when the bubble becomes significantly deformed, due to a low‐order spherical‐harmonic approximation for the potential. The axisymmetric boundary‐integral code models the jet shape accurately and it is found that these bubbles evolve to toroidal geometries when the jet impacts on the opposite surface of the bubble. This highly non‐spherical behaviour is readily observed on high‐speed films of airgun bubbles, and is one key source of energy loss; it damps the pulsations of the bubble and slows its rise speed. Inter‐bubble interactions are investigated using the two deformable bubble models, and the predictions are compared to field data. It was found that as the bubbles approach each other, their periods of oscillation increase in accordance with observations, and jets are formed in the direction of motion upon collapse.     

Jet flow over foredunes

Jet flows, which are localized flows exhibiting a high speed maxima, are relatively common in nature, and in many devices. They have only been occasionally observed on dunes, and their dynamics are poorly known. This paper examines computational fluid dynamic (CFD) two‐dimensional (2D) modelling of jet flow over a foredune topography. Flow was simulated in 10° increments from onshore (0°) to highly oblique alongshore (70°) incident wind approach angles. CFD modelling reveals that the formation of a jet is not dependent on a critical wind speed, and an increase in incident wind velocity does not affect the magnitude of jet flow. A jet is first formed at ~1.0 m seawards of the foredune crest on the Prince Edward Island foredune morphology example examined here. A jet is not developed when the incident wind is from an oblique approach angle greater than ~50° because there is significantly less flow acceleration across a much lower slope at this incident angle. The presence of a scarp does influence the structure of the crest jet, in that the jet is more pronounced where a scarp is present. Surface roughness affects the magnitude of jet expansion and jets are better developed on bare surfaces compared to vegetated ones. Copyright © 2016 John Wiley & Sons, Ltd.     

Multiple equilibria of cross-equatorial Inertial jets

Based on the developed Anderson and Moore's theory about cross-equatorial inertial jets and a nonlinear equivalence shallow water model, new universal functions are determined by the characters of the vortical large-scale air flow (atmosphere) or ocean current (ocean) related to the jet, then the potential vorticity and energy conservation equations along the streamline in the cross-equatorial in-ertial jets can be obtained. Because the governing equations are nonlinear, some limited multiple equi-libria of cross-equatorial inertial jets may exist. According to the character of large-scale air flow or ocean current outside the jets, the existent criterion for multiple eqnilibria in cross-equatorial inertial jets is discussed, and two examples for multiple equilibia of nonlinear governing equations are given.     

Jet instability and the stabilizing effect of topography on jets in two-layer rotating systems

Abstract

Laboratory experiments concerning azimuthal jets in two-layer rotating systems in the absence and presence of bottom topography aligned along the jets have been conducted. The jets were forced by the selective withdrawal of fluid from the upper layer of a two-fluid system contained in a circular dishpan geometry. The principal parameters measured in the experiments were the jet Rossby number, Ro, and a stratification parameter F = r ₁/(λ₁λ₂)^1/2 where r ₁ is the radius of the circular disc used for the selective withdrawal (i.e., r ₁ is the approximate radius of curvature of the jet) and λ₁,λ₂ are the internal Rossby radii of deformation in the upper and lower fluids, respectively.

The no-topography experiments show that for a sufficiently small F, the particular value depending on Ro, the jet is stable for the duration of the experiment. For sufficiently large F, again as a function of Ro, the jet becomes unstable, exhibiting horizontal wave disturbances from modes three to seven. An Ro against F flow regime diagram is presented.

Experiments are then conducted in the presence of a bottom topography having constant cross-section and extending around a mid-radius of the dishpan. The axis of the topography is in the vicinity of the jet axis forced in the no-topography experiments and the crest of the topography is in the vicinity of the interface between the two fluids (i.e., the front associated with the jet). The experiments show that in all cases investigated the jet tends to be stabilized by the bottom topography. Experiments with the topography in place, but with the interface between the fluids being above the topography crest, are shown to be unstable but more irregular than their no-topography counterparts.

Various quantitative measurements of the jet are presented. It is shown, for example, that the jet Rossby number defined in terms of the fluid withdrawal rate from the tank. Q, can be well correlated with a dimensionless vorticity gradient, V_G , across the upper layer jet. This allows for an assessment of the stability characteristics of a jet based on a knowledge of V_G (which can be estimated given a jet profile) and F.     

Nocturnal basin low-level jets: an integrated study

Low-level jets (LLJs) are a very common feature in the nocturnal stably stratified boundary layer. Many factors can intervene in their generation, linked basically to effects of baroclinity. A special kind of low-level jets is composed by the nocturnal katabatic and basin flows, generated over terrain slopes. A study of observed LLJs in the Duero Basin is shown here, combining observational data and modelling experiments. Normalized in respect to the maximum wind height, the dynamic characteristics of the jets are similar: a two-layer system, with a stably stratified layer below the jet maximum and a near neutral layer above, with a very stable layer separating them at the level of the wind maximum. There is vertical mixing above and below the jet, and the connection between these layers takes place occasionally in a very turbulent manner.     

Katabatic flow induced by a cross-slope band of surface cooling

This paper investigates the behavior of katabatic flow induced by an idealized, thermally inhomogeneous surface; a strip of surface cooling that has a finite width in the along-slope direction and is infinitely long in the cross-slope direction. Numerical simulations using the Boussinesq equations of motion and the thermodynamic energy equation are performed for various slope angles and strip lengths. The underlying dynamical processes in the katabatic jet and the near environment are explored by considering the along-slope momentum balance after a steady state has been achieved. The inhomogeneous nature of the surface forcing also induces a response in the environment that extends very far away from the sloped surface. Nearly horizontal jets close to the vertical heights of both sides of the cold strip are observed in the environment. A horizontal vorticity analysis is performed on these horizontal jets to ascertain their dynamical structure.     

A note on the necessary condition for baroclinic instability of monsoon zonal current

Analytic expressions are derived for the minimum easterly and westerly jet strengths necessary for baroclinic instability, in terms of their half-widths and location. For this purpose the necessary condition for an internal jet is utilized and the jets and static stability are represented by simple mathematical functions. Dependency of the minimum jet strengths to their half-width and location are discussed.     

REVIEW ON LOCAL SCOUR DUE TO JETS

The safety of an apron of the energy dissipator is threatened by the large-scale scour in the downstream of the apron due to the erosive action of a horizontal jet issuing from a sluice opening. Also, large-scale deposition of the scoured sediments due to an impinging jet in a plunging pool type energy dissipator affects the passage of flow adversely in the downstream channels. Owing to the significant practical importance, the problem of local scour due to jets has been studied by many investigators, In this paper, a comprehensive review of the up-to-date investigations on local scour due to horizontal and impinging jets is presented including all possible aspects, such as scouring process, parameters affecting scour, time variation of scour velocity distribution on the apron and within the scour hole, development of boundary layer thickness, bed shear stress, scour estimation formulas and protection works.     

Experimental study of upstream influence in the two‐dimensional flow of a stratified fluid over an obstacle†

An experimental investigation was made of the upstream influence in front of two‐dimensional obstacles when they were towed in a linearly stratified fluid. The experiments were performed in a plexiglas channel 30.5 feet long, 2 feet high and 14 inches wide filled with a linearly stratified salt solution. Velocity measurements and flow visualization were obtained by neutrally buoyant liquid droplets and dye lines. Density measurements were made by a salinity probe.

The existence of unattenuated upstream influence in front of an obstacle was quantitatively documented for the first time. It occurred in the form of multiple unattenuated horizontal jets when there was a separated open wake behind the obstacle. These jets were identified to be the super‐position of “columnar disturbance modes”. The total number of columnar modes was determined solely by the Froude number of the flow and was equal to the number of lee‐wave modes excited. The drag due to upstream columnar modes was estimated and found to be lower than the drag due to the lee wave modes:     

On the origin of jets in the ocean

We show a mechanism whereby the jets result during the development of β-plumes (i.e., low-frequency Rossby waves that establish gyre circulations) in a model of ocean-basin circulation. The energy originates in baroclinic meanders of circulation at the eastern boundary of the ocean. Eddies are intimately related and occur as a result of the instability of this process. This mechanism does not rely on the existence of the small-scale turbulence to establish zonal flows. Zonal jets can then be amplified by eddies arranged in certain order in the flow. The underlying dynamics include the propagation of linear and nonlinear basin scale Rossby waves. The related barotropic theory for these waves is developed here. We demonstrate the radiative development of jets and β-plumes in a laboratory experiment using a rotating fluid with a paraboloidal free surface. The dynamical fields are measured by the laboratory analog of the satellite altimetry.     

Structural features of the subauroral ionosphere during the origination of the polarization jet

Narrow jets of rapid westward ion drifts were registered near the plasmapause projection at the F-region altitudes on the Cosmoc-184 satellite and were called “a polarization jet.” In this work, the effect of this polarization jet on the ionospheric structure has been studied, using a three-dimensional model of the high-latitude ionosphere, when strong local magnetospheric electric fields were originated. The calculations indicated that a narrow trough in the latitudinal variations in the electron density at the F-region maximum was formed in the zone where the electric field was switched on. This trough was more pronounced in the early evening hours, when the electron background density was still high, and was less distinct at low back-ground levels during premidnight hours. A comparison of the calculations and experimental data indicated that they were in good agreement with one another, which made it possible to state that the polarization jet was the main mechanism by which narrow electron density troughs were formed in the subauroral ionosphere.     

Interaction between a surface jet and subsurface vortices in a three-layer quasi-geostrophic model

This study focuses on the interaction between mid depth vortices and surface jets and fronts in a three-layer quasi-geostrophic model. Such vortices may be regarded as an idealisation of meddies, eddies of Mediterranean Water in the Northeastern Atlantic Ocean, interacting with the Azores j t and front. Successively, a single vortex, a vortex doublet and a vortex pair (in the middle layer) are studied. When a single vortex is considered, the jet has a critical effect of its motion, temporarily slowing down its zonal drift and accelerating it meridionally as the vortex crosses the front. On the contrary, if the vortex does not cross the front, it can drift fairly rapidly along it. The merger of a vortex doublet (two like-signed vortices) below a surface jet is possible whatever the relative position of this doublet with respect to the jet axis. Nevertheless, doublets initially located below the front, will undergo stronger shear and merger efficiency will be diminished. The merged vortex will be circled at the surface by a large meander of the jet. Finally, eastward jet-dipole interaction experiments are performed with various orientations of the vortex dipoles. Eastward propagating dipoles below the jet follow it without deformation. Southeastward drifting dipoles finally join the previous evolution. Southward and southwestward directed dipoles cross the surface jet southeastward. The presence of meanders initially on the jet does not prevent its crossing by a single vortex. Characteristics of the surface jet meanders are also described for a possible remote detection of this process.     

Magnetic field generation by the motion of a highly conducting fluid

Abstract

Using an asymptotic expansion of Green's function for the problem of magnetic field generation by 3D steady flow of highly conducting fluid a general antidynamo theorem is proved in the case of no exponential stretching of liquid particles. Explicit formulae connecting the spectrum of the magnetic modes with the geometry of the Lagrangian trajectories are obtained. The existence of the fast dynamo action for special flows with exponential stretching is proved under the condition of smoothness of the fields of stretching and non-stretching directions.     

大地电磁数据的Occam反演改进

Occam 反演以其稳定的收敛性,在大地电磁（MT）数据解释中有广泛的应用。但是其每次迭代均用一维搜索方法求拉格朗日因子μ值,需要许多次正演计算,速度非常慢。在讨论了 Occam 反演中数据拟合差随μ变化的基础上,本文采用了μ值在一定步长下逐次递减的求取方法,每次迭代只需一次正演,极大地提高了计算速度。另外,反演求得光滑模型而非最光滑模型,分辨率更高。理论及实际数据的反演试算均表明,和 Occam 反演相比,反演依然稳定,但速度更快,结果也更真实。     

Intensive radiosonde observations of lower tropospheric inversion layers over Yichang,China

Two lower tropospheric inversion layers (named as LTI1 and LTI2) over Yichang (111°18′E, 30°42′N) were studied by using the data from intensive radiosonde observations in January 2007 on an eight-times-daily basis. Our observations reveal that both the inversion layers are closely related to the intensive inertial gravity waves propagating in winter tropospheric jets. However, their formation mechanisms are likely to be different. Gravity-wave-induced intensive turbulence via convective instability may yield a downward energy transport and finally form the LTI1, while we speculate that the reflection of gravity waves by the strong tropospheric jet is responsible for the LTI2.