Horizontal Velocity Components Research Articles

Estimation of anisotropy parameters in vertical transverse isotropy media using the ray‐based tomography

AbstractIn seismic exploration, it is very important to consider the presence of anisotropy in order to image the subsurface correctly. The knowledge of anisotropic parameters leads to more precise characterization of reservoir, fracture density and flow paths. However, conventional geophysical methods do not directly measure these parameters, and it is useful to have a method to estimate them from seismic data. In the weak transverse isotropy approximation, the fields to be considered are the vertical and horizontal velocity components and the Thomsen parameters and . We present a method for estimating the anisotropic Thomsen parameters in the presence of weak vertical transverse isotropy using P‐wave traveltime tomography based on anisotropic ray tracing. Depending on the available information, we propose different approaches to retrieve the unknowns. A conventional three‐dimensional traveltime tomography algorithm has been extended to include anisotropic ray tracing and using the algebraic reconstruction technique or modified simultaneous iterative reconstruction technique to retrieve the unknowns. We test the method on synthetic examples for the inversion of transmitted and reflected traveltimes, and we evaluate the sensitivity of the tomographic results to the available information. Furthermore, we also consider the case of tilted transverse isotropy in a seismic reflection example.

Wave scattering by [formula omitted]-shaped breakwaters in finite depth water

This article illustrates surface gravity wave scattering by ⊓-shaped and inverse ⊓-shaped breakwaters in water of finite depth. The ⊓-shaped breakwater consists of a thick rectangular structure with two thin vertical plates protruding vertically downward when it is floating on the free surface. An inverse ⊓-shaped breakwater is a bottom-standing structure with two thin plates protruding upwards. The breakwater’s geometrical symmetry is used to simplify the wave scattering problems. Using Havelock expansion of water wave potentials, integral equations of Fredholm type are developed for the horizontal component of fluid velocity across the gap below or above the thin plates. The analysis presents the reflection and transmission coefficients in terms of integrals involving the unknown function of the integral equations. A Galerkin expansion with a collocation method is used to solve the integral equations approximately. The developed method produces the known numerical results for a rectangular breakwater without thin plates. The ⊓-shaped breakwater shows lower wave transmission than a traditional rectangular breakwater. Furthermore, increasing plate length makes the wave transmission even less. Fluid velocity is high in the vicinity of plate edge. By the present method, it is shown that the ⊓-shaped breakwaters offer higher reflection and lower transmission. Thus, attaching thin plates to a traditional rectangular breakwater enhances its performance in wave scattering.

Effect of initial droplet position on coalescence-induced jumping on superhydrophobic surfaces with micropillar arrays

Coalescence-induced droplet jumping holds great potential for applications such as water harvesting, self-cleaning, and the thermal management of electronic devices. This study investigates the impact of the droplet's initial position on coalescence-induced jumping on superhydrophobic surfaces with micropillar arrays. Numerical simulations are conducted to examine the differences in droplet jumping at various initial positions with uniform and nonuniform micropillar distributions, and the effects of the droplet's initial position on its velocity and pressure distribution are analyzed. The findings indicate that altering the initial position produces an asymmetric distribution of the high-pressure region at the droplet's base and the pressure at the solid–liquid contact surface during the contraction of the liquid bridge. This asymmetry allows the droplet to jump away from the surface with both vertical and horizontal components of velocity, and to be transported in the horizontal direction. Furthermore, numerical simulations with various initial droplet positions and radii demonstrate that the direction of the horizontal jumping velocity is influenced by both the offset distance and the direction of the initial droplet position, and that the impact of the initial position decreases as the relative size of the droplet with respect to the micropillars increases. The droplet jumping velocity, direction, and horizontal transport distance can be controlled by adjusting the initial droplet position and size. This work reveals the mechanism of coalescence-induced droplet jumping on superhydrophobic surfaces with micropillar arrays and provides an important reference for practical applications.

Oblique Wave Scattering by a Combination of Two Asymmetric Trenches of Finite and Infinite Depths

Abstract The focal point of the current study lies in investigating oblique wave scattering within the framework of linear potential theory, with particular attention to scenarios involving asymmetric trenches of both finite and infinite depths. By employing the eigenfunction expansion method, the physical problem undergoes a transformation into an equivalent boundary value problem. This newly formulated problem is characterized by a system of four weakly singular integral equations, which pertain to the horizontal component of velocity across the gaps situated above the edges of the trenches. The solution to these integral equations is achieved through the utilization of a multi-term Galerkin approximation method. This approach involves expansions using ultraspherical Gegenbauer polynomials as basis functions, coupled with the appropriate weight functions tailored to address the one-third singularity. Graphical representations are employed to depict the numerical evaluations of reflection and transmission coefficients across various non-dimensional parameters. These visualizations offer insight into the behavior and dependencies of these coefficients under different conditions. To validate the accuracy of the current model, it is compared against previously published results available in the literature.

The Plasma In Situ Detection on China’s Space Station Wentian Module: Instrument Description and First Results

The plasma in situ detector is a multi-sensor package designed to in situ measure the bulk parameters of the local ionospheric plasma. The plasma in situ detector is comprised of three sensors: Langmuir probe (LP), retarding potential analyzer (RPA) and ion drift meter (IDM). LP measures electron density and temperature. RPA measures ion density, temperature and ion horizontal velocity. IDM measures the transverse horizontal component of the ram velocity. The plasma in situ detector has been installed outside the wentian module cabin, and the boom has been successfully deployed which extends the spherical sensor of LP beyond the sheath of the cabin. RPA and IDM were installed at the front of the experiment package, with the horizontal axis direction along the forward flight direction of the space station. This paper discusses the general performance characteristics of the in situ detector, the functional performance of each sensor, and initial results of some classical ionospheric features being observed.

Decouple the effect of the horizontal and vertical components of the collision velocity on interfacial morphology in electromagnetic pulse welding

Decouple the effect of the horizontal and vertical components of the collision velocity on interfacial morphology in electromagnetic pulse welding

Numerical Simulation of Radiatively Driven Convection in a Small Ice-Covered Lake with a Lateral Pressure Gradient

The results of a numerical simulation of radiatively driven convection (RDC) in a small ice-covered lake with a lateral pressure gradient are shown. RDC influences aquatic ecosystems as convective flow transfers heat and dissolved and suspended matter through the water column. There is a hypothesis that a continuum of convective cells with areas of ascending and descending water flows exists in a convective mixed layer (CML). Until now, little has been known about how the structure of the CML changes in lakes with lateral transport. In this work, the evolution of the CML in the computational domain with a lateral pressure gradient over several days is reproduced using an Implicit Large Eddy Simulation. We show that after a few days of lateral pressure gradient occurrence, convective cells are replaced by rolls oriented along the lateral transport direction. The change in the CML’s turbulence patterns under a lateral pressure gradient is confirmed by Anisotropic Invariant Map analysis. The study revealed a heterogeneity of pulsations of the horizontal and vertical velocity components over the entire depth of the CML and showed that when a horizontal gradient is present, the velocity pulsations generally increase.

Direct numerical simulation for lid-driven cavity under various Reynolds numbers in fully staggered grid

Finite difference method in a fully staggered grid is applied to solve the incompressible Navier–Stokes equation with direct numerical simulations. Without a turbulent or transient model, lid-driven cavity simulations are conducted with various Reynolds numbers from 102 to 106. The fluid property is fixed, and a lid velocity is changed to set the Reynolds number condition. Time steps are adjusted to keep the consistency of Courant number conditions. Simulation results are compared with the experimental measurements for a Reynolds number of 104 condition, in which the result shows relatively larger values of non-dimensional root mean square (RMS) compared to the other Reynolds number conditions. Vertical and horizontal velocity components show comparably higher RMS distributions around a downstream eddy region and above a bottom surface region, respectively, when the Reynolds number is 104. Time-averaged and RMS distributions show reasonable agreement with the experimental results, and a velocity spectral analysis shows the Kolmogorov spectrum of −5/3 slope for all velocity components. Taylor–Görtler-like (TGL) vortices are observed clearly in the downstream jet region. When the Reynolds number increases, the size of the TGL vortical structure in the spanwise direction decreases and numerous small-scale vortices occur.

Video Based Estimation of Surface Currents in a Tidal Inlet

Abstract Oceanic surface currents are estimated from analysis of short duration video obtained by a nadir facing camera installed on a bridge over a tidal inlet. Data analyzed consisted of 13 two-minute video clips captured approximately every 40 min over a period of 8 hr, covering a significant portion of the tidal cycle. Surface current speed and direction estimates are obtained from each collected video using (i) a method originally developed for analysis of imagery from drones (CopterCurrents) and (ii) a particle tracking method. The horizontal (u, v) surface current velocity components and total horizontal velocity magnitude, obtained from the two methods, were in very good agreement with each other (R 2 = .96 and Root Mean Square (RMS) differences of 0.12 m/s or less). Our analysis suggests that video cameras from stationary structures can provide surface flow measurements over inland waters and navigational channels where deployment of in-situ sensors is not feasible.

MULTI-LINEAR-ELEMENT DEPTH-INTEGRATED MODELS FOR FLOWS WITH A FREE SURFACE

In this study, we derive a new set of depth-integrated models for solving unsteady flows that satisfy the Euler equations and nonlinear free surface boundary conditions in the sigma -coordinates. One of the obvious differences between the present approach and the ones directly solving the 3D Euler equations using Finite Element Method (FEM) is that in the present model the vertical velocity and the pressure field are eliminated by integrating the continuity equation and vertical momentum equation, respectively. Therefore, the present models only solve the horizontal velocity components and the free surface displacement in the two-dimensional horizontal (2DH) space. The new models are also more advantageous in using fewer elements in the vertical direction while achieving better performance. At this stage, the capability and application of the new models in dealing with free surface wave propagation problems are addressed.

Layer-averaged approximation of Navier–Stokes system with complex rheologies

In this work, we present a family of layer-averaged models for the Navier–Stokes equations. For its derivation, we consider a layerwise linear vertical profile for the horizontal velocity component. As a particular case, we also obtain layer-averaged models with the common layerwise constant approximation of the horizontal velocity. The approximation of the derivatives of the velocity components is set by following the theory of distributions to account for the discontinuities at the internal interfaces. Several models has been proposed, depending on the order of approximation of an asymptotic analysis respect to the shallowness parameter. Then, we obtain a hydrostatic model with vertical viscous effects, a hydrostatic model where the pressure depends on the stress tensor, and fully non-hydrostatic models, with a complex rheology. It is remarkable that the proposed models generalize plenty of previous models in the literature. Furthermore, all of them satisfy an exact dissipative energy balance. We also propose a model that is second-order accurate in the vertical direction thanks to a correction of the shear stress approximation. Finally, we show how effective the layerwise linear approach is to notably improve, with respect to the layerwise constant method, the approximation of the velocity profile for some geophysical flows. Namely, a Newtonian fluid and some complex viscoplastic (dry granular and Herschel–Bulkley) materials are considered.

Regularity criteria via horizontal component of velocity for the Boussinesq equations in anisotropic Lorentz spaces

Abstract In this article, we study the regularity criteria of the weak solutions to the Boussinesq equations involving the horizontal component of velocity or the horizontal derivatives of the two components of velocity in anisotropic Lorentz spaces. This result reveals that the velocity field plays a dominant role in regularity theory of the Boussinesq equations.

PROTECTING THE ENVIRONMENT AROUND POLISH QUARRIES FROM HARMFUL SEISMIC VIBRATIONS CAUSED BY ROCK BLASTING

The paper presents the legal and scientific conditions for Polish researchers to determine the vibration velocity and the radius of the safe zone of seismic vibrations generated during rock blasting. Until now, in Poland and worldwide, it has been assumed that seismic vibrations generated during rock blasting with explosives [BM] propagate circularly with equal energy in each direction. However, this is not always the case. A theoretical analysis of the variation of the tangential magnitude Vy of the vibration velocity as a function of the change of the direction angle was carried out for a circular distribution of the vibration velocity. It was shown that the value of the vibration velocity component at the same distance from the vibration source depends on the directional angle between the line of the blast holes and the line connecting the centre of the surface of the excavated BM block and the measuring point. New relationships have been given that take into account the directional angle in the calculation of the maximum values of vibration velocity necessary for the determination of the resulting damage in the building from the SWD. A dynamic impact scale [SWD] for the assessment of building damage as the vibration velocity acting on the building increases is given and discussed. Vibration velocity diagrams measured during the excavation of BM rock have been presented for circular distributions in accordance with theoretical predictions. A vibration velocity diagram for an elliptical distribution, inconsistent with a circular distribution, measured during the excavation of BM rock is presented. It is shown that the directionality of the horizontal tangential component of the vibration velocity exists for both circular and elliptical distribution of vibration velocity in rock excavation with explosive BM. The technical safety of the building in the area of seismic vibrations is determined by the vibration velocity included in zone II of the scale of dynamic influences [SWD] Fig.6A ,6B.

Control of hybrid nanofluid natural convection with entropy generation: A LBM analysis based on the irreversibility of thermodynamic laws

This article analyzes the irreversibility of the natural convection of water/copper nanofluids in a square enclosure. Thermal entropy generation, frictional entropy generation, and total entropy generation are examined by changing the Hartmann number, thickness and length of baffles, and magnetic field with inclinations angle. Three baffles are mounted on the hot wall of the enclosure. The wall in front of the hot wall is cold and the other walls are insulated. The numerical method is employed for this analysis using the Lattice Boltzmann method. The results of this study demonstrate that an increment in the Ha reduces the horizontal and vertical velocity components ​​of the water/copper nanofluids in the enclosure and reduces the temperature gradient. Also, an enhancement in the Ha reduces all types of ETG. An increment in the angle of the magnetic field enhances thermal entropy generation, frictional entropy generation, and total entropy generation. Enhancing the magnetic field, first decreases and then increases the Bejan number.

Alternated Gravel Mounts With Artificial Assembled Boulders Reinforcement Inside Channelized Rivers

Alternated gravel mounts are expected to be a simpler and more cost-efficient alternative to traditional river restauration strategies. To improve their stability, two layers of assembled boulders are placed like fallen dominoes facing downstream around the triangular shape of each mount. Further assembled boulders are placed along both sides of the channel. The ecological improvements are quantified by the definition of refuge, i.e. anywhere inside the flow where fishes might escape the flooding’s force. In this paper, the needs of small sized fishes are considered (body length under 0.30 m). Point gauge and electrical-magnetic current meter are used to measure elevation and horizontal velocity components, respectively. The channel slope is kept at 0.01, while four different discharges are researched. The collected results are very promising: the introduction of assembled boulders is very important to maintain the model’s stability and flatten the water surface along the sides of the channel. The gravel mounts’ triangular shape successfully forces the flow to meander. Areas with slow flowing water are generated near the gravel bed along the channel’s sides. There, the requirements for the definition of refuge are met. As the water volume increases, the flow straightens, particularly inside the channel’s centre, but the refuge able areas are still forming. Each gravel mount is expected to generate a volume suitable for refuge as large as 40% of its own, with limiting factors such as flood’s discharge or shallow water conditions having little effect on this performance.

Electrokinetic cells powered by osmotic gradients: an analytic survey of asymmetric wall potentials and hydrophobic surfaces

Nowadays, the fabrication of microelectromechanical systems has given rise to several studies whose main purpose is to obtain the greater benefit of micro-nano scales, putting special interest in the improvement of the design of such devices. One of several applications is harvesting energy due to electrokinetic phenomena, more specifically, streaming potential. Nonetheless, there is a lack of theoretical studies encompassing coupled asymmetries in both slip conditions and electric potentials (these being associated with the chemical and physical characteristics of the surfaces). By virtue of the previous explanation, ideal assumptions based on the symmetry of some variables must be reconsidered, especially when manufacturing symmetric flat surfaces on a tiny scale is quite difficult to achieve. This work presents a theoretical study in power generation, exploiting streaming potentials produced by an asymmetric membrane which in turn prompts a flux inside a microchannel made of two flat parallel surfaces. The driving force in this electrokinetic battery is the osmotic gradient on both sides of the membrane. The model uses the Debye–Hückel approximation together with the appropriate asymmetric boundary conditions for both slips and potentials on the surfaces. The main variables of interest, such as the dimensionless horizontal velocity component, the pressure field, and the average streaming potential, were estimated.

Stability and decay rate of smooth solutions for the 3D Boussinesq equation with partial horizontal dissipation and thermal damping

In this paper, we investigate the stability and large time behavior of some three dimensional Boussinesq equations with the horizontal dissipation in the horizontal velocity components and thermal damping. Due to the lack of vertical dissipation in the horizontal velocity components and full dissipation in the vertical velocity component, these problems becomes very challenging. Combining the higher order Sobolev norm of the velocity and the temperature and decay estimates of the lower order Sobolev norm of the velocity and the temperature, the stability issue and precise decay rates have been built. The most difficulty is to estimate L1-norm of ‖∇hu‖L∞ in time variable t.

Reynolds number scaling and energy spectra in geostrophic convection.

We report flow measurements in rotating Rayleigh-Bénard convection in the rotationally-constrained geostrophic regime. We apply stereoscopic particle image velocimetry to measure the three components of velocity in a horizontal cross-section of a water-filled cylindrical convection vessel. At a constant, small Ekman number Ek = 5 × 10-8 we vary the Rayleigh number Ra between 1011 and 4 × 1012 to cover various subregimes observed in geostrophic convection. We also include one nonrotating experiment. The scaling of the velocity fluctuations (expressed as the Reynolds number Re) is compared to theoretical relations expressing balances of viscous-Archimedean-Coriolis (VAC) and Coriolis-inertial-Archimedean (CIA) forces. Based on our results we cannot decide which balance is most applicable here; both scaling relations match equally well. A comparison of the current data with several other literature datasets indicates a convergence towards diffusion-free scaling of velocity as Ek decreases. However, the use of confined domains leads at lower Ra to prominent convection in the wall mode near the sidewall. Kinetic energy spectra point at an overall flow organisation into a quadrupolar vortex filling the cross-section. This quadrupolar vortex is a quasi-two-dimensional feature; it only manifests in energy spectra based on the horizontal velocity components. At larger Ra the spectra reveal the development of a scaling range with exponent close to -5/3, the classical exponent for inertial-range scaling in three-dimensional turbulence. The steeper Re(Ra) scaling at low Ek and development of a scaling range in the energy spectra are distinct indicators that a fully developed, diffusion-free turbulent bulk flow state is approached, sketching clear perspectives for further investigation.

Example of a solution for Dorodnitzyn’s limit formula

In the present paper, we show an example of a solution for Dorodnitzyn’s gaseous boundary layer limit formula. Oleinik’s no back-flow condition ensures the existence and uniqueness of solutions for the Prandtl equations in a rectangular domain R⊂R2. It also allowed us to find a limit formula for Dorodnitzyn’s stationary compressible boundary layer with constant total energy on a bounded convex domain in the plane R2. Under the same assumption, we can give an approximate solution u for the limit formula if |u|<<<1 such that: u(z)≅δ∗c∗z+625⋅12i0⋅4U23z4+o(z5),that corresponds to an approximate horizontal velocity component when a small parameter ϵ given by the quotient of the maximum height of the domain divided by its length tends to zero. Here, c>0, δ is the boundary layer’s height in Dorodnitzyn’s coordinates, U is the free-stream velocity at the upper boundary of the domain, and T0 is the absolute surface temperature.

Long Wave Induced Monopolar Vortex: Additional Large Eddy Simulation Case

An additional 3D large eddy simulation with a slightly different surface tension coefficient is carried out to study the detailed flow and turbulence characteristics of a long wave induced shallow water monopolar vortex. The numerical model adopted in this study is interDyMFoam, developed based on an OpenFOAM framework. The numerical model solves filtered Navier-Stokes equations for two immiscible fluids (air, water) with a standard Smagorinsky closure. In addition to the previous model results, newly obtained instantaneous model results are used to increase a number of realizations for ensemble averaging to reach more statistically converged results. The validation quality obtained in this study is shown to be similar to that from the previous simulation results in the low-pass filtered free surface elevation and horizontal component of velocity.