Ambient Fluid Research Articles

Piezoelectric rod sensors for scour detection and vortex-induced vibration monitoring

As extreme events increase in frequency, flow-disrupting large-scale structures become ever more susceptible to collapse due to local scour effects. The objective of this study was to validate the functionality of passive, flow-excited scour sensors that can continue to operate during an extreme event. The scour sensors, or piezo-rods, feature continuous piezoelectric polymer strips embedded within and along the length of slender cylindrical rods, which could then be driven into the soil where scour is expected. When scour erodes away foundation material to reveal a portion of the piezo-rod, ambient fluid flow excitations would cause the piezoelectric element to output a voltage response corresponding to the dynamic bending strains of the sensor. The voltage response is dependent on both the structural dynamic properties of the sensor and the excitation fluid’s velocity. By monitoring both shedding frequency and flow velocity, the exposed length of the piezo-rod (or scour depth) can be calculated. Two series of experimental tests were conducted in this work: (1) the piezo-rod was driven into sediment around a mock pier to collect scour data, and (2) the piezo-rod was used to monitor its own structural response by collecting vortex-shedding frequency data in response to varied flow velocities to establish a velocity–frequency relationship. The results showed that the piezo-rod successfully captured structural vortex-shedding frequency comparable to state-of-practice testing. A one-dimensional numerical model was developed using the velocity–frequency relationship to increase the accuracy of voltage-based length prediction of the piezo-rod. Two-dimensional flow modeling was also performed for predicting localized velocities within a complex flow field. These velocities, in conjunction with the velocity–frequency relationship, were used to greatly improve length-predictive capabilities.

Convection-induced singularity suppression in the Keller-Segel and other non-linear PDEs

In this paper we study the effect of the addition of a convective term, and of the resulting increased dissipation rate, on the growth of solutions to a general class of non-linear parabolic PDEs. In particular, we show that blow-up in these models can always be prevented if the added drift has a small enough dissipation time. We also prove a general result relating the dissipation time and the effective diffusivity of stationary cellular flows, which allows us to obtain examples of simple incompressible flows with arbitrarily small dissipation times. As an application, we show that blow-up in the Keller-Segel model of chemotaxis can always be prevented if the velocity field of the ambient fluid has a sufficiently small dissipation time. We also study reaction-diffusion equations with ignition-type nonlinearities, and show that the reaction can always be quenched by the addition of a convective term with a small enough dissipation time, provided the average initial temperature is initially below the ignition threshold.

Exploring the versatility of the perfused crustacean gill as a model for transbranchial transport processes.

The study of transbranchial ion and gas transport of water-breathing animals has long been a useful means of modeling transport processes of higher vertebrate organs through comparative physiology. The molecular era of biological research has brought forward valuable information detailing shifts in gene expression related to environmental stress and the sub-cellular localization of transporters; however, purely molecular studies can cause hypothetical transport mechanisms and hypotheses to be accepted without any direct physiological proof. Isolated perfused gill experiments are useful for testing most of these hypotheses and can sometimes be used outright to develop a well-supported working model for transport processes relating to an animal's osmoregulation, acid-base balance, nitrogen excretion, and respiratory gas exchange as well as their sensitivity to pollutants and environmental stress. The technique allows full control of internal hemolymph-like saline as well as the ambient environmental fluid compositions and can measure the electrophysiological properties of the gill as well as the transport rates of ions and gases as they traverse the gill epithelium. Additives such as pharmaceuticals or peptides as well as the exclusion of ions from the media are commonly used to identify the importance of specific transporters to transport mechanisms. The technique can also be used to identify the penetrance, retention, and localization of pollutants within the gill epithelium or to explore the uptake and metabolism of nutrients directly from the ambient environment. While this technique can be applied to virtually any isolatable organ, the anatomy and rigidity of the decapod crustacean gill make it an ideal candidate for most experimental designs.

A ternary phase‐field model for wetting of soft elastic structures

AbstractSoft wetting, that is, the interaction of liquid–fluid interfaces with deformable elastic structures, provides a rich variety of physical phenomena (stick‐slip motion, durotaxis, Shuttleworth effect, etc.) which are not yet understood. We propose a novel phase‐field approach to study such problems. The method uses two phase‐fields to describe the three domains (solid, liquid, ambient fluid) by the ternary Navier–Stokes Cahn–Hilliard equations. We use a recent phase‐field approach for fluid‐structure interaction to equip one phase with elastic properties. The resulting method is significantly simpler than all previous approaches for soft wetting, since no grids are used to represent the geometries. Accordingly, the method avoids grid‐based computation of interface curvature, mappings between different grids, complicated mesh generation, and retriangulation, while the elastic object can move freely through the computational domain. As a special feature, the elastic structure is for the first time represented as a neo‐Hookean Kelvin–Voigt–Maxwell material which makes it very versatile. The accuracy of the method is shown in a benchmark simulation of a droplet on an elastic substrate. The geometrical flexibility is illustrated by simulating a rotating solid object within a fluidic interface. Finally, we provide the first 3D simulations of soft wetting including solid surface tensions.

Laterally accreting sinuous channels and their deposits: The Goldilocks of deep-water slope systems

ABSTRACTChannels with a sinuous planform are common in both continental and deep-marine environments on Earth, and similarly in high-resolution images of the surface of Mars. Whereas common in rivers, continuous lateral channel migration and point-bar deposition appear to be much less common in the deep sea. In the bends of rivers, near-bed flow driving point bar growth results from a cross-flow superelevation of the water surface that sets up a lateral hydrostatic pressure gradient driving an inward-directed flow near the bed. However, in deep-marine systems the surface between the turbidity current and overlying ambient fluid sits well above the channel margins, and therefore precludes a similar lateral superelevation of the current top. Here it is argued that the cross-flow component is related to a density gradient that mimics the effect of the hydrostatic pressure gradient in rivers, and develops as coarse suspended particles that experience little uplift, and therefore negligible overspill, become concentrated along the outer bank. This condition develops best in a two-part suspension made up of a highly concentrated, unstratified basal plug of coarse sediment overlain sharply by a dilute cloud of much finer sediment—a density structure that differs from the more typical upward exponential decrease in density. The abundance of coarse and fine sand, but depletion in the intermediate grain size fraction, is related to transgressive shelf processes and its influence on sediment supplied to the system, and in turn, the flow structure of the current. It is under these seemingly uncommon granulometric conditions that continuous laterally migrating channels, and accordingly, riverine-like point-bar deposition, is most common in the deep sea.

Integral properties of turbulent natural convection over a vertical flat plate

This paper investigates global integrals of the volumetric, momentum and temperature fluxes for turbulent natural convection over a vertical plate (TNCVP). The global integral of the mean continuity equation gives a relation for the mean wall-normal velocity outside the boundary layer as W∞ = − d(∫0∞Udz)/dx where U is the mean velocity in the streamwise x direction and z is the wall-normal direction. The global integral of the mean momentum equation gives a relation for the specific wall momentum flux as uτ2 = gβ∫0∞(Θ∞ − Θ)dz − d(∫0∞U2dz)/dx where uτ is the friction velocity, g is the gravitational acceleration and β is the thermal expansion coefficient. Θ = Tw − T is the difference between the wall temperature Tw and the fluid temperature, and Θ∞ = Tw − T∞ is the difference between the wall temperature and the ambient fluid temperature. Finally, the global integral of the mean heat equation gives a relation for the wall temperature flux as uτθτ = − W∞Θ∞ − d(∫0∞UΘdz)/dx where θτ is the frictional temperature. Based on the global integrals of the momentum and heat fluxes, we propose an indirect determination of uτ and θτ. Given the extreme challenge in direct measurement of uτ and θτ in wall-bounded turbulent flows, the indirect determination proposed here offers a powerful tool to subsequent experimental studies of TNCVP.

Motion and deformation of migrating compound droplets in shear-thinning fluids in a microcapillary tube

The deformation dynamics of a moving compound droplet inside a microcapillary tube is investigated in Newtonian and non-Newtonian ambient fluids. The numerical method used is a ternary phase-field model to determine the temporal evolution and the subsequent hydrodynamics of compound droplets traveling inside a microcapillary tube. By solving the axisymmetric momentum equations, the compound droplet movement is identified by tracing the spatiotemporal evolution of a pair of two deformable interfaces. Results indicate that the rheological properties of the continuous phase significantly influence the compound droplet characteristics. The position of the center of the mass of both inner and outer drops along the tube axis increases linearly in a Newtonian ambient fluid while it is nonlinear in a non-Newtonian medium, and the deviation from the linear behavior increases as the concentration of the polymer solution increases. These distinct behaviors occur after a particular normalized time (t*, which is normalized with R/Uavg in which R is the radius of the tube and Uavg is the average inlet velocity) during the early stages of droplet formation (t*∼1). The migration of the compound drop inside a Newtonian fluid approaches a relatively constant velocity after a specific time of the initial movement. Conversely, the movement velocity of both drops increases gradually until the pinch-off moment in non-Newtonian fluids, which means that a moving compound drop has an accelerative motion in all stages of movement in non-Newtonian fluids. The findings presented here are essential for employing compound droplets in droplet microfluidic systems for biological applications.

Scaling patch analysis of turbulent planar plume

Proper scaling in turbulent planar plumes is investigated here using a scaling patch approach. Based on the scaled boundary conditions, a proper velocity scale for the mean axial flow is the plume centerline velocity Uref=Uctr, and a proper temperature scale for the temperature excess is Θref=Tctr−T∞, where Tctr is the plume centerline temperature and T∞ is the ambient fluid temperature. By seeking an admissible scaling, a key concept in the scaling patch approach, for the mean continuity, mean momentum, and mean energy equations, respectively, the following is found: (1) a proper scale for the mean transverse flow is Vref=(dδ/dx)Uctr, where dδ/dx is the growth rate of the plume width. (2) A proper scale for the Reynolds shear stress is Rvu,ref=UctrVref=(dδ/dx)Uctr2, a mix of the scales for the mean axial and transverse flows. (3) A proper scale for the turbulent heat flux is Rvθ,ref=VrefΘctr, a mix of the scales for the mean transverse flow and mean temperature excess. The mean transverse flow thus plays a critical role in the scaling of turbulent planar plumes. Approximate functions are developed for the scaled mean transverse flow, Reynolds shear stress, and turbulent temperature flux, and are found to agree favorably with experimental and numerical simulation data. The integral analysis of the mean momentum equation yields a Richardson number Ri, which remains invariant in the axial direction. The Richardson number is defined as Ri=defgβΘctrδt/(UctrVref)≈1/2, where g is the gravitational acceleration, β is the thermal expansion coefficient, and δt is the plume half-width based on the mean temperature profile. This Richardson number arises directly from the scaling patch analysis of the mean momentum equation, including both the streamwise and transverse velocity scales.

Velocity and density measurements in forced fountains with negative buoyancy

In fluid mechanics, fountains take place when a source fluid is driven by its own momentum into a surrounding ambient fluid, and it is counterbalanced by buoyancy. These phenomena are largely encountered in nature and human activities. Despite the numerous studies on the subject, few experimental data are available about the internal structure of turbulent fountains. Here, we present a set of laboratory experiments with the aim to (i) get direct velocity and density measurements of fountains in a controlled environment and (ii) obtain insights about the basic physics of the phenomenon. The results concern the characteristics of the mean and turbulent flow: we report the analysis of the turbulent kinetic energy, the velocity skewness, and the Reynolds stresses, including a quadrant analysis of the fluctuating velocities. For some tests, the correlation between density and vertical velocity is investigated for both mean and fluctuating values. We have quantified the momentum transport, which is mainly out-downward at the nozzle axis with peaks at the mean rise height, where also maximum levels of the buoyancy and mass fluxes are present. The ability of acoustic Doppler current profilers to identify the rise height of the fountain and to measure the velocity field is also discussed.

Gravity currents with internal stratification in channels of non-rectangular cross-section

We investigate by theoretical means the motion of a gravity current (GC) released from a lock into an ambient fluid in a horizontal channel of non-rectangular cross-section area (CSA) like triangle, trapezoid or semicircle. The lock contains an internal stratification, in particular a layer of density ρL overlain by a layer of density ρU, where ρo<ρU<ρL and ρo is the density of the ambient fluid. Assuming a Boussinesq and large Reynolds flow, we develop a new self-contained model for the prediction of the motion of the GC, in particular the position and speed of the nose xN(t) and uN(t), where t is the time from release. Upon an appropriate scaling the system of equations and boundary conditions is reduced to a form amenable to analysis and solution by the methods employed for the non-stratified flow. The solution reveals an initial slumping with constant uN, and eventually the transition at xV to the viscous regime. A self similar phase of the form xN∼tβ can develop only for CSA of power-law shape, in which case the constant β depends on the shape but not on the stratification. The stability is also considered, and we show that the flow is stable with few exception. Unfortunately, experimental data for comparisons are not available, and we hope that the sharp present results will motivate the performance of needed experimental tests.

Boussinesq and non-Boussinesq gravity currents propagating on unbounded uniform slopes in the deceleration phase

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Removal of a dense bottom layer by a gravity current

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Triple Oxygen Isotope Paleoaltimetry of Crystalline Rocks

Triple oxygen isotopes of hydrothermally altered minerals from crystalline rocks can be used to determine past elevations of mountain ranges. This method uses all three isotopes of oxygen (16O, 17O, and 18O) to create arrays that can be extrapolated back to the meteoric water line. One advantage of this technique is that it relies only on oxygen isotopes in contrast to previous studies that use oxygen and hydrogen isotopes to determine the isotopic composition of meteoric waters. Our analysis suggests that hydrogen isotopes may exchange with ambient fluids. Triple oxygen isotopes provide an independent check on the reliability of hydrogen isotope studies.

Electrohydrodynamic-induced interactions between droplets

Dispersion of droplets in an emulsion is commonly seen in several chemical, pharmaceutical and petroleum industries. Electric field has been shown to affect the stability of these dispersions. We study the dynamics of a pair of leaky dielectric droplets in a leaky dielectric liquid in the presence of an externally applied electric field. A pair of droplets may coalesce or repel each other in the presence of an electric field. Interactions between a pair of drops have been shown to be governed by the ratio $\varepsilon _r/\sigma _r$ , where $\varepsilon _r$ and $\sigma _r$ are the ratios of drop to ambient fluid electric permittivities and conductivities, respectively. When inertia is neglected, the droplets approach each other if $\varepsilon _r/\sigma _r &gt; 1$ , whereas droplets repel when $\varepsilon _r/\sigma _r &lt; 1$ . However, inclusion of inertia permits interesting transient behaviour, where the droplets may attract due to the electrostatic dipole–dipole attraction even for $\varepsilon _r/\sigma _r &lt; 1$ . The approach velocity then is governed by the electrostatic forces and varies as $1/h^4$ , where $h$ is the separation distance between the droplets, in contrast to being hydrodynamically driven as predicted in the Stokes flow limit by Baygents et al. (J. Fluid Mech., vol. 368, 1998, pp. 359–375). For compound droplets, interactions between droplets are essentially governed by the electrical properties of the outer droplet and the ambient fluid. However, transient dynamics may also result in the breakup of a compound droplet and lead to formation of single droplets.

The convective Stefan problem: shaping under natural convection

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Linear vs non-linear analysis on self-induced vibration of OTEC cold water pipe due to internal flow

This paper presents analytical and numerical analyses on self-induced vibration of Ocean Thermal Energy Conversion (OTEC) Cold Water Pipe (CWP) for a 100 MW-net OTEC power plant. The CWP is described as a vertically-hanged, top-tensioned riser subjected to internal flow effect (IFE) and ambient fluid effects (added mass and drag force). In the analytical analysis, two definitions of the drag force equation in the frequency-domain term and time-domain term are considered yielding a linear differential equation and a non-linear differential equation. The stability is assessed by discretizing the equations using Frobenius method and Galerkin Method and then plotting its eigenfrequencies or its eigenvalues in an Argand diagram. Separately, a fully-coupled fluid-structure interaction is carried out in a numerical simulation for particular cases. The scantlings of the riser are chosen from the available size of Fiber Reinforced Plastic (FRP) pipe in a manufacturer and varied accordingly for future production capacity development. The riser is pinned at the top and mounted at the bottom. Results indicate that the predicted critical velocity in the time domain is averagely 20% higher compared to the frequency domain. The effect of the clump weight on the critical velocity is more significant for light material compared with relatively high-density material.

On gravity currents confined by porous boundaries in containers of general cross-sections

We consider an inertial (large Reynolds number) gravity current (GC) released from a lock of length $$x_0$$ and height $$h_0$$ into an ambient fluid of height $$Hh_0$$ which propagates along a channel with permeable floor and/or walls. The cross section (CS) of the container is defined by the general $$-f_1 (z) \le y \le f_2 (z)$$ for $$0 \le z \le Hh_0$$ , while the top and the bottom are at $$z = Hh_0$$ and $$z=0$$ (z is the physical coordinate measured from the bottom of the channel). We use Boussinesq assumption and formulate the shallow-water equations of motion. These equations include a parameter $$\lambda$$ which reflects the ratio between the typical time of propagation of the current over a length $$x_0$$ to the typical time of the drop of the interface due to porous boundary over a height $$h_0$$ . To solve the problem we employ the method of finite-differences. It is demonstrated that initially, the effect of a porosity of the floor or the walls on the distance of propagation of the GC is insignificant, but the “slumping” stage is absent. During the advanced stages, the porosity slows down the current and decreasing the effective distance of propagation. We illustrate the methodology for flow in symmetric channels with typical power-law CSs $$f_1(z) = f_2(z) = 0.5(c+bz^{\alpha })$$ , where $$b,c, \alpha$$ are non-negative constants and show that for the identical characteristics of the porous material, the presence of the porous floor has more significant effect on the velocity of the propagation of the current than the presence of the permeable walls in all tested forms of containers. Special attention is given to triangular CS channels $$f_{1}(z)=f_{2}(z) = bz$$ with permeable walls. We show that in such containers the volume of the current decreases like $$\exp \left( -\sqrt{1+\frac{1}{b^2}}\lambda t\right)$$ (where t is time) and for $$Hh_0 \gg 1$$ its run-out length can be expressed by a compact analytical formula.

Anatomy of subcritical submarine flows with a lutocline and an intermediate destruction layer

Turbidity currents are sediment-laden flows that travel over a sloping bed under a stagnant ambient fluid, driven by the density difference between the current and the ambient. Turbidity currents transport large amounts of carbon, nutrients and fresh water through oceans and play an important role in global geochemical cycling and seafloor ecosystems. Supercritical currents are observed in steeper slopes. Subcritical currents are observed in milder slopes, where the near-bed and interface layers are prevented from interacting across the velocity maximum. Past works show the existence of such a barrier to vertical momentum transfer is essential for the body of the subcritical current to extend over hundreds of kilometers in length without much increase in height. Here we observe the body of subcritical currents to have a three layer structure, where the turbulent near-bed layer and the non-turbulent interface layer are separated by an intermediate layer of negative turbulence production. We explain the mechanism by which this layer prevents the near-bed turbulent structures from penetrating into the interface layer by transferring energy back from turbulence to the mean flow.

Fire Plume in a Sharply Stratified Ambient Fluid

The present work analyses theoretically and numerically fire plumes evolving in a two-layer stratified environment. The ambient fluid consists of a lower cold (heavy) layer and an upper warm (light) layer with a sharp interface. The fire plume is controlled by the fire heat release rate Q. Depending on the density interface location, the temperatures of the layers and on the fire source conditions, the fire plume can rise indefinitely or can be captured by the density stratification. To determine a criterion between these two situations, a theoretical model is proposed. With this model, it is found that the trapping/escaping criterion of the fire plume is determined in terms of a stratification parameter \(\varLambda > 0.88\). This stratification parameter \(\varLambda\) is a function of the fire heat release, the density interface location and the ambient stratification. The model also allows the plume height to be determined analytically. The comparison with the numerical data shows an excellent agreement. Finally, for practical purposes, we propose a simplified correlation to estimate the height of the trapped plume as a function of the interface height, the temperatures of the layers and the fire heat release rate.

Near-wall forces on a neutrally buoyant spherical particle in an axisymmetric stagnation-point flow

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