Vortex Initiation Research Articles

Research on the prediction model of energy separation effect of vortex tube based on trajectory deflection characteristics and its numerical solution method

In this paper, in order to establish the energy separation mechanism of the vortex tube, the hydrodynamic behavior of the compressible fluid in the asymmetric cavity space is investigated, and a numerical model of the trajectory deflection behavior is deduced and established; in order to form the optimal design method of the structural parameters of the vortex tube, the force situation of the fluid microelements entering different regions of the vortex chamber of the vortex tube is analyzed, and the trajectory deflection equations are corrected by combining with the expansion behavior of the fluid and the characterizing equations of vortex strength, transportability, and vortex initiation characteristics are given. The characterization equations of vortex strength, transportability and vortex initiation characteristics are given, and the numerical simulation of their influence parameters is carried out; in order to realize the prediction of the vortex tube performance of a given structure, the multifactor Pearson thermodynamic map is used to correlate and analyze the experimental data of vortex tubes reported publicly in the past years, and the polynomial regression equations are designed and established for the prediction of the vortex tube's energy separation effect and the confidence level and the degree of coincidence of the prediction results are examined. The confidence level and degree of agreement of the prediction results were examined. It is found that: the trajectory deflection motion of the compressible fluid in the asymmetric cavity space is the result of the combined effect of structural air pressure bias and the expansion behavior of the incident fluid; in order to improve the vortex strength in the vortex tube, the vortex initiation chamber space should be as small as possible; the increase of the diameters of the hot-end pipe and the cold-end pipe is conducive to the enhancement of vortex strength, but at the same time, it weakens the vortex transport in the heat pipe; the vortex initiation chamber size has a negative correlation with the hot-end temperature rise, and the inlet fluid pressure has a The negative correlation between the size of the vortex chamber and the temperature rise at the hot end, the positive correlation between the increase of inlet fluid pressure and the resulting temperature rise, and the strong correlation between the inlet fluid pressure and the friction coefficient on the effect of energy separation; the predictive equations for the effect of energy separation obtained by the fitting are in good agreement with the real situation.

Experimental and Numerical Investigations of Mini-Tab Device for Active Flow Control

The next generation of aircraft is likely to exhibit a breadth of aeromechanic and aeroelastic behaviors that will be exacerbated by the turbulent flows generated in urban environments. Exploitation of novel flow control technologies will be critical in offering greater control authority to enable this new generation of aerial vehicles for faster, safer, and more efficient flight. This study experimentally investigates the efficacy of a mini-tab active flow control device using a novel dynamic test rig. Under steady conditions, the mini-tab response exhibited nonlinearity with deployment height. Under dynamic conditions, the lift and pitching moments displayed hysteresis around their quasi-steady counterparts at low reduced frequencies (k=0.05) but displayed significant deviations at middle to high reduced frequencies (k=0.15 to 0.31) due to the formation of a tab vortex that propagates downstream. It was demonstrated, for the first time experimentally, that mini-tab dynamic performance is insensitive to unsteady airfoil motions in pitch and plunge—representative of flutter onset. Finally, an existing mini-tab model was extended to capture vortex formation on the upper and lower airfoil surfaces and modified to incorporate mini-tab rate-dependence on vortex initiation. The model showed good agreement with experimental data in both periodic and transient scenarios.

Origin and Evolution of Synoptic-Scale Vortices Initiated at Low Level Downwind of the Hoggar Mountains

Abstract Numerous low-level vortices are initiated downwind of the Hoggar Mountains and progress toward the Atlantic coast on the northern path of African easterly waves (AEWs). These vortices occur mostly in July and August and more specifically when the northern position of the Saharan heat low (SHL) generates stronger and vertically expanded easterly winds over the Hoggar Mountains. At synoptic time scales, a composite analysis reveals that vortex initiation and westward motion are also statistically triggered by a reinforcement of these easterly winds by a wide and persistent high pressure anomaly developing around the Strait of Gibraltar and by a weak wave trough approaching from the east. The vortices are generated in the lee of the Hoggar, about 1000 km west of this approaching trough, and intensify rapidly. The evolution of the vortex perturbation is afterward comparable with the known evolution of the AEWs of the northern path and suggest a growth due to dry barotropic and baroclinic processes induced in particular by the strong cyclonic shear between the reinforced easterly winds and the monsoon flow. These results show that vortex genesis promoted by changes in orographic forcing due to the strengthening of easterly winds over the Hoggar Mountains is a source of intensification of the northern path of AEWs in July and August. These results also provide a possible mechanism to explain the role of the SHL and of particular midlatitude intraseasonal disturbances on the intensity of these waves.

Experimental study on the combined effects of patch density and elongation on wake structure behind a rectangular porous patch

This paper presents an experimental study on how both variable solid volume fractions and aspect ratios (length/width) of a centre-channel rectangular porous patch under aligned configuration of rigid and emergent stems impact the flow behaviour and wake structure. This study forms an essential extension to the existing fundamentals and knowledge on this topic. Through rigorous experimental tests by velocity measurement and dye visualization, the aspect ratio, rarely addressed before, is confirmed to play a critical role. Vortex street, unable to be triggered under a low solid volume fraction, however, can be generated by elongating the patch (increasing the aspect ratio). The key reason is that patch elongation promotes the generation of the wake vortex street by producing a relatively high transverse velocity gradient in the wake region. Meanwhile, Kelvin–Helmholtz vortex streets are triggered along the two patch lateral edges, re-increasing the in-patch velocity and imposing contributions to the wake vortex streets generation. By scaling the characteristic velocity (at the wake vortex initiation position and patch trailing edge) and solid volume fraction with the patch aspect ratio, three non-dimensional threshold maps can be established to express the combined effects of the solid volume fraction and aspect ratio on the initiation of the wake vortex street. They could be alternatively used for theoretical analysis and implementation on wake formation and structure subject to parameter availability.

Study on influence of admissions on loss generation in a twin-entry nozzleless radial turbine

Twin-entry radial turbine has an evident advantage of enhancing the output power in internal combustion engine, while it is confronted by complex inlet conditions because of the interval flow feeding into two limbs. Although the performance of twin-entry turbine is notably influenced by admission conditions, detailed flow mechanism is yet fully revealed in previous researches. This paper investigates the mechanism of the influence by different admissions on a nozzleless twin-entry turbine via experimentally validated numerical methods. Turbine performance is studied under different admission conditions and the results demonstrate that twin-entry turbine performance is notably different between two partial admission conditions, although the volute passage is symmetrically divided. Rotor decomposition methods are employed for the analysis of loss distributions to understand this performance difference. Flow separation and tornado vortex generated near the rotor inlet is confirmed as the key source for the flow loss in the rotor. The off-design incidence angle near the hub rather than the shroud is the reason for the vortex initiation in the twin-entry turbine. Moreover, the volute flow features demonstrate that volute leakage flow is the reason for the lower incidence angle near the blocked limb. Consequently, the mechanism of the asymmetric performance of the symmetric twin-entry turbine under partial admission conditions is revealed.

A leading-edge vortex initiation criteria for large amplitude foil oscillations using a discrete vortex model

A leading-edge vortex initiation criterion of an oscillating airfoil is shown to provide a means to predict the onset of leading-edge separation. This result is found to collapse the occurrence of separation during the oscillation cycle when scaled using the leading-edge shear velocity determined from the foil oscillating kinematic motion. This is of importance in developing low order models for predicting energy harvesting performance, as is shown in this study using an inviscid discrete vortex model (DVM). Results are obtained for a thin flat airfoil undergoing sinusoidal heaving and pitching motions with reduced frequencies of k=fc/U∞ in the range of 0.06–0.16, where f is the heaving frequency of the foil, c is the chord length, and U∞ is the freestream velocity. The airfoil pitches about the mid-chord, and the heaving and pitching amplitudes of the airfoil are ho=0.5c and θ0=70°, respectively, illustrating results for conditions near peak efficiency for energy harvesting. The DVM uses a panel method, applicable to a wide range of foil geometries. An empirical trailing-edge separation correction is also applied to the transient force results. The vortex shedding criterion is based on the transient local wall stress distribution determined using a computational fluid dynamics (CFD) simulation, indicating the time and location of zero stress at the foil surface. In addition, the local pressure gradient minimum is also used as a local indicator. The effects of a wide range of Reynolds numbers on separation are shown for the given range of reduced frequencies. The use of the effective angle of attack, when modified to include the pitching component, is also shown to correlate the leading-edge vortex initiation time. The advantage of the proposed separation criteria is that it can be fully determined from the motion kinematics and then applied to a wide range of low order models. Model results are given for the transient lift force and compare well with the CFD simulations. It is noted that at higher reduced frequencies the DVM overpredicts portions of the transient loads possibly caused by the reversed viscous flow from the trailing edge.

Flow dynamics and azimuthal behavior of the self-excited acoustic modes in axisymmetric shallow cavities

Self-excitation of acoustic resonance in axisymmetric cavities can lead to a complex flow–acoustic coupling, which may result in severe noise generation. In this work, a large eddy simulation is performed to model the different flow–sound coupling mechanisms during the self-excitation of various excitable acoustic modes in an axisymmetric shallow cavity configuration with an aspect ratio of L/d = 1 over the lock-in region. The compressible Navier–Stokes equations are solved at a resolution sufficient to capture the flow and the acoustic dynamics. The excitation of three acoustic modes of different aerodynamic characteristics over the range of the tested flow velocities was observed. These modes are a stationary diametral mode, a spinning diametral mode, and a longitudinal mode. The initiation and separation of vortices over the cavity mouth accompanying the self-excitation of each mode involve different dynamics. If two antisymmetric series of vortical crescents separate successively at the leading edge, a stationary acoustic mode is excited. The formation of a continuously rotating helical vortex, connecting the leading edge and the trailing edge, leads to the excitation of the diametral spinning mode. The excitation of the longitudinal mode is associated with symmetric rings of vortices. Complex patterns of flow velocities and Reynolds stresses in the circumferential direction are observed for the diametral modes but not for the longitudinal mode. In all cases, the excitation of acoustic resonance requires a synchronization of the vortex separation and impingement processes, which is necessary for efficient feedback to sustain the flow–sound coupling mechanism.

Electrostatic Disturbances of Aerosol Atmospheric Plasma: Beaded Lightning

Numerous sources produce the ionization impact on the planetary atmosphere. The tropospheric cloudiness therewith is originated at such altitudes, which coincide with places of the maximum of the atmospheric ionization that caused by space radiation. Components of cosmic radiation, penetrating down to the stratospheric and tropospheric altitudes, produce in the first place the ionization of aerosols that brings to subsequent amplifying the activity of atmospheric vortices. The ionized aerosol constituent is of primary importance both in the initiation of plasma vortices and in the concentration of energy-mass by air vortices due to the humidity condensation. The ionization process is cascading, that causes the non-linear impact of penetrating rays, which amplifying with growing the air pollution. Various heterogeneities inside plasma subsystems provoke the random intensification of aperiodic electrostatic disturbances, which can exert a significant action on the development of vortices. Sometimes beaded lightning arises during thunderstorm. Using the approach of the Boltzmann kinetic equation, the characteristics of electrostatic oscillations for non-uniform plasma, are analytically derived. The analytical expressions are obtained for non-magnetized plasma. In the limits of the Earth’s atmosphere, these solutions are strictly applicable to the origination of electrostatic modulations along the lines of force of the geomagnetic field and approximately applicable in cases, when the impact of the Earth’s magnetic field is negligible. The explicit expressions are deduced both in the hot plasma approximation and in the cold plasma approximation. It is demonstrated that the formation of chain elements of discharge in hot inhomogeneous plasma is defined by the nonmonotonic distribution of charges and fields. At such conditions, the irregularities breaks up into a cellular structure.

Model Reduction in Discrete-Vortex Methods for Unsteady Airfoil Flows

Discrete-vortex methods are a class of low-order methods widely used to study unsteady aerodynamic phenomena. However, these methods demand high computational costs when subject to large number of vortices in the flowfield. This calls for model reduction in discrete-vortex methods. A model-reduction technique is applied to a recently developed discrete-vortex method in which the criticality of the leading-edge suction parameter (LESP) controls the initiation and termination of leading-edge vortices (LEVs). This method, called the LESP-modulated discrete-vortex method (LDVM), has been successfully used in recent work to study unsteady airfoil flows with LEV shedding. In this research, model reduction in the LDVM is achieved by amalgamating suitable pairs of discrete vortices identified through a condition that requires that the velocity at the airfoil leading edge is not affected by amalgamation. The amalgamated vortex is placed at an optimal location to ensure that the bound circulation and the leading-edge suction are conserved. The reduced-order model is able to predict the flow features and the force and moment coefficients in good agreement with the full model while having significantly lower runtimes. Use of physical quantities like leading-edge suction and bound circulation enables the easy implementation of this model-reduction strategy in other computational methods based on discrete-vortex elements.

Effect of pulsation on the near flow field of a submerged water jet

The current study investigates the effect of pulsation frequency on the near field characteristics of a submerged water jet using the technique of dye visualization. Flow visualization was performed in water over the range: Reynolds number 540–1540, Strouhal number 0.16–1.75, and at constant amplitude of pulsation of 18%. The results show that the mixing and entrainment process at lower Reynolds number occurs due to diffusion process owing to relatively stable shear layer for the case of a steady jet, whereas the external pulsation promotes an early instability in the shear layer where irregular structures promotes mixing between the jet and surrounding fluids. Images of streaklines show that initial mixing and entrainment processes in the potential core of the jet is due to the development of large vortical structures. While beyond the potential core, mixing and entrainment are governed by the small-scale structures. Further results show that the initiation and growth of vortices in the shear layer depends on the pulse frequency. For a given Reynolds number and amplitude, the number of vortical structures and their size changes with frequency. With an increase in the pulsation frequency, there is an increase in the spreading of the jet along with stretching of the vortical structures. An optimum pulsating frequency at which the effect of pulsation on the flow is maximum occurs at St = 0.44, independent of Reynolds number. These results should eventually lead to a better understanding of the physical phenomena responsible for enhanced mixing and entrainment processes in the presence of pulsating jets.

Leading-edge flow criticality as a governing factor in leading-edge vortex initiation in unsteady airfoil flows

A leading-edge suction parameter (LESP) that is derived from potential flow theory as a measure of suction at the airfoil leading edge is used to study initiation of leading-edge vortex (LEV) formation in this article. The LESP hypothesis is presented, which states that LEV formation in unsteady flows for specified airfoil shape and Reynolds number occurs at a critical constant value of LESP, regardless of motion kinematics. This hypothesis is tested and validated against a large set of data from CFD and experimental studies of flows with LEV formation. The hypothesis is seen to hold except in cases with slow-rate kinematics which evince significant trailing-edge separation (which refers here to separation leading to reversed flow on the aft portion of the upper surface), thereby establishing the envelope of validity. The implication is that the critical LESP value for an airfoil–Reynolds number combination may be calibrated using CFD or experiment for just one motion and then employed to predict LEV initiation for any other (fast-rate) motion. It is also shown that the LESP concept may be used in an inverse mode to generate motion kinematics that would either prevent LEV formation or trigger the same as per aerodynamic requirements.

Role of the Convection Scheme in Modeling Initiation and Intensification of Tropical Depressions over the North Atlantic

Abstract The authors analyze how modifications of the convective scheme modify the initiation of tropical depression vortices (TDVs) and their intensification into stronger warm-cored tropical cyclone–like vortices (TCs) in global climate model (GCM) simulations. The model’s original convection scheme has entrainment and cloud-base mass flux closures based on moisture convergence. Two modifications are considered: one in which entrainment is dependent on relative humidity and another in which the closure is based on the convective available potential energy (CAPE). Compared to reanalysis, TDVs are more numerous and intense in all three simulations, probably as a result of excessive parameterized deep convection at the expense of convection detraining at midlevel. The relative humidity–dependent entrainment rate increases both TDV initiation and intensification relative to the control. This is because this entrainment rate is reduced in the moist center of the TDVs, giving more intense convective precipitation, and also because it generates a moister environment that may favor the development of early stage TDVs. The CAPE closure inhibits the parameterized convection in strong TDVs, thus limiting their development despite a slight increase in the resolved convection. However, the maximum intensity reached by TC-like TDVs is similar in the three simulations, showing the statistical character of these tendencies. The simulated TCs develop from TDVs with different dynamical origins than those observed. For instance, too many TDVs and TCs initiate near or over southern West Africa in the GCM, collocated with the maximum in easterly wave activity, whose characteristics are also dependent on the convection scheme considered.

A DPIV study on the effects of separation distance upon the vortical behaviour of jet–cylinder impingements

An experimental investigation based on laser-induced fluorescence (LIF) and digital particle image velocimetry (DPIV) was conducted to provide a better understanding into the effects of jet–cylinder separation distance on the vortical structures and dynamic behaviour resulting from jet impingements upon convex cylinders. Separation distances of 1, 2 and 4 jet diameters were investigated, while cylinder–jet diameter ratio was maintained at 2 throughout. LIF and DPIV results show that jet ring-vortex initiation, wall-separated vortex initiation, vortex dipole formation and vortex separation occur further away from the impingement point as the separation distance decreases. Varying the separation distance also influences the recirculating wake region size at the cylinder lee sides, as well as producing two distinct flow modes between adjacent vortex dipoles along the cylinder straight edges. Mean and instantaneous skin friction coefficient distributions determined from DPIV results not only showcase the different effects of separation distance on the wall shear stress, but also illustrate how the flow dynamics influence the local wall shear stress levels. On the other hand, wall-separated vortex initiation, vortex dipole formation and separation events incur little distinctive changes upon the local wall shear stress distributions that may ease their unique identification.

A Climatology of Subtropical Cyclones in the South Atlantic

A 50-yr climatology (1957–2007) of subtropical cyclones (STs) in the South Atlantic is developed and analyzed. A subtropical cyclone is a hybrid structure (upper-level cold core and lower-level warm core) with associated surface gale-force winds. The tendency for warm season development of North Atlantic STs has resulted in these systems being confused as tropical cyclones (TCs). In fact, North Atlantic STs are a regular source of the incipient vortices leading to North Atlantic TC genesis. In 2004, Hurricane Catarina developed in the South Atlantic and made landfall in Brazil. A TC system had been previously unobserved in the South Atlantic, so the incidence of Catarina highlighted the lack of an ST climatology for the region to provide a context for the likelihood of future systems. Sixty-three South Atlantic STs are documented over the 50-yr period analyzed in this climatology. In contrast to the North Atlantic, South Atlantic STs occur relatively uniformly throughout the year; however, their preferred location of genesis and mechanisms for this genesis do exhibit some seasonal variability. Rossby wave breaking was identified as the mechanism for the ST vortex initiation for North Atlantic STs. A subset of South Atlantic STs forms via this mechanism, however, an additional mechanism for ST genesis is identified here: lee cyclogenesis downstream of the Andes in the Brazil Current region—an area favorable for convection. This formation mechanism is similar to development of type-2 east coast lows in the Tasman Sea off eastern Australia.

Vortex formation by a vibrating cantilever

This paper presents a comparative investigation between numerical flow simulations and the experimental data of a vibrating cantilever. The unsteady flow fields were observed with smoke visualization, and the unsteady velocities were measured by high-resolution PIV (particle image velocimetry). Although the experimental results provide an intuitive understanding about the vortex formation from the vibrating cantilever, it is difficult to determine the underlying mechanism of vortex generation due to the limitation of temporal and spatial resolution. Numerical simulations were conducted using commercial code with a user-defined function describing the cantilever movement. The comparison between the experiment and simulation mainly covers velocity fields, vorticity distributions and the vortex location as well as the vortex size during one cycle. Qualitatively, velocity and vorticity distributions match well between the experiment and the simulation. The size and axial location (with respect to the cantilever tip) of the vortices are also in good agreement with the experimental data. Once validated, numerical simulations provide access to the whole flow field including pressure data. The flow has been evaluated in detail to understand vortex generation at the cantilever. It was found that the static pressure difference across the tip plays an important role in the formation and development of each individual vortex. In addition, it was possible to find the exact moment of vortex initiation using the static pressure difference across the cantilever tip.

G040084 超音波援用メカニカルクリンチングの撹拌作用発現メカニズムに対する組織学的考察([G04008]機械材料・材料加工部門一般セッション(8))

Clinching is one of a remarkable joining method for aluminum sheets because of its high productivity, recyclability and possibility to reduce costs. We have studied about the effects of ultrasonic vibrations on the improvement of peeling strength of clinched joint. Through this study, we found a remarkable phenomenon named stirring phenomenon by ultrasonic stress vibrations; in case ultrasonic stress vibrations were applied to clinching tools, vertical material flows were created and materials were stirred and unified finally. This phenomenon can be a core technology for a new joining method and a new grain refinement method. Therefore, clarification of generation mechanism of this phenomenon is required. In this study, thin aluminum sheets were clinched under various conditions of ultrasonic vibrations. And we observed metallographic changes in the earlier stage of the vortex initiation. As a result, the location where the driving force of stirring effect was generated was revealed. And mechanism for generation of this driving force was discussed considering a unique metallographic structure.

Climatology of Tropical Cyclogenesis in the North Atlantic (1948–2004)

Abstract The threat posed to North America by Atlantic Ocean tropical cyclones (TCs) was highlighted by a series of intense landfalling storms that occurred during the record-setting 2005 hurricane season. However, the ability to understand—and therefore the ability to predict—tropical cyclogenesis remains limited, despite recent field studies and numerical experiments that have led to the development of conceptual models describing pathways for tropical vortex initiation. This study addresses the issue of TC spinup by developing a dynamically based classification scheme built on a diagnosis of North Atlantic hurricanes between 1948 and 2004. A pair of metrics is presented that describes TC development from the perspective of external forcings in the local environment. These discriminants are indicative of quasigeostrophic forcing for ascent and lower-level baroclinicity and are computed for the 36 h leading up to TC initiation. A latent trajectory model is used to classify the evolution of the metrics for 496 storms, and a physical synthesis of the results yields six identifiable categories of tropical cyclogenesis events. The nonbaroclinic category accounts for 40% of Atlantic TCs, while events displaying perturbations from this archetype make up the remaining 60% of storms. A geographical clustering of the groups suggests that the classification scheme is identifying fundamentally different categories of tropical cyclogenesis. Moreover, significant differences between the postinitiation attributes of the classes indicate that the evolution of TCs may be sensitive to the pathway taken during development.

Computational study of scalar mixing in the field of a gaseous laminar line vortex

A computational study of scalar mixing in a laminar vortex is presented for vortices generated between two gas streams (one seeded and another unseeded) flowing parallel to each other in a rectangular flow channel. An isolated line vortex is initiated by momentarily increasing one of the stream velocities in relation to the other in otherwise equal velocity, co-flowing streams separated upstream by a splitter plate. A detailed parametric study was conducted to determine the effects of vortex strength, convection time, and nonuniform temperature on scalar mixing characteristics. A qualitative relationship was developed between the vortex and the convection Reynolds numbers to obtain a well-defined vortical structure. As it is well-known in the literature on mixing layers, the vortex initiation process creates an abundance of the fluid in the vortex core from the pulsed (or high speed) stream. Spatial mixing statistics are obtained in the vortex interaction domain by determining the scalar concentration probability density functions as well as the mean mixed fluid concentration and its variance. Computational results are found to be in excellent agreement with the experiments conducted in the same configuration by one of the authors. Both computations and experiments suggest that the interfacial area generation as a result of vortex interaction is primarily responsible for mixing augmentation at high vortex Reynolds numbers (Rev≥140). Effects of molecular diffusion become more important for weak vortices and at short convection times. Temperature (or density) ratio between co-flowing streams clearly affects the rate of growth of the vortices and this is consistent with the findings in nonuniform density mixing layers. Nonuniform temperatures result in a decrease of the mean mixed fluid concentration regardless of the stream from which the vortex is generated. The mean mixed fluid concentration in the vortex interaction region scales with the product of vortex Reynolds number and nondimensional convective time scale (or degree of stirring) and inversely with temperature ratio. Empirical correlations were developed for this parameter for vortices generated from either stream.

Scalar mixing in the field of a gaseous laminar line vortex

An experimental study of scalar mixing in a laminar vortex is presented for vortices generated between two gas streams flowing parallel to each other in a rectangular flow channel. An isolated line vortex is initiated on demand by momentarily increasing one stream velocity in relation to the other using an electromagnetically actuated piston. The temporal piston motion profile is tailored to generate vortices of different strengths corresponding to vortex Reynolds numbers, Re≡Γ/2πν=130–210. Evolution of mixing is monitored by laser-induced fluorescence of acetone vapor premixed into one of the gas streams as the vortex structure evolves with increasing downstream distance from its point of origin. Vortex is generated by pulsing either of the gas streams (seeded or unseeded stream). Vortex initiation process affects the abundance of the gas in the vortex core from the pulsed stream. Spatial mixing statistics are obtained by determining scalar concentration probability density functions (pdf) and the mean mixed fluid concentrations obtained from these pdfs. It is found that the interfacial area generation as a result of vortex kinematics and molecular diffusion along this interface are principally responsible for mixing. The mean mixed fluid concentration in the vortex interaction region scales with the product of vortex circulation and the elapsed time of interaction. These results are similar to those found in liquid mixing experiments, but the rate of mixing is significantly higher due to higher diffusivity of gases.

Wave-induced longitudinal vortices in a shallow current

An instability theory is presented for the initiation of longitudinal vortices due to waves interacting with a turbulent current in an open channel of finite depth. With a simple model of eddy viscosity the dimensionless shearing rate of the basic current is much weaker than the dimensionless velocity almost everywhere except near the bed. We shall show that in addition to the internal vortex force, a mean shear stress exists on the mean sea level, owing to nonlinear wave–current interactions, despite the absence of wind. This stress adds vertical vorticity to the interior and augments the vortex force mechanism of instability significantly. Effects of current strength and wave conditions on the unstable growth are studied by numerical examples.