Showing papers on "Vortex published in 1970"
TL;DR: In this article, the authors considered the early stages of the formation of a train of vortex rings and found that their stability depends on the products of vortex separation 6 and cutoff distance d times the perturbation wavenumber.
Abstract: x(/3) Trailing vortices do not decay by simple diffusion. Usually they undergo a symmetric and nearly sinusoidal instability, until eventually they join at intervals to form a train of vortex rings. The present theory accounts for the instability during the early stages of its growth. The vortices are idealized as interacting lines; their core diameters are taken into account by a cutoff in the line integral representing self-induction. The equation relating induced velocity to vortex displacement gives rise to an eigenvalue problem for the growth rate of sinusoidal perturbations. Stability is found to depend on the products of vortex separation 6 and cutoff distance d times the perturbation wavenumber. Depending on those products, both symmetric and antisymmetric eigenmodes can be unstable, but only the symmetric mode involves strongly interacting long waves. An argument is presented that d/b = 0.063 for the vortices trailing from an elliptically loaded wing. In that case, the maximally unstable long wave has a length 8.66 and grows by a factor e in a time 9.4(^4#/CL)(6/F0), where AR is the aspect ratio, CL is the lift coefficient, and V0 is the speed of the aircraft. The vortex displacements are symmetric and are confined to fixed planes inclined at 48° to the horizontal.
1,092 citations
TL;DR: In this paper, a preliminary quantitative analysis of how a series of modifications of that basic undulatory mode, found in the vertebrates (and especially in the fishes), tends to improve speed and hydromechanical efficiency.
Abstract: This paper attempts to emulate the great study by Goldstein (1929) ‘On the vortex wake of a screw propeller’, by looking for a dynamical theory of how another type of propulsion system has evolved towards ever higher performance. An ‘undulatory’ mode of animal propulsion in water is rather common among invertebrates, and this paper offers a preliminary quantitative analysis of how a series of modifications of that basic undulatory mode, found in the vertebrates (and especially in the fishes), tends to improve speed and hydromechanical efficiency.Posterior lateral compression is the most important of these. It is studied first in ‘pure anguilliform’ (eel-like) motion of fishes whose posterior cross-sections are laterally compressed, although maintaining their depth (while the body tapers) by means of long continuous dorsal and ventral fins all the way to a vertical ‘trailing edge’. Lateral motion of such a cross-section produces a large and immediate exchange of momentum with a considerable ‘virtual mass’ of water near it.In § 2, ‘elongated-body theory’ (an extended version of inviscid slender-body theory) is developed in detail for pure anguilliform motion and subjected to several careful checks and critical studies. Provided that longitudinal variation of cross-sectional properties is slow on a scale of the cross-sectional depth s (say, if the wavelength of significant harmonic components of that variation exceeds 5s), the basic approach is applicable and lateral water momentum per unit length is closely proportional to the square of the local cross-section depth.The vertical trailing edge can be thought of as acting with a lateral force on the wake through lateral water momentum shed as the fish moves on. The fish's mean rate of working is the mean product of this lateral force with the lateral component of trailing-edge movement, and is enhanced by the virtual-mass effect, which makes for good correlation between lateral movement and local water momentum. The mean rate of shedding of energy of lateral water motions into the vortex wake represents the wasted element in this mean rate of working, and it is from the difference of these two rates that thrust and efficiency can best be calculated.Section 3, still from the standpoint of inviscid theory, studies the effect of any development of discrete dorsal and ventral fins, through calculations on vortex sheets shed by fins. A multiplicity of discrete dorsal (or ventral) fins might be thought to destroy the slow variation of cross-sectional properties on which elongated-body theory depends, but the vortex sheets filling the gaps between them are shown to maintain continuity rather effectively, avoiding thrust reduction and permitting a slight decrease in drag.Further advantage may accrue from a modification of such a system in which (while essentially anguilliform movement is retained) the anterior dorsal and ventral fins become the only prominent ones. Vortex sheets in the gaps between them and the caudal fin may largely be reabsorbed into the caudal-fin boundary layer, without any significant increase in wasted wake energy. The mean rate of working can be improved, however, because the trailing edges of the dorsal and ventral fins do work that is not cancelled at the caudal fin's leading edge, as phase shifts destroy the correlation of that edge's lateral movement with the vortex-sheet momentum reabsorbed there.Tentative improvements to elongated-body theory through taking into account lateral forces of viscous origin are made in §4. These add to both the momentumandenergyof the water's lateral motions, but mayreduce the efficiencyof anguilliform motion because the extra momentum at the trailing edge, resulting from forces exerted by anterior sections, is badly correlated with that edge's lateral movements. Adoption of the ‘carangiform’ mode, in which the amplitude of the basic undulation grows steeply from almost zero over the first half or even two-thirds of a fish's length to a large value at the caudal fin, avoids this difficulty.Any movement which a fish attempts to make, however, is liable to be accompanied by ‘recoil’, that is, by extra movements of pure translation and rotation required for overall conservation of momentum and angular momentum. These recoil movements, a potentially serious source of thrust and efficiency loss in carangiform motion, are calculated in § 4, which shows how they are minimized with the right distribution of total inertia (the sum of fish mass and the water's virtual mass). It seems to be no coincidence that carangiform motion goes always with a long anterior region of high depth (possessing a substantial moment of total inertia) and a region of greatly reduced depth just before the caudal fin.The theory suggests (§5) that reduction of caudal-fin area in relation to depth by development of a caudal fin into a herring-like ‘pair of highly sweptback wings’ should reduce drag without significant loss of thrust. The same effect can be expected (although elongated-body theory ceases to be applicable) from widening of the wing pair (sweepback reduction). That line of development of the carangiform mode in many of the Percomorphi leads towards the lunate tail, a culminating point in the enhancement of speed and propulsive efficiency which has been reached also along some quite different lines of evolution.A beginning in the analysis of its advantages is made here using a ‘twodimensional’ linearized theory. Movements of any horizontal section of caudal fin, with yaw angle fluctuating in phase with its velocity of lateral translation, are studied for different positions of the yawing axis. The wasted energy in the wake has a sharp minimum when that axis is at the ‘three-quarter-chord point’, but rate of working increases somewhat for axis positions distal to that. Something like an optimum regarding efficiency, thrust and the proportion of thrust derived from suction at the section's rounded leading edge is found when the yawing axis is along the trailing edge.This leads on the present over-simplified theory to the suggestion that a hydromechanically advantageous configuration has the leading edge bowed forward but the trailing edge straight. Finally, there is a brief discussion of possible future work, taking three-dimensional and non-linear effects into account, that might throw light on the commonness of a trailing edge that is itself slightly bowed forward among the fastest marine animals.
732 citations
TL;DR: In this paper, a second-order, linear, damped system with self-excited wake-oscillators is proposed to model the aerodynamic lift force and the instantaneous value of a fluctuating lift coefficient, whose characteristics are derived from existing experimental data.
Abstract: The main feature is the representation of fluctuating lift behavior in terms of a proposed wake-oscillator. The primary purpose of the paper is to demonstrate the potential of the wake-oscillator concept for future studies. The elastically mounted cylinder is modeled as a second-order, linear, damped system. The aerodynamic lift force is proportional to the instantaneous value of a fluctuating lift coefficient. The instantaneous lift coefficient is derived from the response of a proposed lift-oscillator, whose characteristics are deduced from existing experimental data. This oscillator is self-excited, its natural frequency is proportional to wind speed, and it is subjected to a coupling term proportional to the transverse cylinder velocity.
413 citations
TL;DR: In this paper, the motion of vortex rings of small cross section is considered and a formula is given for the velocity of a ring in an ideal fluid with an arbitrary distribution of vorticity in the core and an arbitrary circumferential velocity.
Abstract: The motion of vortex rings of small cross section is considered. A formula is given for the velocity of a ring in an ideal fluid with an arbitrary distribution of vorticity in the core and an arbitrary circumferential velocity. A definition of velocity is given for the unsteady diffusing ring in a viscous fluid, and the speed is found by the method used for rings in ideal fluids.
299 citations
TL;DR: In this paper, a derivation of the Eulerian equations of motion directly from the Lagrangian formulation of Hamilton's principle is given, where the circulation round a circuit of material particles of uniform entropy appears as a constant of the motion associated with the indistinguishability of fluid elements with equal density, entropy and velocity.
Abstract: A derivation is given of the Eulerian equations of motion directly from the Lagrangian formulation of Hamilton's principle. The circulation round a circuit of material particles of uniform entropy appears as a constant of the motion associated with the indistinguishability of fluid elements with equal density, entropy and velocity. A discussion is given of the Lin constraint, and it is pointed out that, for a barotropic fluid, the variational principle recently suggested by Seliger & Whitham does not permit velocity fields in which the vortex lines are knotted.
187 citations
TL;DR: In this article, an existence theorem is proved for distributions of vorticity in the core that are arbitrary, apart from the condition imposed by the equation of motion and certain smoothness requirements.
Abstract: This paper is concerned with vortex rings, in an unbounded inviscid fluid of uniform density, that move without change of form and with constant velocity when the fluid at infinity is at rest The work is restricted to rings whose cross-sectional area is small relative to the square of a mean ring radius An existence theorem is proved for distributions of vorticity in the core that are arbitrary, apart from the condition imposed by the equation of motion and certain smoothness requirements The method of proof relies on the nearly plane, or two-dimensional, nature of the flow in the neighbourhood of a small cross-section, and leads to approximate but explicit formulae for the propagation speed and shape of the vortex rings in question
146 citations
TL;DR: In this paper, it was shown that a rotating stratified zonal shear flow is more unstable to zonally symmetric disturbances than would be indicated by the classical inviscid adiabatic criterion, unless σ, the Prandtl number, = 1.
Abstract: It is shown that, even for vanishingly small diffusivities of momentum and heat, a rotating stratified zonal shear flow is more unstable to zonally symmetric disturbances than would be indicated by the classical inviscid adiabatic criterion, unless σ, the Prandtl number, = 1. Both monotonic instability, and growing oscillations ("overstability") are involved, the former determining the stability criterion and having the higher growth rates. The more σ differs from 1, the larger the region in parameter space for which the flow is stable by the classical criterion, but actually unstable. If the baroclinity is sufficiently great for the classical criterion also to indicate instability, the corresponding inviscid adiabatic modes usually have the numerically highest growth rates. An exception is the case of small isotherm slope and small σ. A single normal mode of the linearized theory is also, formally, a finite amplitude solution; however, no theoretical attempt is made to assess the effect of finit...
139 citations
TL;DR: In this article, the authors describe an experimental study of the occurrence, frequency and peak-to-peak amplitude of the wall pressure generated by a helical vortex in rotating flow moving axially through a straight tube.
Abstract: In rotating flow moving axially through a straight tube, a helical vortex will be generated if the angular momentum flux is sufficiently large relative to the flux of linear momentum. This paper describes an experimental study of the occurrence, frequency and peak-to-peak amplitude of the wall pressure generated by this vortex. The experimental results are displayed in dimensionless form in terms of a Reynolds number, a momentum parameter and tube geometry.
135 citations
TL;DR: In this article, the Korteweg-de Vries equation is shown to fail when the tube wall is moved to infinity, and the failure is corrected by singular perturbation procedures.
Abstract: The Korteweg–de Vries equation is shown to govern formation of solitary and cnoidal waves in rotating fluids confined in tubes. It is proved that the method must fail when the tube wall is moved to infinity, and the failure is corrected by singular perturbation procedures. The Korteweg–de Vries equation must then give way to an integro-differential equation. Also, critical stationary flows in tubes are considered with regard to Benjamin's vortex breakdown theories.
128 citations
TL;DR: In this article, it is shown that within the interval of possible Taylor-vortex flows, there exists a subinterval of stable vortex flows, growing out of the instability of Couette flow.
Abstract: Recently, Eckhaus developed a theory for a class of nonlinear stability problems which can be formulated in terms of a scalar partial differential equation with quadratic nonlinearities. It is demonstrated that Eckhaus' work on the development and stability of periodic solutions can be extended to a class of nonlinear matrix partial differential equations. The equations governing axisymmetric viscous flow between concentric rotating cylinders belong to the class of equations considered. When the Taylor number T is slightly above the minimum critical value Tc there exists an interval of possible equilibrium flows (Taylor‐vortex flows) growing out of the instability of Couette flow. It is shown that within the interval of possible Taylor‐vortex flows, there exists a subinterval of stable vortex flows.
121 citations
TL;DR: In this article, it was observed that liquid crystals of the $p$-azoxyanisole type exhibit macroscopic rotational motion above a threshold voltage, which is in agreement with the dynamic predictions of the continuum theory.
Abstract: We have observed that liquid crystals of the $p$-azoxyanisole type exhibit macroscopic rotational motion above a threshold voltage. The vortex motion of the birefringent liquid results in a lattice of cylindrical lenses whose focal lengths are voltage variable. These experiments are in excellent agreement with the dynamic predictions of the continuum theory.
TL;DR: In this paper, the relationship between the nature of flow instability and the inclination angle of the plate was established, and the angular dependence of the Rayleigh number characterizing the onset of instability was also determined.
Abstract: Experiments are carried out to establish the relationship between the nature of the flow instability and the inclination angle of the plate. The angular dependence of the Rayleigh number characterizing the onset of instability is also determined. An electrochemical flow visualization technique is utilized to expose the patterns of fluid motion. It is found that for inclination angles of less than 14° (relative to the vertical), waves are the mode of instability. On the other hand, for inclination angles in excess of 17°, the instability is characterized by longitudinal vortices. The range between 14° and 17° is a zone of continuous transition, with the two modes of instability co-existing.
TL;DR: In this paper, the growth of vortices in the vortex sheets bounding the jet emerging from a sharp-edged two-dimensional slit and from a circular orifice was observed.
Abstract: Observations are reported on the growth of vortices in the vortex sheets bounding the jet emerging from a sharp-edged two-dimensional slit and from a sharp-edged circular orifice. A regular periodic flow is observed near the orifice for both configurations when the Reynolds number of the jet lies between about 500 and 3000. The two-dimensional jet produces a symmetric pattern of vortex pairs with a Strouhal number of 0·43. Vortex rings are formed in the circular jet with a Strouhal number of 0·63. Computer experiments show that a growing pair of vortices in two parallel vortex sheets produces a symmetric pattern of vortices upstream from the original disturbance.
TL;DR: Aircraft downwash consists initially of a vortex pair descending with its accompanying fluid through the atmosphere, and the shapes of them and their evolution depend on the positions of the engines in relation to the wing tip vortices.
Abstract: Aircraft downwash consists initially of a vortex pair descending with its accompanying fluid through the atmosphere. Condensation trails are formed in exhaust emitted into the accompanying fluid and the shapes of them and their evolution depend on the positions of the engines in relation to the wing tip vortices. The atmosphere is stably stratified and so the descending accompanying fluid acquires upward buoyancy. Consequently vorticity is generated at the outside of the accompanying fluid and the flow pattern in the vortex pair is altered so as to produce detrainment of its exterior part. So long as any air which is a mixture of accompanying fluid and exterior air is detrained, the vortices remain stable, but the width of the pair decreases and its downward velocity increases with time as a result of the buoyancy. Eventually the upper stagnation point in the motion relative to the vortices begins to move upwards relative to the vortices so that some mixed fluid is entrained into the circulation and the vortices immediately become unstable, mixing occurs, the pressure in the core rises, and any vortex core trails that may exist appear to burst. The motion produces downward-thrust blobs in trails from centrally placed engines, which correspond to the holes sometimes seen in cloud when distrails are formed.
TL;DR: In this article, the problem of a piston moving in a cylinder was studied experimentally using flow visualization techniques and a vortex motion was observed at the piston face and cylinder wall interface as the cylinder wall moves toward the piston.
Abstract: The problem of a piston moving in a cylinder is studied experimentally using flow visualization techniques. A vortex motion is observed at the piston face and cylinder wall interface as the cylinder wall moves toward the piston. Non-dimensional scaling parameters for the vortex size and stability are determined and semi-empirical theories for the size of the vortex are presented.
TL;DR: In this paper, a scanning Doppler radar has capability for measurement of the tangential shear of radial velocity or gradient of the radial component of velocity in a direction normal to the radial vector.
Abstract: A scanning Doppler radar has capability for measurement of the tangential shear of radial velocity or gradient of the radial component of velocity in a direction normal to the radial vector. Tangential shear of sufficient magnitude in a horizontal direction reveals one term of the expression for vorticity in a horizontal plane. A vortex is reasonably well identified by Doppler radar if the shear is sufficiently steady during the time required for half a revolution of a vortex, and is further confirmed by extension of the shear pattern throughout a depth greater than its diameter, and by invariance of the character of the shear with respect to a change in viewing angle. A vortex in solid rotation has a characteristically uniform signature on a Doppler velocity display which may, however, be smoothed down according to the resolution limitations of the antenna beam. Sharp velocity peaks are rounded down to roughly half the magnitude of the velocity interval encompassed within the half-power antenna ...
TL;DR: In this paper, the growth of undulations along an infinite vortex sheet is modified by including the effects of a boundary, and two Kutta conditions, called rectified and full, are suggested to apply depending on conditions in the unperturbed flow.
Abstract: : The growth of undulations along an infinite vortex sheet is a classical problem of stability theory. That problem is modified by including the effects of a boundary: the vortex sheet is assumed to leave a rigid semi-infinite plate and to undergo spatially growing undulations downstream. The usual solution for a doubly infinite sheet is corrected by the Wiener-Hopf technique to account for the presence of the plate. The correction depends sensitively on whether a Kutta condition is enforced at the trailing edge. Two Kutta conditions, called rectified and full, are suggested to apply depending on conditions in the unperturbed flow. In either case, the correction due to the plate becomes negligible half a wavelength downstream from the trailing edge. (Author)
TL;DR: In this article, an implicit finite difference method of the Crank-Nicolson type was used to obtain the boundary-layer results on both the leeside and windside of a prolate spheroid.
Abstract: This paper presents incompressible laminar boundary-layer results on both the leeside and windside of a prolate spheroid. The results are obtained by an implicit finite difference method of the Crank–Nicolson type. Particular attention has been given to the determination of separation and of embedded streamwise vortices. No restriction on the angle of attack or the thickness ratio is imposed, nor are there invoked any of the common assumptions such as similarity, conical flow and others. The results suggest an embedded vortex region existing between the regular boundary-layer region and the separated region. At higher angle of attack, the vortex region becomes so thick that it itself may be more appropriately called ‘separated’ also. The latter possibility leads to questions of applicability for existing theories on three-dimensional separation.
TL;DR: In this paper, a laboratory model of the tornado-like vortex near the ground is developed and studied, where the circulation is produced by a rotating cylindrical screen and the updraft is generated by an exhaust fan at the opening of the top hood.
Abstract: A laboratory model of the tornado-like vortex near the ground is developed and studied. The circulation is produced by a rotating cylindrical screen and the updraft is produced by an exhaust fan at the opening of the top hood. By means of kerosene smoke, the vortex core and a reverse flow zone were observed in the experiment. The profiles of velocity and pressure were measured at three different circulation strengths. The maximum inward radial velocity in the boundary layer is approximately proportional to the circulation strength. Outside the vortex core, the top hood and ground boundary layers, the flow is a potential vortex flow with a very small inward radial velocity. The vertical velocity distribution generally has a Gaussian profile except that it is slightly downward in the annular reverse flow region. The diameter of the reverse flow region is controlled by the opening size of the outlet on the top hood. The reverse flow region extends to the top of the ground boundary layer only when th...
TL;DR: In this paper, it was shown that vortex rings with constant circulation can be described by an energy such that the velocity and impulse of the rings are connected by the usual relation v = ∂E/∂p.
TL;DR: In this article, the authors describe some experiments in rotating flows in which solitary waves were observed and compare the observed wave forms with the theoretical calculations of Benjamin (1967a) and Davis & Acrivos (1967b).
Abstract: This paper describes some experiments in rotating flows in which solitary waves were observed.In one set of experiments the waves were generated on a swirling flow whose circumferential velocity distribution resembled that of the Rankine combined vortex. This flow was established by stirring the liquid in a large cylindrical container, in much the same way as one stirs a cup of tea, and it was often found at the cessation of the stirring that a wave had been generated. This wave propagated along the vortex core and was reflected at the bottom of the container and at the free surface of the liquid and displayed the remarkable permanence characteristic of solitary waves. It appears that, to a first approximation, the speed of the waves may be calculated simply from the depression of the free surface of the liquid at the centre of the vortex. These waves are the rotating-fluid counterpart to the solitary waves in fluids of great depth recently discussed by Benjamin (1967b) and by Davis & Acrivos (1967).In a second set of experiments, solitary waves were generated in a long cylindrical tube and are analogous to the familiar solitary wave of open-channel flows. The theory indicates that these waves are possible in any swirling flow in which the angular velocity is distributed non-uniformly. Thus, a long liquid-filled tube was started rotating about its axis with a uniform angular velocity, and waves were generated before the fluid had reached a state of uniform rotation. Using the known velocity distribution for a tube of infinite length, comparisons have been made between the observed wave forms and the theoretical calculations of Benjamin (1967a). There is good agreement between the observed wave forms and the theoretical predictions.
TL;DR: In this article, a closed-circuit fan test rig was constructed to obtain pressure, volume flow rate and efficiency for fans of various designs, and detailed measurements within the rotors were also obtained by hot-wire traverses.
Abstract: The cross flow fan has developed from the ideas of Mortier in the late 19th century and recently has been used with conspicuous success in small domestic appliances. No satisfactory theory is known, improvements having come from experimental development.The present work is also experimental. A closed-circuit fan test rig was constructed to obtain pressure, volume flow rate and efficiency for fans of various designs. Detailed measurements within the rotors were also obtained by hot-wire traverses. These tests were supplemented by visualization studies in a water test rig.It is found that improved pressure–flow characteristics are obtained by constructing the casing so that the vortex which forms in the fan is allowed to move circumferentially round the rotor as the output is throttled. This preserves a strong vortex and keeps the total pressure approximately constant as the flow is throttled. In many previous designs, which do not allow this kind of displacement, the vortex tends to move towards the centre...
TL;DR: In this paper, an experimental verification of the vorticity amplification by stretching theory was carried out to obtain quantitative evidence of the effect of vortex stretching and its effects on the average boundary-layer profile.
Abstract: Recently a theory which could explain satisfactorily the strong sensitivity of stagnation-point heat transfer and skin friction on cylinders in cross flow to relatively small turbulent fluctuations in the free-stream was put forth by Sutera et al. [11. This mathematical model proposed that vorticity amplification due to stretching of vortex filaments in the strongly diverging flow near the stagnation point is the underlying mechanism. The basic physical ideas and mathematical formulations relating to vorticity amplification by stretching and the resulting effects on flow, heat transfer and skin friction at a two-dimensional stagnation point were set forth in Reference 1 and in a subsequent paper by Sutera E2]. This theory was later extended to the outer flow field, i.e., outside and far from the boundary layer, by Sadeh et al. I31. Thus, a detailed review of the vorticity-amplification theory need not be repeated here. The primary purpose of the present investigation was the experimental verification of the vorticity-amplification theory presented in References 1, 2 and 3. The experimental work was designed mainly to obtain quantitative evidence of vorticity amplification by stretching and its effects on the average boundary-layer profile. A search for the prezlicted vortex structure near the wall was also carried out.
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19 Jun 1970TL;DR: In this paper, the authors describe the arc process where an arc is struck between an electrode and workpiece, a gas vortex is passed around the electrode and is directed into a constricting nozzle passage where a liquid, usually water, vortex swirling in the same direction as the gas vortex was introduced.
Abstract: High quality, square cuts are obtained in metals by an arc process wherein an arc is struck between an electrode and workpiece, a gas vortex is passed around the electrode and is directed into a constricting nozzle passage where a liquid, usually water, vortex swirling in the same direction as the gas vortex is introduced. The arc passes through the gas and liquid vortex and through the nozzle and is directed in a highly constricted state against the workpiece to be cut.
TL;DR: In this paper, the steady two-cell viscous vortex solution of Sullivan (1959) is extended to yield unsteady 2-cell vortex solutions, which behave asymptotically as certain analogous 1-cell solutions of Rott (1958).
Abstract: The steady two-cell viscous vortex solution of Sullivan (1959) is extended to yield unsteady two-cell viscous vortex solutions which behave asymptotically as certain analogous unsteady one-cell solutions of Rott (1958). The radial flux is a parameter of the solution, and the effect of the radial flow on the circumferential velocity, is analyzed. The work suggests an explanation for the eventual dissipation of meteorological flow systems such as tornadoes.
TL;DR: In this paper, a laminar boundary layer over a flat pool of liquid fuel is calculated for a single-stage liquid pool of fuel at a super-flash temperature subjected to a cross wind, and the boundary is bounded by the lean mixture limit or the blowoff limit of the local fuel-air mixture.
TL;DR: In this paper, it was shown that the interaction of suitable pairs of gravity waves in a shear flow can give rise to aperiodic or weakly periodic secondary motions which resemble the Langmuir vortices associated with the formation of windrows.
Abstract: Interactions of suitable pairs of gravity waves in a shear flow are found to give rise to aperiodic or weakly periodic secondary motions. These secondary flows resemble the ‘Langmuir vortices’ which are associated with the formation of windrows. It seems likely that such wave interactions will play a substantial part in determining the quasi-steady structure of the flow when wind blows over a water surface.
TL;DR: In this paper, the role of vortex motion in the process of energy dissipation in the flow of an ideal incompressible fluid is described by a theorem whose derivation relies upon the exact three-dimensional Magnus formula discussed in the previous paper.
Abstract: The dissipation of energy in the flow of an ideal incompressible fluid is described by a theorem whose derivation relies upon the exact three-dimensional Magnus formula discussed in the previous paper. The theorem, which explicitly demonstrates the role of vortex motion in the process of energy dissipation, can be used to calculate the trajectories of vortices. Also derived is a detailed Josephson equation - an extension of Anderson's "new corollary in classical hydrodynamics" - which provides an exact non-time-average relation between chemical potentials and vortex motion.
TL;DR: In this paper, a 9-level general circulation model was used to simulate the breakdown of the circumpolar vortex in the winter stratosphere for the case of March 1965, where the marching computations were started 2 and 5 days prior to the breakdown.
Abstract: With a 9-level general circulation model, all attempt was made to simulate numerically the breakdown of the circumpolar vortex in the winter stratosphere for the case of March 1965. The marching computations were started 2 and 5 days prior to the breakdown. The simulation of the vortex elongation and destruction was, to a certain extent, successful, but the split vortex in the prediction erroneously merged again after 8 days. The sudden warming was not simulated at all. The development of the Aleutian high associated with the vortex breakdown was not well computed. Studies are made on zonally averaged quantities pertaining to the tropospheric and stratospheric circulations and their coupling. The increase of eddy kinetic energy at the time of the amplification of zonal wavenumber 2 is discussed both for the numerical simulation and for the observed fields. It is reconfirmed that the eddy kinetic energy in the stratosphere is primarily supplied from below in the form of vertical flux of geopotenti...