V. V. Mitkin

Transformation of hanging discontinuities into vortex systems in a stratified flow behind a cylinder

The mechanisms of formation of hanging discontinuities, vortex dipoles, and vortex arrays in the wave wake behind a cylinder moving at a constant velocity in a stratified fluid are investigated using various schlieren methods. The existence of discontinuities is attributable to the distortion of the internal-wave phase pattern in the shear flow and to the varying stratification and subsequent interaction of the waves with the appearing nonuniformities. Hanging discontinuities and vortex systems are low-velocity analogs of shock waves. An analysis of the internal-wave pattern indicates that the values of the normal velocity component differ on the upper and lower edges of the discontinuities. A regime diagram for flows of this kind is given.

Suspended discontinuities in the field of two-dimensional internal waves

Using various shadow methods of visualization for a stratified flow near a horizontal cylinder towed with constant velocity, a new structural element of the flow, namely, the isolated high-gradient interlayers in the field of attached internal waves, is identified. In their basic characteristic features, these layers may be viewed as those belonging to the class of inner boundary layers which are the prevalent mechanism for formation of the fine structure of a continuously stratified medium. The data on optical visualization are confirmed by direct measurements of the electrical conductivity.

Structure of stratified flow around a cylinder at low internal froude number

The flow pattern around a horizontal cylinder towed at constant velocity in a continuously stratified fluid is visualized by the shadow method. The velocities in the leading flow disturbance, i. e., in the flow-blocking region ahead of the cylinder, are presented. In the body wake, a new class of small-size structures in the density gradient field is revealed against the background of a smooth velocity profile. The evolution of the flow pattern with variation of the parameters of body motion is studied.

Formation of Vortices on Soaring Interfaces in Stratified Flows Behind a Cylinder

At present, mechanisms responsible for the formation of fine structures in stable stratified media such as the Earth’s atmosphere [1] or hydrosphere [2] with allowance for high-gradient interfaces and thicker homogeneous layers are being intensely studied in natural and laboratory conditions. In the case of flows around obstacles, extended long-life interfaces generated by both vortices and boundary layers appreciably affect flow dynamics and flow structure, as well as the energy and mass transfer. In certain two-dimensional stratified cuts, isolated interfaces having no singularities on their edges are formed immediately in the internal-wave field [3]. In flow-regime diagrams typical of stratified flows near a horizontal circular cylinder, there exist parameter ranges in which isolated interfaces are observed for both pointed and blunted leading edges [4]. The mutual transformation of solitary interfaces and soaring vortices (or vortex systems) has never been considered. In the present study, we analyze the process of soaring-vortex formation in the field of attached internal waves and of reconstructing their structure in the case of the vortex-system generation. We studied experimentally the flow pattern arising at the onset of the uniform motion of a circular cylinder in a linearly stratified fluid.

Acoustic Sounding of Vortex Rings in a Continuously Stratified Fluid

The experimental simulation of solitary vortex rings in a stratified fluid performed using high-frequency echo-sounding and optical visualization methods shows that on the range from turbulent to laminar regimes the vortex is a volume inhomogeneity with a sound scattering cross-section mv∼U5, where U is the translational velocity. The absolute value of mv is determined by the microscale component of the vortex microstructure, which is commensurable with the sounding sonic wave length.

An Effect of a Lift Force on the Structure of Attached Internal Waves in a Continuously Stratified Fluid

The pattern of attached internal waves [1] as an analogue of lee waves in the atmosphere [2] and ocean [3], as calculated by the source‐sink method [4], agrees satisfactorily with observations and laboratory measurements on waves past perfectly shaped obstacles [5] when the wake effect can be ignored. The wave field around a symmetric body dipped into a continuously stratified fluid is antisymmetric about the horizontal plane passing through the line of motion of the body center. In some flow regimes with waves interacting actively with vortices in the wake, the antisymmetric wave pattern evolves into a symmetric one at a large distance from the obstacle [6]. In a real situation, the obstacles are generally irregular in shape and, therefore, a skew in the flow can affect the field structure of radiated waves. This work is devoted to the experimental study of the internal waves generated by a vertical or inclined plate towed uniformly when not only a drag force but also a lifting force arises. Experiments were made with a setup including a tank measuring 220 〈 40 〈 60 cm 3 , a system creating a saline stratification, a mechanism for the model towing, a carriage intended for the mounting and translating of sensors, a device for acquisition and processing of experimental data, and a schlieren. Linear stratification in the tank is created by the continuous replacement method. The density profile and the velocity distribution are determined with the help of a vertical marker acting as the wake past a freely falling sugar crystal [7]. The layer displacements and the medium buoyancy period T b (in our experiment, this amounts to 14 s) were measured by a contact “one-electrode” conduction transducer that was calibrated directly in experiments by the “lift‐plunge” method. A rectangular plate 2.5 cm wide and 0.1 cm thick was mounted vertically or at some angle to the motion direction and was towed horizontally with a velocity U = 0.08‐0.6 cm/s. The plate is fixed on the carriage mounted over the tank by thin transparent knifes. The flow pattern was observed with the aid of a IAB-458 schlieren equipped with photo-, filming-, and video-systems. Visualization was implemented by two versions of the Maksutov methods, “vertical slit‐knife” and “vertical slit‐filament at the focus” [8], which are suitable in dealing with media exhibiting wide variations in the gradient of the refraction index. The first method records disturbances of the horizontal component of the refraction index gradient and is preferable, due to its high sensitivity, in cases of weak stratification (or low velocities), when perturbations of the density gradient are small and light rays are not intercepted by the construction elements of the experimental setup. The second method visualizes the modulus of the perturbation of the refraction-index gradient in a medium. The filament is disposed at the center of the slit image and, as a consequence, the minimum level of the average visual field illumination corresponds to an undisturbed state. In this case, the loci of crests and troughs, as they vary in contrast, are distinguished from the entire wave pattern. This method is more suitable for observing fine structural perturbations that are not shadowed by a contrast image of waves, which is typical of the knife method. The density label, the vertical marker, is a long-lived hydrodynamic wake past freely falling sugar crystal whose thickness δ ~ 0.25 cm. The time of the wake observation in the shadow picture is 10‐150 s, depending on the velocity distribution in the flow. The continuous profile of the horizontal component of velocity is calculated from the measured displacements of the marker over the known time interval Δ t .

Mirror and diffuse sound scattering by a two-dimensional wake in a continuously stratified fluid

Remote acoustic methods play a key role in studying the dynamics of the atmosphere and ocean. This fact is explained by the low attenuation of sound in sea water and the strong dependence of the sound refractive index on both the atmosphere temperature and humidity [1]. In stratified media free of admixtures, turbulence is believed to be the primary cause of sound scattering. This fact has been confirmed by numerous atmosphere sounding experiments carried out according to a bistatic configuration (i.e., with a remote static emitter and receiver). This method made it possible to identify microstructural bulk fluctuations by measuring scattering angular distributions [1]. However, there are many cases when acoustic-sounding data strongly differ from the results of contact measurements (e.g., in the case of structural-constant measurements). These discrepancies may be caused by the sound reflection from thin high-gradient layers, which is beyond the scope of the bulk scattering model [2]. The construction of a stable bistatic array in the open ocean is a rather complicated engineering task. Therefore, the greater part of relevant data was obtained by means of the acoustic-radar method, i.e., by measuring the backscattering of sound. The character of this scattering can be well established only for bioaggregations according to catching data or to the characteristic migration of sound-scattering water layers. When these bioaggregations are absent, the sound scattering is associated with either the turbulence (this conclusion is based on the characteristic frequency dependence of signals [3]) or the reflection of sound from thin water layers (in the case of the observed anomalous dependence of signals on small vertical deviations of the sonar ray [4‐6]). Laboratory-scale experiments on vertical echo sounding of a wake behind a cylinder moving in a stratified fluid [6, 7] also testify to the latter effect. However, comparative analysis of the efficiency of these scattering mechanisms has not yet been fulfilled. The wake behind a horizontal cylinder uniformly moving in a continuously stratified fluid is an adequate object for implementation of such an analysis. In a wide range of flow regimes, this wake contains mixed nonuniformities, namely, a bulk structure of turbulent spots and thin high-gradient interlayers. Studying the scattering angular distributions makes it possible to distinguish the contributions of separate structural flow components. In this paper, we present, for the first time, our experimental data on the ultrasound scattering by the wake behind a two-dimensional cylinder. These data were obtained by means of a bistatic array that allowed visualization of the flow pattern to be simultaneously performed. Our experiment was carried out in a tank 200 〈 40 〈 60 cm 3 in size which was filled with a water solution

Experimental Investigation of the Velocity Field near a Cylinder in a Contonuously Stratified Fluid

The velocity distributions in the upstream disturbance and lagging wake are measured using markers in the shadow flow pattern near a horizontal cylinder uniformly towed in a stratified fluid. The dimensions of the upstream total blocking zone and the velocity damping laws in the upstream disturbance are determined. On the basis of the experimental results the actual limits of applicability of existing methods of calculating the structure of stratified flow past obstacles are found for small Froude numbers.

Macrostructure and microstructure of a cocurrent stratified flow behind a cylinder

High-resolution optical and probe methods are used to isolate not only large-scale elements (internal waves immersed into a wake and soaring vortices) in a continuously stratified fluid flow around a two-dimensional obstacle but also internal boundary flows. The latter represent thin high-gradient interlayers inside and, sometimes, outside a cocurrent flow [1]. An advancing disturbance and both internal waves and vortices in a lagging wake behind the obstacle, which were investigated in detail by experimental and theoretical methods, are presented in [2‐4]. Parameters of high-gradient shells that belong to the density wake and contact with the boundary layer on the obstacle are determined in [5]. Patterns of internal boundary flows in the field of attached internal waves, which are obtained by different shadow methods, can be found in [6]. In the present paper, we, for the first time, have experimentally determined boundaries for a domain of existence (in the coordinate plane given by the Froude and Reynolds numbers) of isolated discontinuities in a wave wake behind a cylinder. We have also shown that the structure of the extended regime diagram depends on a stratification level. The usually assumed universal character of the extended diagram [3, 4] violates due to an allowance for the entire complex of steadily observed elements, which include fine-structure components of both the wave wake and density wake.