Fine structure of a stratified flow near a flat-plate surface

Abstract

The pattern of disturbances arising during the motion of a strip along a horizontal surface in a continuously stratified fluid with identified upstream and attached internal waves, boundary layers, and edge singularities is calculated in the liner approximation. The flow pattern behind a flat plate moving with a constant velocity in a continuously stratified fluid is studied with the use of the optical schlieren technique; transformation of waves and finely structured elements of the flow with increasing plate velocity is analyzed. The calculated and experimentally observed patterns of internal waves at low velocities are demonstrated to be in good agreement.The interest in studying the fluid flow structure near streamlined obstacles, which was discussed in numerous theoretical and experimental papers (see, e.g., [1, 2]), has been recently revived owing to the search for mechanisms of formation of streaky structures in the boundary layer [3] and vortex loops in the flow [4]. Particular attention is paid to studying the flow past a flat plate aligned in the mean flow direction. Initial inhomogeneities are generated by inserting mechanical, acoustic, or thermal perturbations into the uniform flow in the wind tunnel. The streaks and vortex structures arising in the boundary layer on a flat plate are visualized by numerical methods with the use of hot-wire measurements of the flow and essential assumptions on the flow character [4,5].In addition to contact methods, the optical schlieren technique is also used to study gas flows and flows of an inhomogeneous fluid, because even comparatively small variations of density Δρ (Δρ/ρ 0 10 −4 -10 −7 ) lead to significant changes in the refractive index n (Δn/n ∼ 10 −5 -10 −8 ) [6].Transverse streaky structures whose thin elements are aligned at an angle to the flow direction were visualized by means of the schlieren technique in a continuously stratified fluid in an immediate vicinity of a horizontal plate [7] with flow velocity much smaller than that used in [4]. As the velocity is increased, uniformly distributed transverse streaks are grouped into clusters, the latter being transformed to a vortex street with distance from the obstacle [8]. Streaky structures were also observed in the boundary layer on the side surface of a vertically moving cylinder [9]. In repeated experiments [7-9], with no additional disturbances introduced into the flow, all large-scale and small-scale elements of the flow are well reproduced. The experimental results [4, 7-9] demonstrate that a more detailed mathematical analysis of comparatively slow stratified flows past a flat plate is needed. At the first stage, it is reasonable to use linear models, which effectively describe internal waves with allowance for dissipative factors: fluid viscosity and diffusion of the stratifying component [6].In the general case, linearized three-dimensional equations of fluid motion describe two types of flow elements singular in terms of viscosity, whose thickness depends on the problem geometry [10]. As the e...

Stratified Flow Fine Structure Around a Sloping Plate

“…In the present paper, computations of multiscale flows around a uniformly moving sloping plate are analyzed in a wide range of Reynolds numbers using numerical solution of the fundamental system of fluid mechanics equations, which allows studying flows of both continuously stratified and homogeneous viscous incompressible fluids in a single formulation. These studies complement the previous works performed in the same mathematical formulation for stratified flows around a motionless [4][5][6] and a uniformly moving horizontal strip in the linear [7] and complete nonlinear formulations [8] taking into account the solvability conditions of the system [9,10].…”

“…Generation of new elements with their own kinematics and spatiotemporal scales is due in the dynamic description to a high order and non-linearity of the fundamental system of equations [10]. Complete solutions of the system even in the linear approximation contain several functions [7] which in the non-linear models correspond to flow components interacting with each other and generating new types of perturbations [3,8]. Fig.…”

Numerical analysis and visualization of fine structures of the fields of two-dimensional attached internal waves

“…In the picture of currents caused by the uniform motion of a horizontal plate, parallel with internal waves, we observe small-scale perturbations on the leading and back edges of the plate and a boundary layer monotonically increasing with the distance from the leading edge of the plate [9]. The cited work deals solely with the degenerate case.…”

Numerical Analysis of Large Scale Stratified Flows Around an Horizontal Strip

“…A numerical model adapted from the JETLES code [2] has been developed and validated [3]- [6] from laboratory experiments [7]- [8] performed in a salty water channel at low Reynolds number exhibiting reasonable agreement with data of Schlieren visualization, density marker and probe measurements of internal wave fields. In continuation to previous work concerning a vertical strip towed in a channel, new numerical results are presented for the more delicate case of horizontal plate.…”

“…The chosen test cases allowed demonstrating the ability of selected numerical methods to represent stably stratified flows over horizontal strip [7] and hill type 2D obstacles [8,12] with generation of internal waves.…”