Numerical modeling of the generation of internal waves by uniform stratified flow over a thin vertical barrier

Abstract

SUMMARYNumerical simulations of two-dimensional stratified flow past an obstacle (thin vertical strip) were performed at relatively low Reynolds numbers. A finite differences solver was adopted to simultaneously solve Navier-Stokes equations together with transport equations for salinity (stratifying agent), and the standard Smagorinsky turbulent closure scheme was called in whenever necessary to account for turbulence. The emphases were on the evaluation of code for unsteady stratified flow applications as well as identification of transient and steady internal-wave processes during flow past obstacles. Simulations were compared with laboratory experiments, where observations were made using a high resolution Schlieren technique and conductivity probes. Blocking was observed upstream of the obstacle, surrounded by nearzero frequency internal waves, the phase lines of which joined those of lee waves through a transition zone in the proximity of the obstacle. This pattern was preceded by initial transients of the starting flow in which propagating internal waves played a dominant role. Confluence of isopycnals passing over/under the obstacle in the wake led to interesting flow phenomena, including the radiation of internal waves. The numerical simulations were in good agreement with observations, except that some phenomena could not be captured due to resolution issues of either numerical or experimental techniques. The efficacy of the code in point for stratified flow calculations with relevance to the atmosphere and oceans was confirmed.

Visualization of stratified flows aro und a vertical plate: laboratory experiment and numerical simulation

“…Phase surfaces in the form of internal wave rays in the vertical velocity component field are manifested in the most contrast. The system of weakly pronounced oblique bands in the right part of the figure visualizes the remains of the unsteady internal wave field arising as a result of the impulse start of the body movement, as it was also shown in the previous study [6]. The main perturbations in the vertical component of the density gradient field are concentrated in the upstream perturbation, and the shape of the ligaments reflects the internal wave field phase structure (fig.…”

“…They are traced throughout the whole wake, starting from the bottom side of the plate in the form of a wavy structure. The phase surfaces of the attached waves become oblique with their shape noticeably different from those previously calculated by the authors based on the linearized version of the system (1) or the complete non-linear formulation using one of the earlier raNS models for slightly different velocities of plate movement [6].…”

“…Calculations of the flow pattern past a vertical plate using turbulence models show a good qualitative and quantitative agreement with the observation data of internal wave patterns [6]; however, some fine structural elements, which are clearly observed in the experiments, are not visualized numerically due to the limitations of the problem formulation. Detailed experimental studies on the internal wave patterns generated by stratified flow past a thin barrier in a circular channel were also carried out by Sutherland and linden [7].…”

“…as an extended vertical marker, the wake past a vertically emerging small gas bubble (re<200), or a freely immersing salt or sugar crystal, was observed by the Schlieren visualization method for a time period more than 16T b . In a series of experiments on marker deformation, the vertical distribution of the horizontal velocity component was measured [6].…”

Dynamics and Structure of Stratified Flows Around Wedge: From Diffusion Induced Upto Transient Vortex Regime

“…In formation of flow structure the important role played by edge effects. Since the start of the wedge motion inside the continuously stratified fluid begin to form upstream and downstream disturbances, fine interfaces near upper and lower sides of the wedge, rosettes of transient and fields of attached internal waves and vortex wake as past the moving strip [12]. Well defined vortex systems are formed past the extreme points of the wedge corners (Fig.…”