Internal waves generated by a moving sphere and its wake in a stratified fluid

Abstract

The internal gravity waves and the turbulent wake of a sphere moving through stratified fluid were studied by the fluorescent dye technique. The Reynolds number Re = U. 2 a/v was kept nearly constant at about 3 9 10 3 and the Froude number F = U/a N ranged from 0.5 to 12.5. It is observed that waves generated by the body are dominant only when F< 4 and are replaced by waves generated by the large scale coherent structures of the wake when F>4.

Internal waves generated by the turbulent wake of a sphere

“…Lin et al (1992a) delineated the Reynolds (Re) and Froude (Fi) number ranges where lee waves appear for the case of spheres; here Re = UD/v and Fi= U/ND, where U is the speed of the sphere, D its diameter, v the kinematic viscosity, N=(9(dp/dz)/po) 1/2 the buoyancy frequency, dp/dz the vertical density gradient of the undisturbed flow and Po a reference density (i.e., at the level of the sphere center). Hopfinger et al (1991) and Lin et al (1992a) have measured the wave lengths of lee waves behind spheres, and found good agreement with the predictions of linear theory. Hanazaki (1988) has studied lee wave regimes for a sphere at Re = 200 using numerical simulation.…”

“…While the lower Fi experiments were conducted using the larger spheres, most of the experiments on internal wave fields for higher Fi were performed using the smaller sphere (D = 1.9 cm) to reduce the channel confinement effect; i.e., to reduce D/H (the ratio of sphere diameter to fluid depth) and D/W(the ratio of sphere diameter to channel width) to ensure that internal waves are generated with limited interference from surfaces bounding the fluid. Note that the ratio D/H for the current experiments was smaller than that used by Hopfinger et al (1991), a study which demonstrated, using the large tow tank of the CNRM in France (1 m deep, 3 m wide and 22 m long), that D/H had negligible effect on the wave field.…”

“…They used ensemble averaged conductivity probe records to study the resulting random field of internal waves (both due to the body and the propeller), and pointed out that linear theory suffered major shortcomings. Chomaz et al (1990) and Hopfinger et al (1991) also recently studied the problem of internal waves generated by the body and its wake for spheres moving horizontally through stratified fluids. The latter study visualized internal wave fields using a rake of fluorescein dye lines illuminated by a thin laser sheet for a single Re = 3,000 and 0.25 < Fi < 6.25.…”

An experimental investigation of spin-up from rest of a stratified fluid

“…The horizontal dye planes correspond to isopycnals, and their evolution reveals the vertical motion within the tanks. Horizontal planes were emplaced using a metal frame spanned by cotton strings coated with dried fluorescein dye (Hopfinger et al, 1991). The frame was removed and a horizontal lid placed on top of the tank.…”

A theoretical model of a wake of a body towed in a stratified fluid at large Reynolds and Froude numbers

“…Laboratory studies of turbulent stratified wakes have been carried out since late 1960s (Lin and Pao, 1979;Boyer and Srdic-Mitrovic, 2001;Sysoeva and Chashechkin, 1991;Chomaz et al, 1993;Lin et al, 1992;Bonneton et al, 1993;Lin et al, 19993;Hopfinger et al, 1991;Robey, 1997;Spedding et al, 1996;Spedding, 1997;Bonnier and Eiff, 2002;Riley and Lelong, 2000;Lilly, 1983;Embid and Majda, 1998;Fincham and Spedding, 1997;Spedding, 2001Spedding, , 2002Gourlay et al, 2001). The results of these studies show that there are three distinct regimes of the wake evolution which are defined with respect to the product Nt, where N is the characteristic value of the buoyancy frequency at the level of towing and t is the time elapsed from the moment of the body pass at a given point.…”