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Unfortunately, there are not any detailed measurements of the flow field resulting from the motion of a submarine-like body in a stratified medium. Most of the existing and relatively meager experiments do not deal with wake conductivity measurements at Froude numbers of practical significance. Also, the causes of the wake turbulence are seldom similar.

It is a well-known fact that electric currents generated in a fluid contribute to the total electromagnetic field, but in the absence of fluid motion these modifications of the applied field remain at a steady state. If a hydrodynamic disturbance, such as a wake in a stratified medium, sets part or all of the conducting fluid into motion, an additional electric field is generated in the fluid which is moving across the geomagnetic field. The change in current density then produces a magnetic anomaly which may be observable and thus important for stealthing purposes.

Wakes caused by bodies traveling in homogeneous fluids have been subjected to a large number of studies. A summary for the axisymmetric or circular wake is presented in Schlichting [2]. In this case, the wake width in a homogenous fluid increases as x1/3 vice x1/2 for the two-dimensional case. This relationship can be used for the initial wake growth in a stratified fluid because the effect of the turbulent mixing dominates the wake in that region. As a result, the wake expands in all directions in the same manner as the wake in a homogenous fluid. As the distance behind the body increases, the gravitational effects on the displaced fluid become more dominant. This results in a vertical collapse and a horizontal growth in the wake region. The horizontal spreading causes the vertical collapse to occur at a greater rate relative to the two-dimensional case. This is the source of the major difference between the two- and three-dimensional wakes.

The vertical collapse and the subsequent horizontal spreading also cause a horizontal displacement of the fluid surrounding the mixed region. This fluid then converges above and below the level at which the spreading is taking place resulting in the generation of random internal gravity waves in the bulk fluid. These waves then continue to travel away from the body at the level where the mixed fluid finds density equilibrium with the surrounding fluid. Most of these effects have been documented thirty years ago by Stockhausen, at al. [3] for a circular disk mounted on a self propelled body. Surveys on stratified flows may be found in the papers by Torobin and Gauvin [4], Lin and Pao [5], and Fernando [6]. Laboratory measurements of the evolution of wakes behind a sphere and a right circular cylinder, moving in a linearly stratified fluid at relatively low Froude and Reynolds numbers, were carried out, among others, by Lin et al. [7] and Xu et al. [8]. In both cases, the wake formation was primarily due to the shedding of vortices from the separation points.

In the present investigation, the conductivity measurements were made in the wake of self-propelled bodies (with momentumless wakes) through the use of numerous, temperature-compensated, high accuracy, microscale, conductivity probes [9]. Under normal conditions, i.e., for a submarine-like body in steady rectilinear motion, the characteristics of the wake are dictated primarily by the propeller and, to a lesser extend, by the necklace and sail-plane vortices. However, in transient motions (body undergoing time-dependent maneuvers), nonlinear waves, the unsteady three-dimensional cross-flow separations and body vortices play significant roles. Also, it must be emphasized that there are fundamental differences in the wakes of towed or dragged bodies and the self-propelled bodies. The wake of a towed body represents typical elementary shear flow profiles, where the velocity deficit spreads outward and decreases on the centerline as the flow proceeds downstream. The wake of a momentumless body exhibits a velocity-defect region near the axis and a velocity-excess region in the neighborhood of r/Ro=0.8, before leveling off beyond r/Ro=1.2 (here r is the radial distance and Ro=D/2, the maximum radius of models).

MODELS, FACILITIES, AND TECHNIQUES
Scaling of the Model

The parameters used in the current study were taken from the design specifications for a typical attack submarine. They provide an accurate representation of the conditions that would be encountered under normal operating conditions. Of special importance is the relative conductivity which we define here as the ratio of the time change in conductivity at a given point to that which existed prior to the motion of the body at the same point, i.e., RC(x,y,z)=(ΔC/C)xyz. The effect of the conductivity perturbations on the distortion of the prevailing magnetic field is of special importance and directly related to the ultimate purpose of the investigation.

A standard dimensional analysis shows that the relative conductivity depends on the internal Froude number Fr=Uo/ND (or its inverse ND/Uo, known as the stratification parameter), the Reynolds number Re =UoD/v, and Uot/D or Nt (here N is measured in rad/s, not in Hz). The foregoing is predicated on the assumptions that (i) the Schmidt number (v/ κ) is not important since the timescales for the salt diffusion are considerably larger than those for the occurrence of fluid-dynamical events of interest, (ii) the geometrical



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