Session E13: Geophysical Fluid Dynamics: Bluff Bodies in Stratified Flows

Fluttering in Stratified Flows

The descent motion of heavy objects under the influence of gravitational and aerodynamic forces is relevant to many branches of engineering and science. Examples range from estimating the behavior of re-entry space vehicles to studying the settlement of marine larvae and its influence on underwater ecology. The behavior of regularly shaped objects freely falling in homogeneous fluids is relatively well understood. For example, the complex interaction of a rigid coin with the surrounding fluid will cause it to either fall steadily, flutter, tumble, or be chaotic. Less is known about the effect of density stratification on the descent behavior. Here, we experimentally investigate the descent of discs in both pure water and in a linearly salt-stratified fluids where the density is varied from 1.0 to 1.14 of that of water where the Brunt-Vaisala frequency is 1.7 rad/sec and the Froude number Fr $<$ 1. We found that stratification enhances the radial dispersion of the disc at landing, and simultaneously, decrease the descent speed and the inclination (or nutation) angle while falling. We conclude by commenting on the relevance of these results to the use of unpowered vehicles and robots for space exploration and underwater missions.   

Internal Gravity Wave Fluxes Radiated by a Stably Stratified Turbulent Wake

The study of the turbulent wake generated by a bluff body moving through a stably stratified fluid has important applications for naval hydrodynamics as well as geophysical flows around topography. Significant progress has been made in terms of investigating the structure and dynamics of the turbulent wake core and the associated near and far-field spectral properties of the wake-radiated internal gravity wave (IGW) fields, namely in the context of high Reynolds stratified turbulence within the wake itself. Nevertheless, little has been done to quantify the amount of energy and momentum radiated away by the IGWs generated by the wake. Through analysis of a broad Large Eddy Simulation dataset, spanning values of body-based Reynolds and Froude numbers, $Re=~5 \times 10^3,~10^5$ and $4 \times 10^5$ and $Fr=4, 16$ and $64$, we compute the energy and momentum fluxes of IGWs radiated by the stratified turbulent wake of a towed sphere and explore the relevant parametric dependence. The analysis further aims to determine the potential of the IGWs as a sink for energy and momentum relative to the dissipation of turbulent kinetic energy in the wake itself. Finally, we discuss the implications that for our findings for wake mean-flow self-similarity and turbulence subgrid scale models.   

Near wake characteristics in a stably-stratified fluid

Decaying stratified turbulence that is free to evolve in the presence of a stable density gradient eventually reaches a state dominated by low Froude number dynamics where persistent patterns emerge. Whether or not information from the initial turbulence creator persists in the formation of these patterns is still an open question. For example the late time evolution of bluff body wakes have been shown to have universal characteristics that are independent of the details of the original generator while experiments on the near wake of a towed grid suggest that the earliest stages of flow development do depend on the initial conditions. Here we present near wake characteristics of two grids with varied mesh spacing and similar solidity, a disk, and a sphere, all of equivalent drag, for $Re = \{1000, 3000\}$ and $Fr = \{1,4\}$. Quantitative measures in the wake signature deriving from whole-field PIV measurements will be used to specify when and how near wakes are similar, or different from each other, and from expectations or suppositions in the literature.   

Experiments and simulations of low \textrm{Re} sphere wakes with and without stratification

Bluff body wakes in both stratified and unstratified background have been studied extensively due to their geophysical and naval applications. A global map showing the dependence of near-wake structures behind a towed sphere on initial Reynolds number and Froude number, has been provided by Lin et al.\ (\textit{J. Fluid Mech.}, 240, 315\--354, 1992) and Chomaz et al.\ (\textit{J. Fluid Mech.}, 254, 1\--21, 1993). Here full-field measurements of the sphere wakes in both homogeneous and linearly stratified ambient are provided by simulations and experiments, at Reynolds number $\textrm{Re} \leq 1000$ and Froude number $\textrm{Fr} \geq 0.5$. In a homogeneous fluid, the structural transitions with increasing $\textrm{Re}$ are consistent with previous studies. The stratified results from simulations and experiments are in good agreement. Stratified wakes undergo similar transitions with decreasing \textrm{Fr} for \textrm{Re} in current range, except that similar transitions occur at larger \textrm{Re} as \textrm{Fr} decreases, thus making the wake structure at high \textrm{Re}, low \textrm{Fr} similar to that at low \textrm{Re}, high \textrm{Fr} .   

The sensitivity of stratified flow stability to base flow modifications

We present a novel theory that determines the sensitivity of linear stability to changes in the density or velocity of a base flow. The sensitivity is based on global direct and adjoint eigenmodes of the linearized Boussinesq equation, and is inspired by constant-density sensitivity analysis. The theory can be applied broadly to incompressible flows with small density variations, but it specifically provides new insight into the stability of density-stratified flows. Examples are given for the flows around a transverse thin plate at a Reynolds number of 30, a Prandtl number of 7.19, and Froude numbers of $\infty$ and 1. In the unstratified flow, the sensitivity is largest in the recirculation bubble; the stratified flow, however, exhibits high sensitivity in regions immediately upstream and downstream of the bluff body.   

Stabilization of triadic resonance of a finite amplitude gravity wave in the ocean : when a daughter wave is engaged with two fianc\'es

Triadic instability is a very generic mechanism by which a primary wave of finite amplitude is destabilized by two secondary (daugther) waves forming a resonant triad. For gravity wave in the ocean, as shown by Phillips, O.M. (CUP, 1967) the resonant triads form several continuous family that may be represented in twodimension (2D) as resonant lines in the 2D wave vector space of the secondary wave. We show here that the crossing of two od these branches may results in a double triadic instability where the instability is reduced. Building on McEwan, A.D. & Plumb, R.A. (Dyn. Atm. & Oceans, 1977) we show that this double triadic instability stabilization domain expends from a singular point to a finite significant region when the amplitude of the primary wave is increased. Comparison with direct computation of the instability branches shows that, from very small to order unity primary wave amplitude, the theoretical prediction stay valid and is able to explain the strong departure from the classical triadic instability theory.