Effects of rotation and stratification:an introduction

Large-scale flows in the natural environment can be influenced by the planetary rotation and also by density differences. This chapter aims to provide an informal introduction into the effects of background rotation and stratification.</p

The behaviour of vortex structures near solid obstacles

This lecture will address the problem of a dipolar vortex approaching solid objects like a cylinder, a row of closely positioned cylinders, or a sharp-edged plate. Vorticity generated at the no-slip surface of the obstacle or due to flow separation at sharp edges is advected away from the wall and may thus interact with the primary vortex structure. This may lead to very complicated behaviour, like splitting and partial rebound of the primary dipole. Laboratory experiments have been performed in a rotating fluid tank, the background rotation providing a mechanism for making the relative flow approximately two-dimensional. The flow evolution has been visualized by adding dye, while quantitative information about the vorticity distribution was obtained by PIV measurements. In addition to numerical flow simulations, some analytical studies have been carried out, which provide important information about the vortex-wall interaction.</p

Effects of rotation and stratification: an introduction

Large-scale flows in the natural environment can be influenced by the planetary rotation and also by density differences. This chapter aims to provide an informal introduction into the effects of background rotation and stratification

Numerical simulation of tripolar vortices in 2D flow

The formation of a tripolar vortex in a two-dimensional flow is simulated numerically for two different cases, viz. the tripole arising from a collision of two Lamb dipoles, and the emergence of a tripole from an initially axisymmetric, unstable vortex. This latter situation was also considered in a laboratory experiment by van Heijst, Kloosterziel and Williams, and the numerical results show very good agreement with their observations, both qualitatively and quantitatively. Under certain conditions a higher wavenumber instability is found, resulting in a triangular vortex which itself turns out to be unstable. The results of the numerical simulation agree fairly well with laboratory observations of this higher-order instability scenario

Preface

The book presents a state-of-the-art overview of current developments in the field in a way accessible to attendees coming from a variety of fields. Relevant examples are turbulence research, (environmental) fluid mechanics, lake hydrodynamics and atmospheric physics. Topics discussed range from the fundamentals of rotating and stratified flows, mixing and transport in stratified or rotating turbulence, transport in the atmospheric boundary layer, the dynamics of gravity and turbidity currents eventually with effects of background rotation or stratification, mixing in (stratified) lakes, and the Lagrangian approach in the analysis of transport processes in geophysical and environmental flows. The topics are discussed from fundamental, experimental and numerical points of view. Some contributions cover fundamental aspects including a number of the basic dynamical properties of rotating and or stratified (turbulent) flows, the mathematical description of these flows, some applications in the natural environment, and the Lagrangian statistical analysis of turbulent transport processes and turbulent transport of material particles (including, for example, inertial and finite-size effects). Four papers are dedicated to specific topics such as transport in (stratified) lakes, transport and mixing in the atmospheric boundary layer, mixing in stratified fluids and dynamics of turbidity currents. The book is addressed to doctoral students and postdoctoral researchers, but also to academic and industrial researchers and practicing engineers, with a background in mechanical engineering, applied physics, civil engineering, applied mathematics, meteorology, physical oceanography or physical limnology

Modelling the separation and eddy formation of coastal currents in a stratified tank

International audienc

The behaviour of vortex structures near solid obstacles

This lecture will address the problem of a dipolar vortex approaching solid objects like a cylinder, a row of closely positioned cylinders, or a sharp-edged plate. Vorticity generated at the no-slip surface of the obstacle or due to flow separation at sharp edges is advected away from the wall and may thus interact with the primary vortex structure. This may lead to very complicated behaviour, like splitting and partial rebound of the primary dipole. Laboratory experiments have been performed in a rotating fluid tank, the background rotation providing a mechanism for making the relative flow approximately two-dimensional. The flow evolution has been visualized by adding dye, while quantitative information about the vorticity distribution was obtained by PIV measurements. In addition to numerical flow simulations, some analytical studies have been carried out, which provide important information about the vortex-wall interaction

Instability onset of the boundary layer on a rotating cylinder in a stratified fluid

International audienceWe consider the instability of the laminar shear layer on a circular cylinder that is impulsively set into rotation about its vertical axis with angular speed Ω. The outer wall of this large gap Taylor-Couette flow is at a radial distance of about 10 times the inner cylinder radius, and the gap is either filled with a homogeneous or linearly stratified fluid. In a homogeneous fluid, the thickness of the boundary layer on the cylinder, d, grows until it becomes centrifugally unstable with a wavelength that is determined by the boundary layer thickness d. In a linearly stratified fluid with stratification N, the flow instability is set by the Froude number F = Ω /N. For F>1 the onset of the centrifugal instability is well predicted by the Taylor-Görtler number and theory for homogenous fluids. When F <=1, the onset of the instability is for a relatively higher Reynolds number, and bifurcates from a vortex regime to a wave regime with a pure inertial wave in the boundary layer. The mechanism of instability is determined by parametric resonance and the generation of waves with subharmonic frequencies typical for Parametric Subharmonic Instability. The results are discussed in view of former results on stratified TC flow