Towed body measurements of flow noise from a turbulent boundary layer under sea conditions.

Results from an underwater experiment under sea conditions on flow noise beneath a flat-plate turbulent boundary layer are presented. The measurements were performed with a towed body at towing speeds U=2.3,…,6.1 m/s and depths h=-150,…,-100 m. Flow noise is measured with a linear array of equally spaced hydrophones (Δx=70 mm) that is orientated in streamwise direction and embedded within a laterally attached flat plate. In order to separate flow noise from ocean ambient noise and other acoustical noise sources wavenumber-frequency filtering is applied. The (nondimensionalized) spectral power density of flow noise Φ(ω) ⟨U∞⟩/ (⟨δ(∗)⟩ (1/2ρ ⟨U∞⟩)(2)) is found to scale like (ω⟨δ(∗)⟩/⟨U∞⟩)(-4.3) in a wide frequency range at higher towing speeds. Here, ω, ⟨δ(∗)⟩, and ⟨U∞⟩ denote frequency, boundary layer displacement thickness, and potential flow velocity in the array region, respectively. Potential flow velocity is estimated from numerical simulations around a symmetrical, two-dimensional body with a semi-elliptical nose. Evidence is given that a χ(2)-(Tsallis) superstatistics provides a reasonable representation of the probability distribution function of flow noise at higher towing speeds.

Localized modulation of rotating waves in Taylor-Couette flow.

We report the results of an experimental study on the multiplicity of states in Taylor-Couette flow as a result of axial localization of azimuthally rotating waves. Localized states have been found to appear hysteretically from time-dependent Taylor-Couette flow at Reynolds numbers significantly above the onset of wavy Taylor vortices. These localized states have the shape of a modulated rotating wave and differ significantly from global modulated wavy Taylor vortex states in their spatial characteristics. Axial localization of rotating waves is accompanied with a significant increase in size of the underlying pair of Taylor vortices. Our work reveals that localization provides a mechanism for the appearance of multiple time-dependent states in Taylor-Couette flow.

End wall effects on the transitions between Taylor vortices and spiral vortices.

We present numerical simulations as well as experimental results concerning transitions between Taylor vortices and spiral vortices in the Taylor-Couette system with rigid, nonrotating lids at the cylinder ends. These transitions are performed by wavy structures appearing via a secondary bifurcation out of Taylor vortices and spirals, respectively. In the presence of these axial end walls, pure spiral solutions do not occur as for axially periodic boundary conditions but are substituted by primary bifurcating, stable wavy spiral structures. Similarly to the periodic system, we found a transition from Taylor vortices to wavy spirals mediated by so-called wavy Taylor vortices and, on the other hand, a transition from wavy spirals to Taylor vortices triggered by a propagating defect. We furthermore observed and investigated the primary bifurcation of wavy spirals out of the basic circular Couette flow with Ekman vortices at the cylinder ends.

Spirals vortices in Taylor-Couette flow with rotating endwalls.

A Hopf bifurcation with translational invariance has been widely considered as an appropriate model for the appearance of spiral vortices in counter-rotating Taylor-Couette flow. Our experimental work demonstrates that flow conditions close to the axial boundaries are responsible for the type of bifurcation scenario, i.e., either asymmetric pure traveling waves or more complex behavior, such as defect states or symmetric mixed states appearing from a Hopf bifurcation. The measurements were performed in the first Taylor-Couette experiment with independently rotating endwalls confining the system in axial direction. The rotation rate of the (synchronous) endwalls is found to be an essential control parameter for the spatial amplitude distribution of the traveling waves and also reflects symmetry of the corresponding flow pattern appearing from the Hopf bifurcation.

Nonlinear defects separating spiral waves in Taylor-Couette flow.

Stable domain walls which are realized by a defect between oppositely traveling spiral waves in a pattern-forming hydrodynamic system, i.e., Taylor-Couette flow, are studied numerically as well as experimentally. A nonlinear mode coupling resulting from the nonlinearities in the underlying momentum balance is found to be essential for the stability of the defects. These nonlinearly driven defects separate spiral domains and act either as a phase generating or annihilating defect. Specific phase differences of either 0 or pi between the participating traveling waves are a characteristic feature of this defect. The influence of a symmetry breaking externally imposed flow on the spiral domains and the defects is studied. The numerical and experimental results are in excellent agreement.

Onset of wavy vortices in Taylor-Couette flow with imperfect reflection symmetry.

We reveal experimentally a mechanism that alters the critical behavior of a Hopf bifurcation substantially due to the presence of imperfections of the reflection symmetry in a hydrodynamic system. The onset of rotating waves in Taylor vortex flow, which is widely considered as a "classical" example for a Hopf bifurcation in hydrodynamics, is investigated primarily by transient response experiments. While wavy vortex flow is not influenced by such (unavoidable) experimental imperfections, the critical behavior of the axially subharmonic rotating wave with wavy outflow boundaries, also called the small-jet mode, is qualitatively altered. Experimental evidence is provided that the modified critical behavior at the Hopf bifurcation is associated with imperfections of the reflection symmetry of the Taylor-Couette setup. The experimental results on Hopf bifurcation are discussed in the context of a cusp-Hopf bifurcation model recently proposed by Harlim and Langford [Int. J. Bifurcation Chaos Appl. Sci. Eng. 17, 2547 (2007)] and compared to experimental results on imperfect pitchfork bifurcation in small-aspect ratio Taylor-Couette flow.

Localized spirals in Taylor-Couette flow.

We present a type of spiral vortex state that appears from a supercritical Hopf bifurcation below the linear instability of circular Couette flow in a Taylor-Couette system with rigid end plates. These spirals have been found experimentally as well as numerically as "pure" states but also coexist with "classical" spirals (or axially standing waves for smaller systems) which typically appear from linear instability in counterrotating Taylor-Couette flow. These spiral states have an axial distribution of the strongly localized amplitude in the vicinity of the rigid end plates that confine the system in the axial direction. Furthermore, they show significantly different oscillation frequencies compared to the critical spiral frequencies. Despite the localization of the amplitude near the ends, the states appear as global states with spirals that propagate either toward the middle from each end of the system or vice versa. In contrast to classical spirals, these states exhibit a spatial or a spatiotemporal reflection symmetry.

Stabilization of domain walls between traveling waves by nonlinear mode coupling in Taylor-Couette flow.

We present a new mechanism that allows the stable existence of domain walls between oppositely traveling waves in pattern-forming systems far from onset. It involves a nonlinear mode coupling that results directly from the nonlinearities in the underlying momentum balance. Our work provides the first observation and explanation of such strongly nonlinearly driven domain walls that separate structured states by a phase generating or annihilating defect. Furthermore, the influence of a symmetry breaking externally imposed flow on the wave domains and the domain walls is studied. The results are obtained for vortex waves in the Taylor-Couette system by combining numerical simulations of the full Navier-Stokes equations and experimental measurements.

Imperfect Hopf bifurcation in spiral Poiseuille flow.

We present the results of an experimental study on the transition to spiral vortices in flow between concentric counter-rotating cylinders in the presence of an axial through-flow, i.e., in spiral Poiseuille flow. The experiments were performed in an apparatus having an aspect ratio Gamma=L/d=22.8 ( L axial length, d gap width between cylinders) and end plates enabling an in and outflow of mass. As a result of an applied axial through-flow the "classical" Hopf bifurcation to spiral vortices (SPI) splits up and a primary and secondary branch of down and upstream propagating SPI, respectively, as well as a transient quasiperiodic flow appear. Downstream propagating SPI resulting from the primary supercritical Hopf bifurcation are either convectively or absolutely unstable. The bifurcation structure observed in this open flow experiment is in qualitative agreement with predictions from theory of Hopf bifurcation with broken reflection symmetry [J. D. Crawford and E. Knobloch, Nonlinearity 1, 617 (1988)] and also in quantitative agreement with results from recent numerical calculations [A. Pinter, M. Lücke, and C. Hoffmann, Phys. Rev. E 67, 026318 (2003); C. Hoffmann, M. Lücke, and A. Pinter, Phys. Rev. E 69, 056309 (2004)].

Chaos from Hopf bifurcation in a fluid flow experiment.

Results of an experimental study of a Hopf bifurcation with broken translation symmetry that organizes chaotic homoclinic dynamics from a T2 torus in a fluid flow as a direct consequence of physical boundaries are presented. It is shown that the central features of the theory of Hopf bifurcation in O(2)-symmetric systems where the translation symmetry is broken are robust and are appropriate to describe the appearance of modulated waves, homoclinic bifurcation, Takens-Bogdanov point, and chaotic dynamics in a fluid flow experiment.

Standing waves in flow between finite counterrotating cylinders.

Experimental evidence for standing waves resulting from a supercritical Hopf bifurcation that appears as the first pattern-forming instability in counterrotating Taylor-Couette flow is presented. Depending on the aspect ratio two different types of standing waves, denoted as SW0 and SW(pi), could be observed. Both modes have an azimuthal wave number m=1 but differ in symmetry. While for SW(pi), a spatiotemporal glide-reflection symmetry could be found, SW0 is purely spatial reflection symmetric. The transition between the two modes is found to be organized in a cusp bifurcation unfolded by variations of the aspect ratio. The "classical" spiral vortex flow appears in this control parameter regime only as a result of a secondary steady bifurcation from SW0. This transition is found to be either subcritical or supercritical. The experimentally observed bifurcation structure has been predicted by theory of Hopf bifurcation to spiral vortex flow in finite counterrotating Taylor-Couette systems.

Gluing bifurcations in a dynamically complicated extended flow.

We report the results of the first experimental study of imperfect gluing bifurcations in an extended fluid flow. It is shown that the central features of the theory are robust and are appropriate to describe the dynamics of a nontrivial physical system. The results include the first experimental evidence for a route to chaos which is an essential part of the theory of imperfect gluing bifurcations.

Imperfect homoclinic bifurcations.

Experimental observations of an almost symmetric electronic circuit show complicated sequences of bifurcations. These results are discussed in the light of a theory of imperfect global bifurcations. It is shown that much of the dynamics observed in the circuit can be understood by reference to imperfect homoclinic bifurcations without constructing an explicit mathematical model of the system.