Errata; Periodic patterns, linear instability, symplectic structure and mean-flow dynamics for three-dimensional surface waves

1996 ◽  
Vol 354 (1718) ◽  
pp. 2591-2592
Keyword(s):  
Surface Waves ◽  
Symplectic Structure ◽  
Three Dimensional ◽  
Linear Instability ◽  
Flow Dynamics ◽  
Mean Flow ◽  
Periodic Patterns ◽  
Dimensional Surface

On Three-Dimensional Nonlinear Subharmonic Resonant Surface Waves in a Fluid: Part I—Theory

1988 ◽  
Vol 55 (1) ◽  
pp. 213-219 ◽  
Author(s):  
X. M. Gu ◽  
P. R. Sethna ◽  
A. Narain
Keyword(s):  
Surface Tension ◽  
Steady State ◽  
Energy Dissipation ◽  
Surface Waves ◽  
Three Dimensional ◽  
Critical Depth ◽  
Transient Phenomena ◽  
Vertical Excitation ◽  
Rectangular Container ◽  
Dimensional Surface

Three-dimensional surface waves in a rectangular container subjected to vertical excitation are studied. The analysis includes the effects of surface tension, energy dissipation, and critical depth. Both steady state and transient phenomena are discussed.

scholarly journals Parabolized stability analysis of jets from serrated nozzles

2016 ◽  
Vol 789 ◽  
pp. 36-63 ◽  
Author(s):  
Aniruddha Sinha ◽  
Kristján Gudmundsson ◽  
Hao Xia ◽  
Tim Colonius
Keyword(s):  
Linear Stability ◽  
Near Field ◽  
Pressure Fluctuations ◽  
Three Dimensional ◽  
Hydrodynamic Pressure ◽  
Linear Instability ◽  
Base Flow ◽  
Linear Stability Theory ◽  
Instability Wave ◽  
Mean Flow

We study the viscous spatial linear stability characteristics of the time-averaged flow in turbulent subsonic jets issuing from serrated (chevroned) nozzles, and compare them to analogous round jet results. Linear parabolized stability equations (PSE) are used in the calculations to account for the non-parallel base flow. By exploiting the symmetries of the mean flow due to the regular arrangement of serrations, we obtain a series of coupled two-dimensional PSE problems from the original three-dimensional problem. This reduces the solution cost and manifests the symmetries of the stability modes. In the parallel-flow linear stability theory (LST) calculations that are performed near the nozzle to initiate the PSE, we find that the serrated nozzle reduces the growth rates of the most unstable eigenmodes of the jet, but their phase speeds are approximately similar. We obtain encouraging validation of our linear PSE instability wave results vis-à-vis near-field hydrodynamic pressure data acquired on a phased microphone array in experiments, after filtering the latter with proper orthogonal decomposition (POD) to extract the energetically dominant coherent part. Additionally, a large-eddy simulation database of the same serrated jet is investigated, and its POD-filtered pressure field is found to compare favourably with the corresponding PSE solution within the jet plume. We conclude that the coherent hydrodynamic pressure fluctuations of jets from both round and serrated nozzles are reasonably consistent with the linear instability modes of the turbulent mean flow.

Nonlinear stability, bifurcation and vortical patterns in three-dimensional granular plane Couette flow

2013 ◽  
Vol 716 ◽  
pp. 349-413 ◽  
Author(s):  
Meheboob Alam ◽  
Priyanka Shukla
Keyword(s):  
Three Dimensional ◽  
Travelling Wave ◽  
Finite Amplitude ◽  
Linear Instability ◽  
Travelling Wave Solutions ◽  
Plane Couette Flow ◽  
Mean Flow ◽  
Instability Modes ◽  
The Mean ◽  
Nonlinear Solutions

AbstractThe effects of three-dimensional (3D) perturbations, having wave-like modulations along both the streamwise and spanwise/vorticity directions, on the nonlinear states of five types of linear instability modes, the nature of their bifurcations and the resulting nonlinear patterns are analysed for granular plane Couette flow using an order-parameter theory which is an extension of our previous work on two-dimensional (2D) perturbations (Shukla & Alam, J. Fluid Mech., vol. 672, 2011b, pp. 147–195). The differential equations for modal amplitudes (the fundamental mode, the mean-flow distortion, the second harmonic and the distortion of the fundamental mode), up to cubic-order in perturbation amplitude, are solved using a spectral-based numerical technique, yielding an estimate of the first Landau coefficient that accounts for the leading-order nonlinear effect on finite-amplitude perturbations. In the near-critical regime of flows, we found evidence of mean-flow resonance, characterized by the divergence of the first Landau coefficient, that occurs due to the interaction/resonance between a linear instability mode and a mean-flow mode. The nonlinear solutions are found to appear via both pitchfork and Hopf bifurcations from the underlying linear instability modes, leading to supercritical nonlinear states of stationary and travelling wave solutions. The subcritical travelling wave solutions have also been uncovered in the linearly stable regimes of flow. It is shown that multiple nonlinear states of both stationary and travelling waves can coexist for a given parameter combination of mean density and Couette gap. The 3D nonlinear solutions persist for a range of spanwise wavenumbers up to ${k}_{z} = O(1)$ that originate from 2D instabilities which occur beyond a moderate value of the mean density. For purely 3D instabilities in dilute flows (having no analogue in 2D flows), the supercritical finite-amplitude solutions persist for a much larger range of spanwise wavenumber up to ${k}_{z} = O(10)$. For all instabilities, the vortical motion on the cross-stream plane has been characterized in terms of the fixed/critical points of the underlying flow field: saddles, nodes (sources and sinks) and vortices have been identified. While the cross-stream velocity field for supercritical solutions in dilute flows contains nodes and saddles, the subcritical solutions are dominated by large-scale vortices in the background of saddle-node-type motions. The latter type of flow pattern also persists at moderate densities in the form of supercritical nonlinear solutions that originate from the dominant 2D instability modes for which the vortex appears to be driven by two nearby saddles. The location of this vortex is found to be correlated with the local maxima of the streamwise vorticity.

scholarly journals Steady three-dimensional water-wave patterns on a finite-depth fluid

2001 ◽  
Vol 436 ◽  
pp. 145-175 ◽  
Author(s):  
T. J. BRIDGES ◽  
F. DIAS ◽  
D. MENASCE
Keyword(s):  
Fluid Layer ◽  
Travelling Waves ◽  
Three Dimensional ◽  
Finite Depth ◽  
Mean Flow ◽  
Constant Depth ◽  
Periodic Patterns ◽  
Wave Patterns

The formation of doubly-periodic patterns on the surface of a fluid layer with a uniform velocity field and constant depth is considered. The fluid is assumed to be inviscid and the flow irrotational. The problem of steady patterns is shown to have a novel variational formulation, which includes a new characterization of steady uniform mean flow, and steady uniform flow coupled with steady doubly periodic patterns. A central observation is that mean flow can be characterized geometrically by associating it with symmetries. The theory gives precise information about the role of the ten natural parameters in the problem which govern the wave–mean flow interaction for steady patterns in finite depth. The formulation is applied to the problem of interaction of capillary–gravity short-crested waves with oblique travelling waves, leading to several new observations for this class of waves. Moreover, by including oblique travelling waves and short-crested waves in the same analysis, new bifurcations of short-crested waves are found, which give rise to mixed waves which may have complicated spatial structure.

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