scholarly journals Drift instability of standing Faraday waves

2002 ◽  
Vol 467 ◽  
pp. 57-79 ◽  
Author(s):  
ELENA MARTÍN ◽  
CARLOS MARTEL ◽  
JOSÉ M. VEGA
Keyword(s):  
Surface Wave ◽  
Reference Frame ◽  
Faraday Waves ◽  
Mean Flow ◽  
Weakly Nonlinear ◽  
Spatial Phase ◽  
New States ◽  
Slow Evolution ◽  
Drift Instability ◽  
Streaming Flow

We consider the weakly nonlinear evolution of the Faraday waves produced in a vertically vibrated two-dimensional liquid layer, at small viscosity. It is seen that the surface wave evolves to a drifting standing wave, namely a wave that is standing in a moving reference frame. This wave is determined up to a spatial phase, whose calculation requires consideration of the associated mean flow. This is just the streaming flow generated in the boundary layer attached to the lower plate supporting the liquid. A system of equations is derived for the coupled slow evolution of the spatial phase and the streaming flow. These equations are numerically integrated to show that the simplest reflection symmetric steady state (the usual array of counter-rotating eddies below the surface wave) becomes unstable for realistic values of the parameters. The new states include limit cycles (the array of eddies oscillating laterally), drifted standing waves (patterns that are standing in a uniformly propagating reference frame) and some more complex attractors.

scholarly journals Precessional instability of a fluid cylinder

2011 ◽  
Vol 666 ◽  
pp. 104-145 ◽  
Author(s):  
ROMAIN LAGRANGE ◽  
PATRICE MEUNIER ◽  
FRANÇOIS NADAL ◽  
CHRISTOPHE ELOY
Keyword(s):  
Reynolds Number ◽  
Nonlinear Effects ◽  
Intermittent Flow ◽  
Mean Flow ◽  
Weakly Nonlinear ◽  
Weakly Nonlinear Theory ◽  
Aspect Ratios ◽  
Image Velocimetry ◽  
Precessional Motion ◽  
Weakly Nonlinear Model

In this paper, the instability of a fluid inside a precessing cylinder is addressed theoretically and experimentally. The precessional motion forces Kelvin modes in the cylinder, which can become resonant for given precessional frequencies and cylinder aspect ratios. When the Reynolds number is large enough, these forced resonant Kelvin modes eventually become unstable. A linear stability analysis based on a triadic resonance between a forced Kelvin mode and two additional free Kelvin modes is carried out. This analysis allows us to predict the spatial structure of the instability and its threshold. These predictions are compared to the vorticity field measured by particle image velocimetry with an excellent agreement. When the Reynolds number is further increased, nonlinear effects appear. A weakly nonlinear theory is developed semi-empirically by introducing a geostrophic mode, which is triggered by the nonlinear interaction of a free Kelvin mode with itself in the presence of viscosity. Amplitude equations are obtained coupling the forced Kelvin mode, the two free Kelvin modes and the geostrophic mode. They show that the instability saturates to a fixed point just above threshold. Increasing the Reynolds number leads to a transition from a steady saturated regime to an intermittent flow in good agreement with experiments. Surprisingly, this weakly nonlinear model still gives a correct estimate of the mean flow inside the cylinder even far from the threshold when the flow is turbulent.

Heat transfer from a circular cylinder by acoustic streaming

1967 ◽  
Vol 30 (2) ◽  
pp. 337-355 ◽  
Author(s):  
Peter D. Richardson
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Natural Convection ◽  
Circular Cylinder ◽  
Prandtl Number ◽  
Acoustic Streaming ◽  
Mean Flow ◽  
Wide Range ◽  
Transverse Oscillations ◽  
Streaming Flow

An analysis is described for convection from a circular cylinder subjected to transverse oscillations relative to the fluid in which it is immersed. The analysis is based upon use of the acoustic streaming flow field. It is assumed that the frequency involved is sufficiently small that the acoustic wavelength in the fluid is much larger than the cylinder diameter, and that there is no externally imposed mean flow across or along the cylinder. Solutions are presented which are appropriate for a wide range of Prandtl number, and the cases of small and of large streaming Reynolds number are distinguished. The analysis compares favourably with experiments when the influence of natural convection is small.

scholarly journals Surface wave predictions in weakly nonlinear directional seas

2017 ◽  
Vol 65 ◽  
pp. 79-89 ◽  
Author(s):  
Abushet Simanesew ◽  
Karsten Trulsen ◽  
Harald E. Krogstad ◽  
José Carlos Nieto Borge
Keyword(s):  
Surface Wave ◽  
Weakly Nonlinear

Effect of Surface Wave on Development of Turbulent Boundary Layer Over a Train of Rib Roughness

2019 ◽  
Vol 141 (6) ◽  
Author(s):  
Santosh Kumar Singh ◽  
Pankaj Kumar Raushan ◽  
Koustuv Debnath ◽  
B. S. Mazumder
Keyword(s):  
Boundary Layer ◽  
Surface Wave ◽  
Turbulent Boundary Layer ◽  
Mean Flow ◽  
Mean Velocity ◽  
Measured Velocity ◽  
Law Of The Wall ◽  
Wave Channel ◽  
Surface Data ◽  
Large Roughness

In this paper, detailed experimental results are reported to study the effect of the surface wave of different frequencies on unidirectional current over the bed-mounted train of rib roughness. The model roughness used in this study is transverse square ribs that lengthened across the entire width of the recirculating wave channel. The center-to-center rib pitch (P) was constant during the experiments, thus generating a broad range of near-bed flow patterns for each of the three different surface wave frequencies studied here. The relative submergence associated with the roughness height (k) was 8, which fall in the category of large roughness. Velocity measurements were conducted using acoustic Doppler velocimeter (ADV), and a surface wave of different frequencies was generated using the plunger-type wavemaker. The measured velocity data were analyzed to determine the relative importance of mean flow over the train of rib roughness. Mean velocity profiles illustrate the well-known downward shift from the flat surface data of the semi-logarithmic portion of the law of the wall. The width of the turbulent boundary layer increases with the superposition of surface wave compared to that of the current-only flow. The results also show that the mean reattachment length decreases due to the superposition of surface wave on unidirectional current.

Fully coupled resonant-triad interactions in a free shear layer

1994 ◽  
Vol 278 ◽  
pp. 101-121 ◽  
Author(s):  
R. Mallier ◽  
S. A. Maslowe
Keyword(s):  
Flow Direction ◽  
Mixing Layer ◽  
Adverse Pressure Gradient ◽  
Critical Layer ◽  
Free Shear Layer ◽  
Mean Flow ◽  
Weakly Nonlinear ◽  
Initial Interaction ◽  
The Mean ◽  
Fully Coupled

We report the results of an investigation of the weakly nonlinear evolution of a triad of waves, each slightly amplified on a linear basis, that are superimposed on a tanh y mixing layer. The triad consists of a plane wave and a pair of oblique modes that act as a subharmonic of order 1/2. The oblique modes are inclined at approximately ±60°. to the mean flow direction and because the resonance conditions are satisfied exactly the analysis is entirely self-consistent as an asymptotic theory. The nonlinearity first occurs within the critical layer and the initial interaction is of the parametric resonance type. This produces faster than exponential growth of the oblique waves, behaviour observed recently in the experiments of Corke & Kusek (1993). The critical-layer dynamics lead subsequently to coupled integro-differential equations governing the amplitude evolution and, as first shown in related work by Goldstein & Lee (1992) on boundary layers in an adverse pressure gradient, these equations develop singularities in a finite time.

scholarly journals Eddy-Driven Recirculations from a Localized Transient Forcing

2012 ◽  
Vol 42 (3) ◽  
pp. 430-447 ◽  
Author(s):  
Stephanie Waterman ◽  
Steven R. Jayne
Keyword(s):  
Group Velocity ◽  
Rossby Wave ◽  
Wave Spectrum ◽  
Mean Flow ◽  
Weakly Nonlinear ◽  
Recirculation Gyres ◽  
Flow Interactions ◽  
Flow Effects ◽  
Wave Limit ◽  
Many Sources

Abstract The generation of time-mean recirculation gyres from the nonlinear rectification of an oscillatory, spatially localized vorticity forcing is examined analytically and numerically. Insights into the rectification mechanism are presented and the influence of the variations of forcing parameters, stratification, and mean background flow are explored. This exploration shows that the efficiency of the rectification depends on the properties of the energy radiation from the forcing, which in turn depends on the waves that participate in the rectification process. The particular waves are selected by the relation of the forcing parameters to the available free Rossby wave spectrum. An enhanced response is achieved if the parameters are such to select meridionally propagating waves, and a resonant response results if the forcing selects the Rossby wave with zero zonal group velocity and maximum meridional group velocity, which is optimal for producing rectified flows. Although formulated in a weakly nonlinear wave limit, simulations in a more realistic turbulent system suggest that this understanding of the mechanism remains useful in a strongly nonlinear regime with consideration of mean flow effects and wave–mean flow interaction now needing to be taken into account. The problem presented here is idealized but has general application in the understanding of eddy–eddy and eddy–mean flow interactions as the contrasting limit to that of spatially broad (basinwide) forcing and is relevant given that many sources of oceanic eddies are localized in space.

On the weakly nonlinear development of Tollmien-Schlichting wavetrains in boundary layers

1996 ◽  
Vol 323 ◽  
pp. 133-171 ◽  
Author(s):  
Xuesong Wu ◽  
Philip A. Stewart ◽  
Stephen J. Cowley
Keyword(s):  
Numerical Solutions ◽  
Asymptotic Methods ◽  
Nonlinear Effects ◽  
Mean Flow ◽  
Flow Distortion ◽  
Weakly Nonlinear ◽  
Nonlinear Development ◽  
Finite Distance ◽  
Tollmien Schlichting ◽  
High Reynolds

The nonlinear development of a weakly modulated Tollmien-Schlichting wavetrain in a boundary layer is studied theoretically using high-Reynolds-number asymptotic methods. The ‘carrier’ wave is taken to be two-dimensional, and the envelope is assumed to be a slowly varying function of time and of the streamwise and spanwise variables. Attention is focused on the scalings appropriate to the so-called ‘upper branch’ and ‘high-frequency lower branch’. The dominant nonlinear effects are found to arise in the critical layer and the surrounding ‘diffusion layer’: nonlinear interactions in these regions can influence the development of the wavetrain by producing a spanwise-dependent mean-flow distortion. The amplitude evolution is governed by an integro-partial-differential equation, whose nonlinear term is history-dependent and involves the highest derivative with respect to the spanwise variable. Numerical solutions show that a localized singularity can develop at a finite distance downstream. This singularity seems consistent with the experimentally observed focusing of vorticity at certain spanwise locations, although quantitative comparisons have not been attempted.

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