20 results
Parasitic waves and micro-breaking on highly nonlinear gravity–capillary waves in a convergent channel
- Chang Xu, Marc Perlin
-
- Journal:
- Journal of Fluid Mechanics / Volume 962 / 10 May 2023
- Published online by Cambridge University Press:
- 08 May 2023, A46
-
- Article
- Export citation
-
Gravity–capillary waves are waves influenced by both the effects of surface tension and gravity; these waves are at small scales with wavelength range from approximately 10 cm to less than 1 cm. Gravity–capillary waves play a significant role in air–sea interactions, and they exhibit much different features compared with gravity waves. They can be observed widely on the sea surface. Parasitic waves (capillary waves generated by and that ride on gravity and/or gravity–capillary waves) and micro-breaking can be observed on the water surface with winds; however, the presence of wind makes it difficult to analyse the mechanisms of the wave itself. In this paper, parasitic waves and micro-breaking on gravity–capillary waves are examined experimentally, both in the absence of wind. Parasitic waves and axisymmetric micro-breaking waves are generated mechanically in a convergent channel, where energy density increases due to spatial convergence. Three experimental techniques are used to measure wave properties: planar laser-induced fluorescence, particle image velocimetry and shadowgraphs. The wave profile evolution and vortices beneath the parasitic waves are studied. The micro-breaking of gravity–capillary waves is observed on a surface with added surfactant. The surfactant increases the Bond number, and makes breaking possible in these small-scale waves. Energy dissipation of parasitic waves and micro-breaking is quantified, and the enhanced dissipation caused by parasitic waves is identified through the experiments. In this study, mechanically generated breaking waves with wavelengths less than 10 cm are studied for the first time, without the effect of wind. The results yield insight into wave characteristics and energy dissipation on the air–sea interface at small scales.
Gravity–capillary multi-component wave patterns generated by a single-frequency wave-maker oscillation and subsequent resonances
- Chang Xu, Marc Perlin
-
- Journal:
- Journal of Fluid Mechanics / Volume 926 / 10 November 2021
- Published online by Cambridge University Press:
- 16 September 2021, A39
-
- Article
-
- You have access Access
- Open access
- HTML
- Export citation
-
Cross-waves are standing waves with crests perpendicular to a wave-maker; they are subharmonic waves excited by parametric instability. The modulational and chaotic behaviours of nonlinear cross-waves have been studied widely since the 1970s. Most of the previous work has focused on gravity waves where surface tension can be neglected. In this work we study cross-waves that are highly dependent on surface tension as well as gravity. By oscillating a planar wave-maker either vertically or horizontally with frequencies of 25 Hz through 40 Hz at one end of a rectangular basin, two-dimensional multi-component surface patterns are realized. Using the free-surface synthetic Schlieren technique to measure the surface elevations, multi-dimensional Fourier transforms are utilized to track the evolutionary spectrum of the water surface in both the temporal and spatial domains. Wavelet transforms are implemented to show the development of the various frequency components. Three-wave resonances with and without first subharmonics are observed for small nonlinearity. Three-dimensional oblique propagating cross-waves are generated at higher nonlinearity; unlike most previous cross-wave experiments, this staggered pattern propagates far downstream. Experimental evidence shows that two oblique propagating waves form a two-dimensional short-crested pattern, and that the lateral component of the waves develops into parametric sloshing modes corresponding to the width of the tank. Two regimes of nonlinear wave patterns, resonant triads and oblique propagating cross-waves, are delineated.
Characterization of superhydrophobic surfaces for drag reduction in turbulent flow
- James W. Gose, Kevin Golovin, Mathew Boban, Joseph M. Mabry, Anish Tuteja, Marc Perlin, Steven L. Ceccio
-
- Journal:
- Journal of Fluid Mechanics / Volume 845 / 25 June 2018
- Published online by Cambridge University Press:
- 27 April 2018, pp. 560-580
-
- Article
- Export citation
-
A significant amount of the fuel consumed by marine vehicles is expended to overcome skin-friction drag resulting from turbulent boundary layer flows. Hence, a substantial reduction in this frictional drag would notably reduce cost and environmental impact. Superhydrophobic surfaces (SHSs), which entrap a layer of air underwater, have shown promise in reducing drag in small-scale applications and/or in laminar flow conditions. Recently, the efficacy of these surfaces in reducing drag resulting from turbulent flows has been shown. In this work we examine four different, mechanically durable, large-scale SHSs. When evaluated in fully developed turbulent flow, in the height-based Reynolds number range of 10 000 to 30 000, significant drag reduction was observed on some of the surfaces, dependent on their exact morphology. We then discuss how neither the roughness of the SHSs, nor the conventional contact angle goniometry method of evaluating the non-wettability of SHSs at ambient pressure, can predict their drag reduction under turbulent flow conditions. Instead, we propose a new characterization parameter, based on the contact angle hysteresis at higher pressure, which aids in the rational design of randomly rough, friction-reducing SHSs. Overall, we find that both the contact angle hysteresis at higher pressure, and the non-dimensionalized surface roughness, must be minimized to achieve meaningful turbulent drag reduction. Further, we show that even SHSs that are considered hydrodynamically smooth can cause significant drag increase if these two parameters are not sufficiently minimized.
On the scaling of air entrainment from a ventilated partial cavity
- Simo A. Mäkiharju, Brian R. Elbing, Andrew Wiggins, Sarah Schinasi, Jean-Marc Vanden-Broeck, Marc Perlin, David R. Dowling, Steven L. Ceccio
-
- Journal:
- Journal of Fluid Mechanics / Volume 732 / 10 October 2013
- Published online by Cambridge University Press:
- 30 August 2013, pp. 47-76
-
- Article
- Export citation
-
The behaviour of a nominally two-dimensional ventilated partial cavity was examined over a wide range of size scales and flow speeds to determine the influence of Froude, Reynolds, and Weber number on the cavity shape, dynamics, and gas entrainment rate. Two geometrically similar experiments were conducted with a 14:1 length scale ratio. The results were compared to a two-dimensional semi-analytical model of the cavity flow, and Froude scaling was found to be sufficient to match basic cavity shapes. However, the air flux required to maintain a stable cavity did not scale with Froude number alone, as the dynamics of the cavity closure changed with increasing Reynolds number. The required air flux differed over one order of magnitude between the lowest and highest Reynolds number flows. But, for sufficiently high Reynolds numbers, the rate of scaled entrainment appeared to approach Reynolds number independence. Modest changes in surface tension of the small-scale experiment suggested that the Weber number was important only at the lowest speeds and smaller length scale. Otherwise, the Weber numbers of the flows were sufficiently high to make the effects of interfacial tension negligible. We also observed that modest unsteadiness in the inflow to the large-scale cavity led to a significant increase in the required air flux needed to maintain a stable cavity, with the required excess gas flux nominally proportional to the flow’s perturbation amplitude. Finally, discussion is provided on how these results relate to model testing of partial cavity drag reduction (PCDR) systems for surface ships.
On the scaling of air layer drag reduction
- Brian R. Elbing, Simo Mäkiharju, Andrew Wiggins, Marc Perlin, David R. Dowling, Steven L. Ceccio
-
- Journal:
- Journal of Fluid Mechanics / Volume 717 / 25 February 2013
- Published online by Cambridge University Press:
- 01 February 2013, pp. 484-513
-
- Article
- Export citation
-
Air-induced drag reduction was investigated on a 12.9 m long flat plate test model at a free stream speed of $6. 3~\mathrm{m} ~{\mathrm{s} }^{- 1} $. Measurements of the local skin friction, phase velocity profiles (liquid and gas) and void fraction profiles were acquired at downstream distances to 11.5 m, which yielded downstream-distance-based Reynolds numbers above 80 million. Air was injected within the boundary layer behind a 13 mm backward facing step (BFS) while the incoming boundary layer was perturbed with vortex generators in various configurations immediately upstream of the BFS. Measurements confirmed that air layer drag reduction (ALDR) is sensitive to upstream disturbances, but a clean boundary layer separation line (i.e. the BFS) reduces such sensitivity. Empirical scaling of the experimental data was investigated for: (a) the critical air flux required to establish ALDR; (b) void fraction profiles; and (c) the interfacial velocity profiles. A scaling of the critical air flux for ALDR was developed from balancing shear-induced lift forces and buoyancy forces on a single bubble within a shear flow. The resulting scaling successfully collapses ALDR results from the current and past studies over a range of flow conditions and test model configurations. The interfacial velocity and void fraction profiles were acquired and scaled within the bubble drag reduction (BDR), ALDR and transitional ALDR regimes. The BDR interfacial velocity profile revealed that there was slip between phases. The ALDR results showed that the air layer thickness was nominally three-quarters of the total volumetric flux (per unit span) of air injected divided by the free stream speed. Furthermore, the air layer had an average void fraction of 0.75 and a velocity of approximately 0.2 times the free stream speed. Beyond the air layer was a bubbly mixture that scaled in a similar fashion to the BDR results. Transitional ALDR results indicate that this regime was comprised of intermittent generation and subsequent fragmentation of an air layer, with the resulting drag reduction determined by the fraction of time that an air layer was present.
Frequency spectra evolution of two-dimensional focusing wave groups in finite depth water
- Zhigang Tian, Marc Perlin, Wooyoung Choi
-
- Journal:
- Journal of Fluid Mechanics / Volume 688 / 10 December 2011
- Published online by Cambridge University Press:
- 24 October 2011, pp. 169-194
-
- Article
- Export citation
-
An experimental and numerical study of the evolution of frequency spectra of dispersive focusing wave groups in a two-dimensional wave tank is presented. Investigations of both non-breaking and breaking wave groups are performed. It is found that dispersive focusing is far more than linear superposition, and that it undergoes strongly nonlinear processes. For non-breaking wave groups, as the wave groups propagate spatial evolution of wave frequency spectra, spectral bandwidth, surface elevation skewness, and kurtosis are examined. Nonlinear energy transfer between the above-peak () and the higher-frequency () regions, with being the spectral peak frequency, is demonstrated by tracking the energy level of the components in the focusing and defocusing process. Also shown is the nonlinear energy transfer to the lower-frequency components that cannot be detected easily by direct comparisons of the far upstream and downstream measurements. Energy dissipation in the spectral peak region () and the energy gain in the higher-frequency region () are quantified, and exhibit a dependence on the Benjamin–Feir Index (BFI). In the presence of wave breaking, the spectral bandwidth reduces as much as 40 % immediately following breaking and eventually becomes much smaller than its initial level. Energy levels in different frequency regions are examined. It is found that, before wave breaking onset, a large amount of energy is transferred from the above-peak region () to the higher frequencies (), where energy is dissipated during the breaking events. It is demonstrated that the energy gain in the lower-frequency region is at least partially due to nonlinear energy transfer prior to wave breaking and that wave breaking may not necessarily increase the energy in this region. Complementary numerical studies for breaking waves are conducted using an eddy viscosity model previously developed by the current authors. It is demonstrated that the predicted spectral change after breaking agrees well with the experimental measurements.
Flow-induced degradation of drag-reducing polymer solutions within a high-Reynolds-number turbulent boundary layer
- BRIAN R. ELBING, MICHAEL J. SOLOMON, MARC PERLIN, DAVID R. DOWLING, STEVEN L. CECCIO
-
- Journal:
- Journal of Fluid Mechanics / Volume 670 / 10 March 2011
- Published online by Cambridge University Press:
- 22 February 2011, pp. 337-364
-
- Article
- Export citation
-
Polymer drag reduction, diffusion and degradation in a high-Reynolds-number turbulent boundary layer (TBL) flow were investigated. The TBL developed on a flat plate at free-stream speeds up to 20ms−1. Measurements were acquired up to 10.7m downstream of the leading edge, yielding downstream-distance-based Reynolds numbers up to 220 million. The test model surface was hydraulically smooth or fully rough. Flow diagnostics included local skin friction, near-wall polymer concentration, boundary layer sampling and rheological analysis of polymer solution samples. Skin-friction data revealed that the presence of surface roughness can produce a local increase in drag reduction near the injection location (compared with the flow over a smooth surface) because of enhanced mixing. However, the roughness ultimately led to a significant decrease in drag reduction with increasing speed and downstream distance. At the highest speed tested (20ms−1) no drag reduction was discernible at the first measurement location (0.56m downstream of injection), even at the highest polymer injection flux (10 times the flux of fluid in the near-wall region). Increased polymer degradation rates and polymer mixing were shown to be the contributing factors to the loss of drag reduction. Rheological analysis of liquid drawn from the TBL revealed that flow-induced polymer degradation by chain scission was often substantial. The inferred polymer molecular weight was successfully scaled with the local wall shear rate and residence time in the TBL. This scaling revealed an exponential decay that asymptotes to a finite (steady-state) molecular weight. The importance of the residence time to the scaling indicates that while individual polymer chains are stretched and ruptured on a relatively short time scale (~10−3s), because of the low percentage of individual chains stretched at any instant in time, a relatively long time period (~0.1s) is required to observe changes in the mean molecular weight. This scaling also indicates that most previous TBL studies would have observed minimal influence from degradation due to insufficient residence times.
The mean velocity profile of a smooth-flat-plate turbulent boundary layer at high Reynolds number
- GHANEM F. OWEIS, ERIC S. WINKEL, JAMES M. CUTBRITH, STEVEN L. CECCIO, MARC PERLIN, DAVID R. DOWLING
-
- Journal:
- Journal of Fluid Mechanics / Volume 665 / 25 December 2010
- Published online by Cambridge University Press:
- 06 December 2010, pp. 357-381
-
- Article
- Export citation
-
Smooth flat-plate turbulent boundary layers (TBLs) have been studied for nearly a century. However, there is a relative dearth of measurements at Reynolds numbers typical of full-scale marine and aerospace transportation systems (Reθ = Ueθ/ν > 105, where Ue = free-stream speed, θ = TBL momentum thickness and ν = kinematic viscosity). This paper presents new experimental results for the TBL that forms on a smooth flat plate at nominal Reθ values of 0.5 × 105, 1.0 × 105 and 1.5 × 105. Nominal boundary layer thicknesses (δ) were 80–90mm, and Karman numbers (δ+) were 17000, 32000 and 47000, respectively. The experiments were conducted in the William B. Morgan Large Cavitation Channel on a polished (k+ < 0.2) flat-plate test model 12.9m long and 3.05m wide at water flow speeds up to 20ms−1. Direct measurements of static pressure and mean wall shear stress were obtained with pressure taps and floating-plate skin friction force balances. The TBL developed a mild favourable pressure gradient that led to a streamwise flow speed increase of ~2.5% over the 11m long test surface, and was consistent with test section sidewall and model surface boundary-layer growth. At each Reθ, mean streamwise velocity profile pairs, separated by 24cm, were measured more than 10m from the model's leading edge using conventional laser Doppler velocimetry. Between these profile pairs, a unique near-wall implementation of particle tracking velocimetry was used to measure the near-wall velocity profile. The composite profile measurements span the wall-normal coordinate range from y+ < 1 to y > 2δ. To within experimental uncertainty, the measured mean velocity profiles can be fit using traditional zero-pressure-gradient (ZPG) TBL asymptotics with some modifications for the mild favourable pressure gradient. The fitted profile pairs satisfy the von-Kármán momentum integral equation to within 1%. However, the profiles reported here show distinct differences from equivalent ZPG profiles. The near-wall indicator function has more prominent extrema, the log-law constants differ slightly, and the profiles' wake component is less pronounced.
Energy dissipation in two-dimensional unsteady plunging breakers and an eddy viscosity model
- ZHIGANG TIAN, MARC PERLIN, WOOYOUNG CHOI
-
- Journal:
- Journal of Fluid Mechanics / Volume 655 / 25 July 2010
- Published online by Cambridge University Press:
- 12 May 2010, pp. 217-257
-
- Article
- Export citation
-
An experimental study of energy dissipation in two-dimensional unsteady plunging breakers and an eddy viscosity model to simulate the dissipation due to wave breaking are reported in this paper. Measured wave surface elevations are used to examine the characteristic time and length scales associated with wave groups and local breaking waves, and to estimate and parameterize the energy dissipation and dissipation rate due to wave breaking. Numerical tests using the eddy viscosity model are performed and we find that the numerical results well capture the measured energy loss. In our experiments, three sets of characteristic time and length scales are defined and obtained: global scales associated with the wave groups, local scales immediately prior to breaking onset and post-breaking scales. Correlations among these time and length scales are demonstrated. In addition, for our wave groups, wave breaking onset predictions using the global and local wave steepnesses are found based on experimental results. Breaking time and breaking horizontal length scales are determined with high-speed imaging, and are found to depend approximately linearly on the local wave steepness. The two scales are then used to determine the energy dissipation rate, which is the ratio of the energy loss to the breaking time scale. Our experimental results show that the local wave steepness is highly correlated with the measured dissipation rate, indicating that the local wave steepness may serve as a good wave-breaking-strength indicator. To simulate the energy dissipation due to wave breaking, a simple eddy viscosity model is proposed and validated with our experimental measurements. Under the small viscosity assumption, the leading-order viscous effect is incorporated into the free-surface boundary conditions. Then, the kinematic viscosity is replaced with an eddy viscosity to account for energy loss. The breaking time and length scales, which depend weakly on wave breaking strength, are applied to evaluate the magnitude of the eddy viscosity using dimensional analysis. The estimated eddy viscosity is of the order of 10−3 m2s−1 and demonstrates a strong dependence on wave breaking strength. Numerical simulations with the eddy viscosity estimation are performed to compare to the experimental results. Good agreement as regards energy dissipation due to wave breaking and surface profiles after wave breaking is achieved, which illustrates that the simple eddy viscosity model functions effectively.
Bubble-induced skin-friction drag reduction and the abrupt transition to air-layer drag reduction
- BRIAN R. ELBING, ERIC S. WINKEL, KEARY A. LAY, STEVEN L. CECCIO, DAVID R. DOWLING, MARC PERLIN
-
- Journal:
- Journal of Fluid Mechanics / Volume 612 / 10 October 2008
- Published online by Cambridge University Press:
- 10 October 2008, pp. 201-236
-
- Article
- Export citation
-
To investigate the phenomena of skin-friction drag reduction in a turbulent boundary layer (TBL) at large scales and high Reynolds numbers, a set of experiments has been conducted at the US Navy's William B. Morgan Large Cavitation Channel (LCC). Drag reduction was achieved by injecting gas (air) from a line source through the wall of a nearly zero-pressure-gradient TBL that formed on a flat-plate test model that was either hydraulically smooth or fully rough. Two distinct drag-reduction phenomena were investigated; bubble drag reduction (BDR) and air-layer drag reduction (ALDR).
The streamwise distribution of skin-friction drag reduction was monitored with six skin-friction balances at downstream-distance-based Reynolds numbers to 220 million and at test speeds to 20.0ms−1. Near-wall bulk void fraction was measured at twelve streamwise locations with impedance probes, and near-wall (0 < Y < 5mm) bubble populations were estimated with a bubble imaging system. The instrument suite was used to investigate the scaling of BDR and the requirements necessary to achieve ALDR.
Results from the BDR experiments indicate that: significant drag reduction (>25%) is limited to the first few metres downstream of injection; marginal improvement was possible with a porous-plate versus an open-slot injector design; BDR has negligible sensitivity to surface tension; bubble size is independent of surface tension downstream of injection; BDR is insensitive to boundary-layer thickness at the injection location; and no synergetic effect is observed with compound injection. Using these data, previous BDR scaling methods are investigated, but data collapse is observed only with the ‘initial zone’ scaling, which provides little information on downstream persistence of BDR.
ALDR was investigated with a series of experiments that included a slow increase in the volumetric flux of air injected at free-stream speeds to 15.3ms−1. These results indicated that there are three distinct regions associated with drag reduction with air injection: Region I, BDR; Region II, transition between BDR and ALDR; and Region III, ALDR. In addition, once ALDR was established: friction drag reduction in excess of 80% was observed over the entire smooth model for speeds to 15.3ms−1; the critical volumetric flux of air required to achieve ALDR was observed to be approximately proportional to the square of the free-stream speed; slightly higher injection rates were required for ALDR if the surface tension was decreased; stable air layers were formed at free-stream speeds to 12.5ms−1 with the surface fully roughened (though approximately 50% greater volumetric air flux was required); and ALDR was sensitive to the inflow conditions. The sensitivity to the inflow conditions can be mitigated by employing a small faired step (10mm height in the experiment) that helps to create a fixed separation line.
Boundary conditions in the vicinity of the contact line at a vertically oscillating upright plate: an experimental investigation
- Chao-Lung Ting, Marc Perlin
-
- Journal:
- Journal of Fluid Mechanics / Volume 295 / 25 July 1995
- Published online by Cambridge University Press:
- 26 April 2006, pp. 263-300
-
- Article
- Export citation
-
To determine a suitable boundary-condition model for the contact line in oscillatory flow, an upright plate, oscillated vertically with sinusoidal motion in dye-laden water with an air interface, is considered experimentally. Constrained by the desirability of a two-dimensional flow field, eight frequencies in the 1–20 Hz range, each with seven different stroke amplitudes (0.5–6 mm) are chosen. The Reynolds number varies from 1.6 to 1878.3 in the experiments, large relative to the Reynolds number in the conventional uni-directional contact-line experiments (e.g. Dussan V.'s 1974 experiments). To facilitate prediction, a high-speed video system is used to record the plate displacement, the contact-line displacement, and the dynamic behaviour of the contact angle. Several interesting contact-line phenomena are shown in the present results. An expression for λ, the dimensionless capillary coefficient, is formulated such that the dynamic behaviour at the contact line is predicted reasonably well. A particle-tracking-velocimetry (PTV) technique is used to detect particle trajectories near the plate such that the boundary condition along the entire plate can be modelled. Two sets of PTV experiments are conducted. One set is for stick contact-line motion, the other set is for stick–slip contact-line motion. The results from the PTV experiments show that a vortex is formed near the meniscus in the stick-slip contact-line experiments; however, in the stick contact-line experiments, no such vortex is present. Using the present experimental results, a model is developed for the boundary condition along the vertically oscillating vertical plate. In this model, slip occurs within a specific distance from the contact line while the flow obeys the no-slip condition outside this slip region. Also, the mean slip length is determined for each experimental stroke amplitude.
On parasitic capillary waves generated by steep gravity waves: an experimental investigation with spatial and temporal measurements
- Marc Perlin, Huanjay Lin, Chao-Lung Ting
-
- Journal:
- Journal of Fluid Mechanics / Volume 260 / 10 February 1994
- Published online by Cambridge University Press:
- 26 April 2006, p. 376
-
- Article
- Export citation
Moderate and steep Faraday waves: instabilities, modulation and temporal asymmetries
- Lei Jiang, Chao-Lung Ting, Marc Perlin, William W. Schultz
-
- Journal:
- Journal of Fluid Mechanics / Volume 329 / 25 December 1996
- Published online by Cambridge University Press:
- 26 April 2006, pp. 275-307
-
- Article
- Export citation
-
Mild to steep standing waves of the fundamental mode are generated in a narrow rectangular cylinder undergoing vertical oscillation with forcing frequencies of 3.15 Hz to 3.34 Hz. A precise, non-intrusive optical wave profile measurement system is used along with a wave probe to accurately quantify the spatial and temporal surface elevations. These standing waves are also simulated by a two-dimensional spectral Cauchy integral code. Experiments show that contact-line effects increase the viscous natural frequency and alter the neutral stability curves. Hence, as expected, the addition of the wetting agent Photo Flo significantly changes the stability curve and the hysteresis in the response diagram. Experimentally, we find strong modulations in the wave amplitude for some forcing frequencies higher than 3.30 Hz. Reducing contact-line effects by Photo-Flo addition suppresses these modulations. Perturbation analysis predicts that some of this modulation is caused by noise in the forcing signal through ‘sideband resonance’, i.e. the introduction of small sideband forcing can generate large modulations of the Faraday waves. The analysis is verified by our numerical simulations and physical experiments. Finally, we observe experimentally a new form of steep standing wave with a large symmetric double-peaked crest, while simulation of the same forcing condition results in a sharper crest than seen previously. Both standing wave forms appear at a finite wave steepness far smaller than the maximum steepness for the classical standing wave and a surface tension far smaller than that for a Wilton ripple. In both physical and numerical experiments, a stronger second harmonic (in time) and temporal asymmetry in the wave forms suggest a 1:2 resonance due to a non-conventional quartet interaction. Increasing wave steepness leads to a new form of breaking standing waves in physical experiments.
Experiments on ripple instabilities. Part 3. Resonant quartets of the Benjamin–Feir type
- Marc Perlin, Joe Hammack
-
- Journal:
- Journal of Fluid Mechanics / Volume 229 / August 1991
- Published online by Cambridge University Press:
- 26 April 2006, pp. 229-268
-
- Article
- Export citation
-
Instabilities and long-time evolution of gravity-capillary wavetrains (ripples) with moderate steepnesses (ε < 0.3) are studied experimentally and analytically. Wave-trains with frequencies of 8 ≤ f ≤ 25 Hz are generated mechanically in a channel containing clean, deep water; no artificial perturbations are introduced. Frequency spectra are obtained from in situ measurements; two-dimensional wavenumber spectra are obtained from remote sensing of the water surface using a high-speed imaging system. The analytical models are in viscid, uncoupled NLS (nonlinear Schrödinger) equations: one that describes the temporal evolution of longitudinal modulations and one that describes the spatial evolution of transverse modulations.
The experiments show that the evolution of wavetrains with sensible amplitudes and frequencies exceeding 9.8 Hz is dominated by modulational instabilities, i.e. resonant quartet interactions of the Benjamin–Feir type. These quartet interactions remain dominant even for wavetrains that are unstable to resonant triad interactions (f > 19.6 Hz) – if selective amplification does not occur (see Parts 1 and 2). The experiments further show that oblique perturbations with the same frequency as the underlying wavetrain, i.e. rhombus-quartet instabilities, amplify more rapidly and dominate all other modulational instabilities. The inviscid, uncoupled NLS equations predict the existence of modulational instabilities for wavetrains with frequencies exceeding 9.8 Hz, typically underpredict the bandwidth of unstable transverse modulations, typically overpredict the bandwidth of unstable longitudinal modulations, and do not predict the dominance of the rhombus-quartet instability. When the effects of weak viscosity are incorporated into the NLS models, the predicted bandwidths of unstable modulations are reduced, which is consistent with our measurements for longitudinal modulations, but not with our measurements for transverse modulations.
Both the experiments and NLS equations indicate that wavetrains in the frequency range 6.4–9.8 Hz are stable to modulational instabilities. However, in these experiments, wavetrains with sensible amplitudes excite one of the members of the Wilton ripples family. When second-harmonic resonance occurs, both the first-and second-harmonic wavetrains undergo rhombus-quartet instabilities. When third-harmonic resonance occurs, only the third-harmonic wavetrain undergoes rhombus-quartet instabilities.
On parasitic capillary waves generated by steep gravity waves: an experimental investigation with spatial and temporal measurements
- Marc Perlin, Huanjay Lin, Chao-Lung Ting
-
- Journal:
- Journal of Fluid Mechanics / Volume 255 / October 1993
- Published online by Cambridge University Press:
- 26 April 2006, pp. 597-620
-
- Article
- Export citation
-
An experimental investigation of steep, high-frequency gravity waves (∼ 4 to 5 Hz) and the parasitic capillary waves they generate is reported. Spatial, as well as temporal, non-intrusive surface measurements are made using a new technique. This technique employs cylindrical lenses to magnify the vertical dimension in conjunction with an intensified, high-speed imaging system, facilitating the measurement of the disparate scales with a vertical surface-elevation resolution on the order of 10 μm. Thus, high-frequency parasitic capillary waves and the underlying gravity wave are measured simultaneously and accurately in space and time. Time series of spatial surface-elevation measurements are presented. It is shown that the location of the capillary waves is quasi-stationary in a coordinate system moving with the phase speed of the underlying gravity wave. Amplitudes and wavenumbers of the capillaries are modulated in space; however, they do not propagate with respect to the gravity wave. As capillary amplitudes are seen to decrease significantly and then increase again in a recurrence-like phenomenon, it is conjectured that resonance mechanisms are present. Measured surface profiles are compared to the theories of Longuet-Higgins (1963) and Crapper (1970) and the exact, two-dimensional numerical formulation of Schwartz & Vanden-Broeck (1979). Significant discrepancies are found between experimental and theoretical wavetrains in both amplitude and wavenumber. The theoretical predictions of the capillary wave amplitudes are much smaller than the measured amplitudes when the measured phase speed, amplitude, and wavelength of the gravity wave are used in the Longuet-Higgins model. In addition, this theory predicts larger wavenumbers of the capillaries as compared to experiments. The Crapper model predicts the correct order-of-magnitude capillary wave amplitude on the forward face of the gravity wave, but predicts larger amplitudes on the leeward face in comparison to the experiments. Also, it predicts larger capillary wavenumbers than are experimentally determined. Comparison of the measured profiles to multiple solutions of the stationary, symmetric, periodic solutions determined using the Schwartz & Vanden-Broeck numerical formulation show similar discrepancies. In particular, the assumed symmetry of the waveform about crest and trough in the numerical model precludes a positive comparison with the experiments, whose underlying waves exhibit significantly larger capillaries on their forward face than on their leeward face. Also, the a priori unknown multiplicity of numerical solutions for the same dimensionless surface tension and steepness parameters complicates comparison. Finally, using the temporal periodicity of the wave field, composite images of several successive wavelengths are constructed from which potential energy and surface energy are calculated as a function of distance downstream.
Experiments on ripple instabilities. Part 2 Selective amplification of resonant triads
- Marc Perlin, Diane Henderson, Joe Hammack
-
- Journal:
- Journal of Fluid Mechanics / Volume 219 / October 1990
- Published online by Cambridge University Press:
- 26 April 2006, pp. 51-80
-
- Article
- Export citation
-
Resonant three-wave interactions among capillary–gravity water waves are studied experimentally using a test wavetrain and smaller background waves (noise) generated mechanically in a channel. The spectrum of the background waves is varied from broad-banded to one with discrete components. When the noise spectrum is broad-banded, the test wavetrain amplifies all waves in its low-frequency band of allowable triads B[ell ], as anticipated from RIT (resonant interaction theory). When the noise spectrum has a discrete component in the high-frequency band of allowable triads Bh, the test wavetrain selectively amplifies a triad with two waves from B[ell ], contrary to expectations based on RIT. (Although, in accordance with RIT, no waves in Bh are amplified.) We conjecture that the mechanism for selective amplification comprises a sequence of exceedingly weak, higher-order interactions, normally neglected in RIT. This sequence allows the small amount of energy in a discrete spectral component to cascade to two waves in B[ell ], which then amplify, as anticipated from RIT, and dominate all other waves in B[ell ]. The conjectured sequence of nonlinear interactions is tested using both frequency and wave-vector data, which are obtained by in situ probes and by remote sensing of the water surface with a highspeed imaging system. Our predictions of selective amplification, as well as its absence, are consistent with all of the experiments presented herein and in Part 1. Selective amplification occurs for signal-to-noise (amplitude) ratios as large as 200, and its effects are measurable within ten wavelengths of the wavemaker. When selective amplification occurs, it has a profound impact on the long-time evolution of a ripple wavetrain.
Bubble friction drag reduction in a high-Reynolds-number flat-plate turbulent boundary layer
- WENDY C. SANDERS, ERIC S. WINKEL, DAVID R. DOWLING, MARC PERLIN, STEVEN L. CECCIO
-
- Journal:
- Journal of Fluid Mechanics / Volume 552 / 10 April 2006
- Published online by Cambridge University Press:
- 29 March 2006, pp. 353-380
-
- Article
- Export citation
-
Turbulent boundary layer skin friction in liquid flows may be reduced when bubbles are present near the surface on which the boundary layer forms. Prior experimental studies of this phenomenon reached downstream-distance-based Reynolds numbers ($Re_{x}$) of several million, but potential applications may occur at $Re_{x}$ orders of magnitude higher. This paper presents results for $Re_{x}$ as high as 210 million from skin-friction drag-reduction experiments conducted in the USA Navy's William B. Morgan Large Cavitation Channel (LCC). Here, a near-zero-pressure-gradient flat-plate turbulent boundary layer was generated on a 12.9 m long hydraulically smooth flat plate that spanned the 3 m wide test section. The test surface faced downward and air was injected at volumetric rates as high as 0.38 m$^{3}$ s$^{-1}$ through one of two flush-mounted 40 $\mu$m sintered-metal strips that nearly spanned the test model at upstream and downstream locations. Spatially and temporally averaged shear stress and bubble-image-based measurements are reported here for nominal test speeds of 6, 12 and 18 m s$^{-1}$. The mean bubble diameter was $\sim$300 $\mu$m. At the lowest test speed and highest air injection rate, buoyancy pushed the air bubbles to the plate surface where they coalesced to form a nearly continuous gas film that persisted to the end of the plate with near-100% skin-friction drag reduction. At the higher two flow speeds, the bubbles generally remained distinct and skin-friction drag reduction was observed when the bubbly mixture was closer to the plate surface than 300 wall units of the boundary-layer flow without air injection, even when the bubble diameter was more than 100 of these wall units. Skin-friction drag reduction was lost when the near-wall shear induced the bubbles to migrate from the plate surface. This bubble-migration phenomenon limited the persistence of bubble-induced skin-friction drag reduction to the first few metres downstream of the air injector in the current experiments.
Unsteady ripple generation on steep gravity–capillary waves
- LEI JIANG, HUAN-JAY LIN, WILLIAM W. SCHULTZ, MARC PERLIN
-
- Journal:
- Journal of Fluid Mechanics / Volume 386 / 10 May 1999
- Published online by Cambridge University Press:
- 10 May 1999, pp. 281-304
-
- Article
- Export citation
-
Parasitic ripple generation on short gravity waves (4 cm to 10 cm wavelengths) is examined using fully nonlinear computations and laboratory experiments. Time-marching simulations show sensitivity of the ripple steepness to initial conditions, in particular to the crest asymmetry. Significant crest fore–aft asymmetry and its unsteadiness enhance ripple generation at moderate wave steepness, e.g. ka between 0.15 and 0.20, a mechanism not discussed in previous studies. The maximum ripple steepness (in time) is found to increase monotonically with the underlying (low-frequency bandpass) wave steepness in our simulations. This is different from the sub- or super-critical ripple generation predicted by Longuet-Higgins (1995). Unsteadiness in the underlying gravity–capillary waves is shown to cause ripple modulation and an interesting ‘crest-shifting’ phenomenon – the gravity–capillary wave crest and the first ripple on the forward slope merge to form a new crest. Including boundary layer efects in the free-surface conditions extends some of the simulations at large wave amplitudes. However, the essential process of parasitic ripple generation is nonlinear interaction in an inviscid flow. Mechanically generated gravity–capillary waves demonstrate similar characteristic features of ripple generation and a strong correlation between ripple steepness and crest asymmetry.
Period tripling and energy dissipation of breaking standing waves
- LEI JIANG, MARC PERLIN, WILLIAM W. SCHULTZ
-
- Journal:
- Journal of Fluid Mechanics / Volume 369 / 25 August 1998
- Published online by Cambridge University Press:
- 25 August 1998, pp. 273-299
-
- Article
- Export citation
-
We examine the dynamics of two-dimensional steep and breaking standing waves generated by Faraday-wave resonance. Jiang et al. (1996) found a steep wave with a double-peaked crest in experiments and a sharp-crested steep wave in computations. Both waveforms are strongly asymmetric in time and feature large superharmonics. We show experimentally that increasing the forcing amplitude further leads to breaking waves in three recurrent modes (period tripling): sharp crest with breaking, dimpled or flat crest with breaking, and round crest without breaking. Interesting steep waveforms and period-tripled breaking are related directly to the nonlinear interaction between the fundamental mode and the second temporal harmonic. Unfortunately, these higher-amplitude phenomena cannot be numerically modelled since the computations fail for breaking or nearly breaking waves. Based on the periodicity of Faraday waves, we directly estimate the dissipation due to wave breaking by integrating the support force as a function of the container displacement. We find that the breaking events (spray, air entrainment, and plunging) approximately double the wave dissipation.
Highly nonlinear standing water waves with small capillary effect
- WILLIAM W. SCHULTZ, JEAN-MARC VANDEN-BROECK, LEI JIANG, MARC PERLIN
-
- Journal:
- Journal of Fluid Mechanics / Volume 369 / 25 August 1998
- Published online by Cambridge University Press:
- 25 August 1998, pp. 253-272
-
- Article
- Export citation
-
We calculate spatially and temporally periodic standing waves using a spectral boundary integral method combined with Newton iteration. When surface tension is neglected, the non-monotonic behaviour of global wave properties agrees with previous computations by Mercer & Roberts (1992). New accurate results near the limiting form of gravity waves are obtained by using a non-uniform node distribution. It is shown that the crest angle is smaller than 90° at the largest calculated crest curvature. When a small amount of surface tension is included, the crest form is changed significantly. It is necessary to include surface tension to numerically reproduce the steep standing waves in Taylor's (1953) experiments. Faraday-wave experiments in a large-aspect-ratio rectangular container agree with our computations. This is the first time such high-amplitude, periodic waves appear to have been observed in laboratory conditions. Ripple formation and temporal symmetry breaking in the experiments are discussed.