scholarly journals Resonantly forced gravity–capillary lumps on deep water. Part 1. Experiments

2011 ◽  
Vol 672 ◽  
pp. 268-287 ◽  
Author(s):  
JAMES D. DIORIO ◽  
YEUNWOO CHO ◽  
JAMES H. DUNCAN ◽  
T. R. AKYLAS
Keyword(s):  
Surface Pressure ◽  
Deep Water ◽  
Measurement Techniques ◽  
Phase Speed ◽  
Wave Pattern ◽  
Capillary Waves ◽  
Pressure Amplitude ◽  
Pressure Source ◽  
Nonlinear Features ◽  
Pressure Magnitude

The wave pattern generated by a pressure source moving over the free surface of deep water at speeds, U, below the minimum phase speed for linear gravity–capillary waves, cmin, was investigated experimentally using a combination of photographic measurement techniques. In similar experiments, using a single pressure amplitude, Diorio et al. (Phys. Rev. Lett., vol. 103, 2009, 214502) pointed out that the resulting surface response pattern exhibits remarkable nonlinear features as U approaches cmin, and three distinct response states were identified. Here, we present a set of measurements for four surface-pressure amplitudes and provide a detailed quantitative examination of the various behaviours. At low speeds, the pattern resembles the stationary state (U = 0), essentially a circular dimple located directly under the pressure source (called a state I response). At a critical speed, but still below cmin, there is an abrupt transition to a wave-like state (state II) that features a marked increase in the response amplitude and the formation of a localized solitary depression downstream of the pressure source. This solitary depression is steady, elongated in the cross-stream relative to the streamwise direction, and resembles freely propagating gravity–capillary ‘lump’ solutions of potential flow theory on deep water. Detailed measurements of the shape of this depression are presented and compared with computed lump profiles from the literature. The amplitude of the solitary depression decreases with increasing U (another known feature of lumps) and is independent of the surface pressure magnitude. The speed at which the transition from states I to II occurs decreases with increasing surface pressure. For speeds very close to the transition point, time-dependent oscillations are observed and their dependence on speed and pressure magnitude are reported. As the speed approaches cmin, a second transition is observed. Here, the steady solitary depression gives way to an unsteady state (state III), characterized by periodic shedding of lump-like disturbances from the tails of a V-shaped pattern.

scholarly journals The generation of gravity–capillary solitary waves by a pressure source moving at a trans-critical speed

2016 ◽  
Vol 810 ◽  
pp. 448-474 ◽  
Author(s):  
Naeem Masnadi ◽  
James H. Duncan
Keyword(s):  
Free Surface ◽  
Numerical Simulations ◽  
Model Equation ◽  
Surface Deformation ◽  
Phase Speed ◽  
Capillary Waves ◽  
Deformation Pattern ◽  
Pressure Source ◽  
Exponential Decay Law ◽  
Response State

The unsteady response of a water free surface to a localized pressure source moving at constant speed $U$ in the range $0.95c_{min}\lesssim U\leqslant 1.02c_{min}$, where $c_{min}$ is the minimum phase speed of linear gravity–capillary waves in deep water, is investigated through experiments and numerical simulations. This unsteady response state, which consists of a V-shaped pattern behind the source, and features periodic shedding of pairs of depressions from the tips of the V, was first observed qualitatively by Diorio et al. (Phys. Rev. Lett., vol. 103, 2009, 214502) and called state III. In the present investigation, cinematic shadowgraph and refraction-based techniques are utilized to measure the temporal evolution of the free-surface deformation pattern downstream of the source as it moves along a towing tank, while numerical simulations of the model equation described by Cho et al. (J. Fluid Mech., vol. 672, 2011, pp. 288–306) are used to extend the experimental results over longer times than are possible in the experiments. From the experiments, it is found that the speed–amplitude characteristics and the shape of the depressions are nearly the same as those of the freely propagating gravity–capillary lumps of inviscid potential theory. The decay rate of the depressions is measured from their height–time characteristics, which are well fitted by an exponential decay law with an order one decay constant. It is found that the shedding period of the depression pairs decreases with increasing source strength and speed. As the source speed approaches $c_{min}$, this period tends to approximately 1 s for all source magnitudes. At the low-speed boundary of state III, a new response with unsteady asymmetric shedding of depressions is found. This response is also predicted by the model equation.

scholarly journals Observations of gravity–capillary lump interactions

2017 ◽  
Vol 814 ◽  
Author(s):  
Naeem Masnadi ◽  
James H. Duncan
Keyword(s):  
Solitary Waves ◽  
Nonlinear Response ◽  
Three Dimensional ◽  
Phase Speed ◽  
Wave Pattern ◽  
Capillary Waves ◽  
Stable Pattern ◽  
Half Angle ◽  
Linear Gravity ◽  
Shaped Pattern

In this experimental study, we investigate the interaction of gravity–capillary solitary waves generated by two surface pressure sources moving side by side at constant speed. The nonlinear response of a water surface to a single source moving at a speed just below the minimum phase speed of linear gravity–capillary waves in deep water ($c_{min}\approx 23~\text{cm}~\text{s}^{-1}$) consists of periodic generation of pairs of three-dimensional solitary waves (or lumps) in a V-shaped pattern downstream of the source. In the reference frame of the laboratory, these unsteady lumps propagate in a direction oblique to the motion of the source. In the present experiments, the strengths of the two sources are adjusted to produce nearly identical responses and the free-surface deformations are visualized using photography-based techniques. The first lumps generated by the two sources move in intersecting directions that make a half-angle of approximately $15^{\circ }$ and collide in the centreplane between the sources. A steep depression is formed during the collision, but this depression quickly decreases in amplitude while radiating small-amplitude radial waves. After the collision, a quasi-stable pattern is formed with several rows of localized depressions that are qualitatively similar to lumps but exhibit periodic amplitude oscillations, similar to a breather. The shape of the wave pattern and the period of oscillations depend strongly on the distance between the sources.

Effects of plane progressive irrotational waves on thermal boundary layers

1971 ◽  
Vol 50 (2) ◽  
pp. 321-334 ◽  
Author(s):  
James Witting
Keyword(s):  
Boundary Layers ◽  
Deep Water ◽  
Maximum Amplitude ◽  
Capillary Waves ◽  
Temperature Gradients ◽  
Two Dimensional ◽  
Inviscid Incompressible Fluid ◽  
Mean Temperature ◽  
The Waves ◽  
Thermal Boundary Layers

The average changes in the structure of thermal boundary layers at the surface of bodies of water produced by various types of surface waves are computed. the waves are two-dimensional plane progressive irrotational waves of unchanging shape. they include deep-water linear waves, deep-water capillary waves of arbitrary amplitude, stokes waves, and the deep-water gravity wave of maximum amplitude.The results indicate that capillary waves can decrease mean temperature gradients by factors of as much as 9·0, if the average heat flux at the air-water interface is independent of the presence of the waves. Irrotational gravity waves can decrease the mean temperature gradients by factors no more than 1·381.Of possible pedagogical interest is the simplicity of the heat conduction equation for two-dimensional steady irrotational flows in an inviscid incompressible fluid if the velocity potential and the stream function are taken to be the independent variables.

Diffraction Waves About an Advancing Wedge Model in Deep Water

1990 ◽  
Vol 34 (02) ◽  
pp. 105-122
Author(s):  
Hideaki Miyata ◽  
Makoto Kanai ◽  
Noriaki Yoshiyasu ◽  
Yohichi Furuno
Keyword(s):  
Numerical Simulation ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Wedge Angle ◽  
Wave Pattern ◽  
Regular Waves ◽  
Nonlinear Characteristics ◽  
Diffracted Waves ◽  
Nonlinear Features ◽  
Incident Waves

The diffraction of regular waves by advancing wedge models is studied both experimentally and numerically. The nonlinear features of diffracted waves are visualized by wave pattern pictures and the formation is analyzed by the grid-projection method. The experimental observation indicates that the diffracted waves have a number of nonlinear characteristics similar to shock waves due to the interaction of incident waves with the advancing obstacle in the flow-field caused by the advancing motion. Bow waves of both oblique type and normal detached type are observed at remarkably lower Froude numbers than in the case of a ship in steady advance motion. Their occurrence systematically depends on the Froude number and the wedge angle. The numerical simulation of this phenomenon by a finite-difference method shows approximate agreement with the experimental results.

ON HIGH-RESOLUTION PRESSURE AMPLITUDE AND PHASE MEASUREMENTS COMPARING FAST-RESPONSE PRESSURE TRANSDUCERS AND UNSTEADY PRESSURE-SENSITIVE PAINT

2021 ◽  
pp. 1-13
Author(s):  
Martin Bitter ◽  
Stephan Stotz ◽  
Reinhard Niehuis
Keyword(s):  
Second Harmonic ◽  
Measurement Techniques ◽  
Pressure Amplitude ◽  
Pressure Sensitive Paint ◽  
Simultaneous Application ◽  
Pressure Transducers ◽  
Unsteady Pressure ◽  
Flow Sensing ◽  
Pressure Sensitive ◽  
Perturbation Frequency

Abstract This paper presents the simultaneous application of fastresponse pressure transducers and unsteady pressure-sensitive paint (unsteady PSP) for the precise determination of pressure amplitudes and phases up to 3,000 Hz. These experiments have been carried out on a low-pressure turbine blade cascade under engine-relevant conditions (Re, Ma, Tu) in the High-Speed Cascade Wind Tunnel. Periodic blade/vane interactions were simulated at the inlet to the cascade using a wake generator operating at a constant perturbation frequency of 500 Hz. The main goal of this paper is the detailed comparison of amplitude and phase distributions between both flow sensing techniques at least up to the second harmonic of the wake generator's fundamental perturbation frequency (i.e. 1,000 Hz). Therefore, a careful assessment of the key drivers for relative deviations between measurement results as well as a detailed discussion of the data processing is presented for both measurement techniques. This discussion outlines the mandatory steps which were essential to achieve the quality as presented down to pressure amplitudes of several pascal even under challenging experimental conditions. Apart from the remarkable consistency of the results, this paper reveals the potential of (unsteady) PSP as a future key flow sensing technique in turbomachinery research, especially for cascade testing. The results demonstrate that PSP was able to successfully sense pressure dynamics with very low fluctuation amplitudes down to 8 Pa.

scholarly journals Some numerical experiments on firn ventilation with heat transfer

1993 ◽  
Vol 18 ◽  
pp. 161-165 ◽  
Author(s):  
M.R. Albert
Keyword(s):  
Heat Transfer ◽  
Surface Pressure ◽  
Thermal Effects ◽  
Numerical Experiments ◽  
Temperature Gradients ◽  
Pressure Amplitude ◽  
Two Dimensional ◽  
One Dimensional ◽  
Thermal Signature ◽  
Spatially Varying

Preliminary estimates of the thermal signature of ventilation in polar firn are obtained from two-dimensional numerical calculations. The simulations show that spatially varying surface pressure can induce airflow velocities of 10−5m s−1at 1.5 m depth in uniform firn, and higher velocities closer to the surface. The two-dimensional heat-transfer results generally agree with our earlier one-dimensional conclusions that the thermal effects of ventilation tend to decrease the temperature gradient in the top portions of the pack. Field observations of ventilation through temperature measurements are most likely to be observed when the firn temperature at depths on the order of 10 m is close to the air temperature, since steep temperature gradients can mask the thermal effects of ventilation. Preliminary indications are that, as long as surface-pressure amplitude is sufficient to move the air about in the top tens of centimeters in the snow, the resulting temperature profile during ventilation is fairly insensitive to the frequency of the surface-pressure forcing for pressure frequencies in the range 0.1–10.0 Hz.

On the microphysical behaviour of wind-forced water surfaces and consequent re-aeration

2014 ◽  
Vol 743 ◽  
pp. 399-447 ◽  
Author(s):  
William L. Peirson ◽  
James W. Walker ◽  
Michael L. Banner
Keyword(s):  
Measurement Techniques ◽  
Critical Factor ◽  
Capillary Waves ◽  
Heat Fluxes ◽  
Gas Transfer ◽  
Mechanical Coupling ◽  
Diffusion Layers ◽  
Water Surfaces ◽  
Presence And Absence ◽  
Low Solubility

AbstractA detailed laboratory investigation of the mechanical and low-solubility gas coupling between wind and water has been undertaken using a suite of microphysical measurement techniques. Under a variety of wind conditions and in the presence and absence of mechanically generated short waves, approximately fetch-independent surface conditions have been achieved over short laboratory fetches of several metres. The mechanical coupling of the surface is found to be consistent with Banner (J. Fluid Mech. vol. 211, 1990, pp. 463–495) and Banner & Peirson (J. Fluid Mech. vol. 364, 1998, pp. 115–145). Bulk observations of re-aeration are consistent with previous laboratory studies. The surface kinematical behaviour is in accordance with the observations of Peirson & Banner (J. Fluid Mech. vol. 479, 2003, pp. 1–38). Also, their predictions of a strong enhancement of low-solubility gas flux at the onset of microscale breaking is confirmed and direct observations show a concomitant onset of very thin aqueous diffusion sublayers. It is found that the development of strong parasitic capillary waves towards the incipient breaking limit does not noticeably enhance constituent transfer. Across the broad range of conditions investigated during this study, the local instantaneous constituent transfer rate remains approximately log-normally distributed with an approximately constant standard deviation of $0.62\pm 0.15({\mathrm{log}}_e(\mathrm{m}~ {\mathrm{s}}^{-1}))$. Although wind-forced water surfaces are shown to be punctuated by intense tangential stresses and local surface convergence, localized surface convergence does not appear to be the single critical factor determining exchange rate. Larger-scale orbital wave straining is found to be a significant constituent transfer process in contrast to Witting (J. Fluid Mech. vol. 50, 1971, pp. 321–334) findings for heat fluxes, but the measured effects are consistent with his model. By comparing transfer rates in the presence and absence of microscale breaking, low-solubility gas transfer was decomposed into its turbulent/capillary ripple, gravity-wave-related and microscale breaking contributions. It was found that an efficiency factor of approximately $17\, \%$ needs to be applied to Peirson & Banner’s model, which is extended to field conditions. Although bulk thermal effects were observed and thermal diffusion layers are presumed thicker than their mass diffusion counterparts, significant thermal influences were not observed in the results.

scholarly journals Transverse instability of gravity–capillary solitary waves on deep water in the presence of constant vorticity

2019 ◽  
Vol 871 ◽  
pp. 1028-1043
Author(s):  
M. Abid ◽  
C. Kharif ◽  
H.-C. Hsu ◽  
Y.-Y. Chen
Keyword(s):  
Growth Rate ◽  
Solitary Wave ◽  
Solitary Waves ◽  
Deep Water ◽  
Capillary Waves ◽  
Two Dimensional ◽  
Transverse Instability ◽  
Constant Vorticity ◽  
Dimensional Gravity ◽  
Wave Properties

The bifurcation of two-dimensional gravity–capillary waves into solitary waves when the phase velocity and group velocity are nearly equal is investigated in the presence of constant vorticity. We found that gravity–capillary solitary waves with decaying oscillatory tails exist in deep water in the presence of vorticity. Furthermore we found that the presence of vorticity influences strongly (i) the solitary wave properties and (ii) the growth rate of unstable transverse perturbations. The growth rate and bandwidth instability are given numerically and analytically as a function of the vorticity.

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