Waves In Viscous Fluid Research Articles

Optical coherence viscometry.

We report a technique, named optical coherence viscometry (OCV), to measure the viscosity of Newtonian fluids in a noncontact manner. According to linear wave theory with small amplitudes, capillary waves are associated with fluid mechanical properties. To perform this measurement and avoid the overdamped effects of capillary waves in viscous fluids, transient acoustic radiation force was applied to generate capillary waves. Within a very limited field-of-view using optical coherence tomography, wave motion acquired in the time domain was analyzed using Fourier methods to study the wave velocity dispersion and attenuation relationships for capillary waves, which can reduce the fluid quantity drastically into tissue culture scale. We measure the viscosities of water, water–glycerol solutions with three concentrations, and biological plasma using the proposed OCV and compare the experimental results to theoretical calculations. OCV is sensitive to wave perturbations and can be a promising technique for measuring the viscosity of biological fluids and could be applied in future applications for measurements for lipid membranes in cell biology and tissue engineering investigation.

Frequency dispersion of small-amplitude capillary waves in viscous fluids.

This work presents a detailed study of the dispersion of capillary waves with small amplitude in viscous fluids using an analytically derived solution to the initial value problem of a small-amplitude capillary wave as well as direct numerical simulation. A rational parametrization for the dispersion of capillary waves in the underdamped regime is proposed, including predictions for the wave number of critical damping based on a harmonic-oscillator model. The scaling resulting from this parametrization leads to a self-similar solution of the frequency dispersion of capillary waves that covers the entire underdamped regime, which allows an accurate evaluation of the frequency at a given wave number, irrespective of the fluid properties. This similarity also reveals characteristic features of capillary waves, for instance that critical damping occurs when the characteristic time scales of dispersive and dissipative mechanisms are balanced. In addition, the presented results suggest that the widely adopted hydrodynamic theory for damped capillary waves does not accurately predict the dispersion when viscous damping is significant, and an alternative definition of the damping rate, which provides consistent accuracy in the underdamped regime, is presented.

The damping of viscous gravity waves

Using a solution of the linearized Navier–Stokes equations, an approximate formula has been derived for the damping rate of gravity waves in viscous fluids. The proposed solution extends the results found by Lamb (1932) [5] for waves propagating in deep-water conditions for large Reynolds numbers and those derived by Biesel (1949) [14] under more general hypotheses. Specifically, comparisons with the Lamb solution highlight large differences in intermediate and shallow depths and/or for moderate Reynolds numbers while significant discrepancies are observed with the Biesel solution in deep-water conditions. For these reasons, the proposed solution is of great importance for the estimation of the viscous dissipations during the wave motion and represents a useful benchmark for the validation of numerical solvers. With respect to this, the theoretical findings have been compared with numerical simulations obtained by means of a well-known Smoothed Particle Hydrodynamics solver.

Nonlinear gravitational waves on the surface of viscous fluid: Lagrangian approach

The problems of the asymptotic theory of weakly nonlinear surface waves in viscous fluid are discussed. For standing waves on deep water, the solutions obtained in the first- and second-order approximations in a small parameter—wave steepness—are analyzed. The evolution equation for the amplitude of wave packet envelope is obtained where the inverse Reynolds number is equal to the squared steepness. It is shown that this is a nonlinear Schrodinger equation with linear dissipation.

Temperature Effects on the Propagation of Transient Ultrasonic Waves in Viscous Fluids

The purpose of the present work is to study the propagation phenomenon of transient ultrasonic waves in viscous fluids submitted to temperature variations. Laplace transform is used in order to obtain a solution to the propagation equation of acoustic waves in viscous fluids. This solution is expressed under the form of a convolution product between the pressure at the output of the transmitting transducer and a function, depending on time and position, called the impulse response of the propagation filter. This impulse response depends upon the propagation medium viscosity which varies with temperature. It is considered that the volume viscosity coefficient is governed by a law similar to Andrade's formulae; this assumption is validated by experimental results with a quite good accuracy.

Two-dimensional direct numerical simulation of parametrically excited surface waves in viscous fluid

Standing surface waves on a viscous fluid driven parametrically by a vertical harmonic oscillation are investigated, based on direct numerical simulations of the two-dimensional Navier–Stokes equation, together with appropriate boundary conditions. The condition for the onset of the waves in the experiments by Lioubashevski et al. [Phys. Rev. Lett. 76, 3959 (1996)] is reproduced by our numerical simulation. The time evolution and the flow structures are investigated in detail. The form of the surface elevation is analyzed and the dependence of the saturated amplitude on the forcing strength shows a normal bifurcation. Instead of a localized state, spatially uniform standing waves are formed in an extended system. Using initial perturbations of the uniform state, numerical simulations show that the uniform standing waves are stable to two-dimensional disturbances, which suggests that three-dimensionality is essential for the spatially localized state to occur.

Energy velocity of complex harmonic plane waves in viscous fluids

This paper presents a theoretical investigation of the energy velocity of complex harmonic plane waves in viscous fluids. The complex harmonic plane wave, which is characterized by a complex wave vector and a complex frequency, may propagate in absorbing fluids. The initial nonconservative energy balance equation is modified into another energy equation, in which the new loss density is, on average, nil. It appears that the energy velocity, which is defined from this system that is conservative on average only, is not always oriented along the phase velocity direction. More precisely, the energy velocity may be interpreted as the phase velocity in the direction of the real part of the slowness bivector.

An explicit numerical time domain formulation to simulate pulsed pressure waves in viscous fluids exhibiting arbitrary frequency power law attenuation

An explicit time domain algorithm is developed which is capable of numerically simulating pulsed pressure waves propagating through media whose attenuation increases with frequency according to a power law dependency. Because of possible noninteger exponents in the power law formulation, standard temporal differential operators cannot be defined and traditional finite difference approximations are therefore inappropriate. We derive a method that is consistent with the fact that the complex wavenumber often must include a nonlinear phase if system causality is to be ensured. This phase is derived from the power law attenuation and, due to their interdependency, the two terms in the wave equation corresponding to attenuation and phase can be combined into a single factor. This so-called dispersion wave equation is mapped into complex discrete-time frequency. In this domain, noninteger exponents can be eliminated via a power series expansion, and the resulting equations transform naturally to discrete time operators. The algorithm is tested by comparing numerically evaluated attenuation with the exact power law form, and the issues of stability in relation to the convergence of the power series and the accuracy of the mapping are investigated.

An experimental study of the onset of parametrically pumped surface waves in viscous fluids

We measure the threshold accelerations necessary to excite surface waves in a vertically vibrated fluid container (the Faraday instability). Under the proper conditions, the thresholds and onset wavelengths agree with recent theoretical predictions for a laterally infinite, finite-depth container filled with a viscous fluid. Experimentally, we show that by using a viscous, non-polar fluid, the finite-size effects of sidewalls and the effects of surface contamination can be made negligible. We also show that finite-size corrections are of order h/L, where h is the fluid depth and L the container size. Based on these measurements, one can more easily interpret certain unexpected observations from previous experimental studies of the Faraday instability.

Solitary waves in a shallow viscous fluid sustained by an adverse temperature gradient.

We show that shallow water waves in a viscous fluid are not damped if the fluid is adequately heated from below. The critical temperature gradient needed to sustain the wave as well as its frequency are determined analytically. The nonlinear evolution of the wave is governed by the Korteweg--de Vries equation.

Velocity and attenuation of ultrasound in suspensions of particles in fluids

The theory of the scattering of compression waves in viscous fluids is examined. The effects of fluid viscosity, of differences in density and in elastic modulus between the particles and the fluid, of heat transfer and of concentration are considered. Ultrasonic phase velocity and attenuation are derived. Results for the phase velocity are compared with several other formulations. The feasibility of using ultrasound to characterise suspensions is discussed.

MASS TRANSPORT IN PROGRESSIVE WAVES OF PERMANENT TYPE

Mass transport phenomenon was first recognized by Stokes in 1847 using a Lagrangian description. Later, a basic theory for the mass transport in water waves in viscous fluid and of finite depth was derived by Longuet-Higgins in 1953. Theoretical solutions of mass transport in progressive waves of permanent type are subjected to the definitions of wave celerity in deriving the various finite amplitude wave theories. As it has been generally acknowledged that the Stokes wave theory can not yield a correct prediction of mass transport in the shallow depths, some new theories have been developed. Recently the authors(1974 § 1977) have derived a new finite amplitude wave theory in shallow water for quasi- Stokes and cnoidal waves by the so-called reductive perturbation method, in which the mass transport is formulated both in Lagrangian and Eulerian descriptions. On the experimental verification, Russell and 0sorio(1957) investigated and compared Longuet-Higgins' solution with experimental data of Lagrangian mass transport velocity obtained in a normal closed wave tank of finite length. Since then, many investigations, and nearly all of them, have employed the finite length of wave tank in carrying out their experiments. However, no experiment has yet been attempted at verifying the Stokes drift in progressive waves of permanent type in a wave tank of infinite length. It is not realistic nor economical in constructing such an infinitely long flume to investigate experimentally the mass transport velocity in progressive waves. Instead of using such an ideal wave tank, a new one incorporated with natural water re-circulation was equipped to carry out experiments by the authors(1978). It was confirmed from these experiments that mass transport in progressive waves of permanent type exists in the Same direction of wave propagation throughout the depth, and agrees with both the Stokes drift and the authors' new formulations, within the test range of experiments.

Mass transport in progressive water waves

An experimental investigation evidenciated drift profiles in agreement with those predicted by the theory of progressive waves in viscous fluid.

Resonance amplification and viscous attenuation of atmospheric bow waves

A theory for resonance amplification of standing interfacial gravity waves in viscous fluids is applied to obtain a prediction of the wavelengths for bow waves observed in some satellite photographs of orographic clouds. A second theory, predicting the rate of viscous attenuation of such waves, yields reasonable lengths for the branches of the bow waves whenever the predicted wavelengths are used along with an effective eddy viscosity of 106 cm2/sec for the inversion layer and 107 cm2/sec below the inversion. The latter value is consistent with that required for the occurrence of Karman vortex trails in the wake of obstacles.

On the Forces Due to Acoustic Wave Motion in a Viscous Medium and Their Use in the Measurement of Acoustic Intensity

The hydrodynamic flow associated with acoustic waves in viscous fluids is usually regarded as a disturbing effect in measuring acoustic intensities by radiation pressure. It is shown, however, by a simple application of the hydrodynamic momentum theorem, that the sum of the forces due to acoustic radiation and to the hydrodynamic flow, when a beam of plane waves is incident upon an absorber, is independent of the absorption in the medium and (within considerable limits) of the distance between the acoustic source and the absorber, if certain conditions are observed. This makes it possible to measure, in a simple way, the intensity of an acoustic beam at the source by measuring the total force due to radiation and flow without knowledge of the absorption coefficient of the fluid and without the use of thin screening films, which are commonly applied in order to eliminate the flow.