Steep sharp-crested gravity waves on deep water

A new type of steep two-dimensional irrotational symmetric periodic gravity wave with local singular point inside the flow domain is revealed on inviscid incompressible fluid of infinite depth. The speed of fluid particles in the vicinity of the crest of these waves is greater than their phase speed. Corresponding particle trajectories provide insight into how gravity waves overturn and break.     

Compact equation for gravity waves on deep water

Using the fact of vanishing four waves interaction for water gravity waves for 2D potential fluid, we have significantly simplified the well-known but cumbersome Zakharov equation. The Hamiltonian of the obtained equation is very simple and includes only the fourth order nonlinear term. It raises the question of the integrability of free surface hydrodynamics. This new equation is very suitable both for analytic study and for numerical simulation.     

Optical visualization of internal gravity waves in stratified fluid

The refractive index changes associated with flows in salt water systems allow such flows to be visualized by means of optical methods, e.g. schlieren and interferometry. Experiments that have been conducted by our group with internal gravity waves in stratified brine are reviewed. The experiments encompass visualization and quantitative measurement of internal gravity waves generated by a body oscillating around a fixed position and a test body moving with constant speed vertically through the stratified brine. It is also shown that the velocity field of an internal gravity wave can be measured by means of particle image velocimetry. References to respective wave theories are made.     

Surface waves in ferrofluids under vertical magnetic field

We present here new experimental results about the waves at the horizontal free surface of a magnetic fluid submitted to a normal magnetic field. The waves are generated by a small modulation at frequency of the vertical field . Using a shadowgraph method, we are able to measure the wavevector k of the 2D waves for a given value of and . The dispersion relation of the surface waves is established experimentally. On the other hand, we propose a theoretical derivation of the dispersion equation which includes a more complete treatment of the magnetic term than the previous works. Finally, we conclude that a linear and inviscid analysis is sufficient to fit well the experimental data, except in the vicinity of the critical field where a surface instability occurs. Received 11 May 1998     

On shear free normal flows of a perfect fluid

Flows of a perfect fluid in which the flow-lines form a time-like shear-free normal congruence are investigated. The space-time is quite severely restricted by this condition on the flow: it must be of Petrov Type I and is either static or degenerate. All the degenerate fields are classified and the field equations solved completely, except in one class where one ordinary differential equation remains to be solved. This class contains the spherically symmetric non-uniform density fields and their analogues with planar or hyperbolic symmetry. The type D fields admit at least a one-parameter group of local isometries with space-like trajectories. All vacuum fields which admit a time-like shear-free normal congruence are shown to be static. Finally, shear-free perfect fluid flows which possess spherical or a related symmetry are considered, and all uniform density solutions and a few non-uniform density solutions are found. The exact solutions are tabulated in section 7.Supported by a Science Research Council Research Studentship and by a Turner and Newall Research Fellowship.     

Nonlinear dynamics of density waves in granular flows through narrow vertical channels

We study granular flows through narrow channels driven by gravity in the framework of the kinetic theory for dissipative dense gases. We derive equations of motion for quasi-one-dimensional systems. In a certain range of flow density, the steady homogeneous regime is found to be unstable against the formation of density waves. We show moreover that near the onset of the instability, the governing equation for the flow density is a mixture of the Korteweg-de-Vries equation, which leads to soliton, and the Bürger equation which exhibits spatio-temporal chaos. The competition between chaos and solitons may lead either to regular spatially ordered density waves or to chaotic dynamics. We argue that these two types of dynamics can be encountered experimentally according to the channel width and the dissipative properties of the granular media. Received: 11 March 1998 / Revised and Accepted: 3 July 1998     

三层密度分层流体毛细重力波二阶Stokes波解

以小振幅波理论为基础,利用摄动方法研究了三层密度分层流体的毛细重力波,给出了三层成层状态下各层流体速度势的二阶渐近解及毛细重力波波面位移的二阶Stokes波解.结果表明:一阶解及二阶解除了依赖于各层流体的厚度及密度,与表面张力也有很重要的关系.     

Two-dimensional evolution equation of finite-amplitude internal gravity waves in a uniformly stratified fluid

We derive a fully nonlinear evolution equation that can describe the two-dimensional motion of finite-amplitude long internal waves in a uniformly stratified three-dimensional fluid of finite depth. The derived equation is the two-dimensional counterpart of the evolution equation obtained by Grimshaw and Yi [J. Fluid Mech. 229, 603 (1991)]. In the small-amplitude limit, our equation is reduced to the celebrated Kadomtsev-Petviashvili equation.     

Stability of low oscillations in a two-layer inviscid fluid by vertical moving in gravity

The development of small oscillations in a system formed by a heavy layer of an ideal incompressible fluid covering a half-space of an ideal fluid with another density is studied. The entire system is moved as a rigid entity in the vertical direction according to some prescribed law. The apparatus of linearization of the equations and the boundary conditions is used. The investigation of the characteristic equations shows that the gravitational stability depends on the condition on the upper boundary of the layer, namely, the presence of free boundary of the layer or the condition of impenetrability through the rectilinear boundary. The qualitative estimates for the growth or decay of the initial perturbations are presented analytically.     

Evidence of internal gravity waves in the lower thermosphere at midlatitudes

Summary Wind measurements were made by the CNR Meteor Radar Station at Budrio (45°N, 12°E) in the April–September 1978 period in order to emphasize the role of internal gravity (IG) waves in the lower thermosphere ((80÷110) km). After briefly describing the basic properties of these waves, we determine some of their characteristics using both the conventional spectral-analysis methods and alternatively, for short-time data series, the maximum-entropy method (MEM). The Fourier analysis of these data indicates that the gravity waves with periods of 2<T<8 h have amplitudes increasing with height (up to (30÷40) ms⁻¹ at 100 km, in June), vertical wave-lengths of (8÷40) km and horizontal wave-lengths exceeding the corresponding ones by a factor of 50 or more. In May and September, by using the MEM method with a sampling of (10°20) min, gravity waves with periods of about 100 min and 2 h, respectively, have been tentatively identified. In August, the rates of energy loss per unit mass for internal gravity waves range from 0.015 to 0.045 W kg⁻¹ in the (80°100) km region and the momentum deposition by these waves is 2.4 m s⁻¹ h⁻¹ at 90 km. Under some specific conditions, the observed accelerations of the prevailing wind ((3÷4) m s⁻¹ d⁻¹) due to momentum deposition over a period of 4 consecutive days (24–27 August) may approach the above-calculated maximum value.

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Riassunto Misure di vento effettuate presso la Stazione Radar Meteorica del CNR di Budrio (45°N, 12°E) nel periodo aprile-settembre 1978 consentono di mettere in evidenza il ruolo delle onde interne di gravità (IG) nella bassa termosfera ((80÷110) km). Dopo aver descritto brevemente le proprietà basilari di tali onde, sono state determinate alcune loro caratteristiche facendo ricorso sia ai metodi tradizionali dell'analisi spettrale sia, in alternativa, per serie con un numero limitato di dati, al metodo della massima entropia (MEM). L'analisi di Fourier indica che le onde di gravità con periodo tra 2 e 8 ore hanno ampiezza crescente con l'altezza (fino a (30÷40) m s⁻¹ a 100 km in giugno), lunghezze d'onda verticali di (8÷40) km e orizzontali che superano le corrispondenti verticali di un fattore 50 o più. In maggio e settembre, facendo ricorso al metodo MEM e raggruppando i dati ogni (10÷20) min, sono state identificate, anche se non con sicurezza, onde di gravità con periodo rispettivamente di circa 100 min e di 2 ore. In agosto la perita di energia per unità di massa delle onde interne di gravità assume nella regione tra 80 e 100 km valori compresi tra 0.015 e 0.045 W kg⁻¹ e la quantità di moto trasferita da queste onde a 90 km è 2.4 m s⁻¹ per ora. In particolari condizioni le accelerazioni del vento prevalente ((3÷4) m s⁻¹ al giorno) osservate in seguito al trasferimento delle quantità di moto in un periodo di 4 giorni consecutivi (24–27 agosto) possono essere compatibili con il valore elevato calcolato in precedenza.

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Резюме Проведены измерения ветров с помощью CNR радарной станции атмосферных явлений в Будрио (45° N, 12° E) в период с апреля по сентябрь 1978, обращая особое внимание на роль внутренних гравитационных волн в нижней термосфере ((80÷110) км). После краткого описания основных свойств этих волн мы определяем некоторые характеристики этих волн, используя обычные методы спектрального анализа и для кратковременной последовательности данных метод максимальной энтропии. Фурье-анализ этих данных показывает что гравитационные волны с периодами 2<T<8 часов имеют амплитуды, увеличивающиеся с высотой (вплоть до (30÷40) мс⁻¹ на высоте 100 км, в июне), вертикальные длины волн (8÷40) км и горизонтальные длины волн, превьшающие соответствующие значения вертикальных в 50 или более раз. В мае и сентябре, используя метод максимальной энтропии с выборкой (10÷20) минут, были предварительно индентифицированы гравитационные волны с периодами соответственно около 100 минут и 2 часов. В августе интенсивность энергетических потерь на единицу массы для внутренних гравитационных волн составляла от 0.015 до 0.045 Вт кг⁻¹ в области (80÷100) км и ослабление импульса этих волн составляет 2.4 мс⁻¹ час⁻¹ на высоте 90 км. При некоторых специаляных условиях наблюденных ускорения преобладающих ветров ((3÷4) мс⁻¹ день⁻¹), из-за ослабления импулчса, в течение 4 последовательных дней (24–27 августа) могут достигать вышеуказанного максимального значения.

     

Long waves in streamwise varying shear flows: new mechanisms for a weakly nonlinear instability

The weakly nonlinear dynamics of long waves embedded in marginally stable shear flows that vary in the streamwise direction are shown to be governed by a variable-coefficient Boussinesq equation. Depending on the local stability characteristics of the flow, new nonmodal or modal instabilities may emerge that serve as natural mechanisms for achieving amplitude thresholds necessary for weakly nonlinear instability and the transition to fully finite-amplitude states.     

Noise correlations in shear flows

We consider the effects of a shear on velocity fluctuations in a flow. The shear gives rise to a transient amplification that not only influences the amplitude of perturbations but also their time correlations. We show that, in the presence of white noise, time correlations of transversal velocity components are exponential and that correlations of the longitudinal components are exponential with an algebraic prefactor. Cross correlations between transversal and downstream components are strongly asymmetric and provide a clear indication of non-normal amplification. We suggest experimental tests of our predictions. Received 26 February 2002 / Received in final form 11 March 2003 Published online 20 June 2003 RID="a" ID="a"e-mail: bruno.eckhardt@physik.uni-marburg.de RID="b" ID="b"Also at: Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore, India     

Surface acoustic waves at a free-metallized interface

Light scattering was used to study surface acoustic waves at a free-metalized interface on piezoelectric lithium niobate. An interaction region of several acoustic wavelengths was observed in which a reflected surface wave and a continuous spectrum of bulk waves are generated.