In both Boussinesq and non-Boussinesq cases the Green's function of internal gravity waves is calculated, exactly for monochromatic waves and asymptotically for impulsive waves. From its differentiation the pressure and velocity fields generated by a point source are deduced. by the same method the Boussinesq monochromatic and impulsive waves radiated by a pulsating sphere are investigated.Boussinesq monochromatic waves of frequency ω < N are confined between characteristic cones θ = arccos(ω/N) tangent to the source region (N being the buoyancy frequency and θ the observation angle from the vertical). In that zone the point source model is inadequate. For the sphere an explicit form is given for the waves, which describes their conical 1/r½ radial decay and their transverse phase variations.Impulsive waves comprise gravity and buoyancy waves, whose separation process is non-Boussinesq and follows the arrival of an Airy wave. As time t elapses, inside the torus of vertical axis and horizontal radius 2Nt/β for gravity waves and inside the circumscribing cylinder for buoyancy waves, both components become Boussinesq and have wavelengths negligible compared with the scale height 2/β of the stratification. Then, gravity waves are plane propagating waves of frequency N cos θ, and buoyancy waves are radial oscillations of the fluid at frequency N; for the latter, initially propagating waves comparable with gravity waves, the horizontal phase variations have vanished and the amplitude has become insignificant as the Boussinesq zone has been entered. In this zone, outside the torus of vertical axis and horizontal radius Nta, a sphere of radius a [Lt ] 2/β is compact compared with the wavelength of the dominant gravity waves. Inside the torus gravity waves vanish by destructive interference. For the remaining buoyancy oscillations the sphere is compact outside the vertical cylinder circumscribing it, whereas the fluid is quiescent inside this cylinder.

The Green's function method is applied to the generation of internal gravity waves by a moving point mass source. Arbitrary motion of a source of arbitrary time dependence is treated using the impulsive Green's function, while ‘classical’ approaches of uniform motion of a steady or oscillatory source are recovered using the monochromatic Green's function. Waves have locally the structure of impulsive waves, emitted at the retarded time tr, and having propagated with the group velocity; at each position and time an implicit equation defines tr, in terms of which the waves are written. A source both oscillating and moving generates two systems of waves, with respectively positive and negative frequencies, and when oscillations vanish these systems merge into one.Three particular cases are considered: the uniform horizontal and vertical motions of a steady source, and the uniform horizontal motion of an oscillatory source. Waves spread downstream of the steady source. For the oscillatory source they can extend both upstream and downstream, depending on the ratio of the source frequency to the buoyancy frequency, and are contained inside conical wavefronts, parts of which are caustics. For horizontal motion, moreover, the steady analysis (based on the monochromatic Green's function) reveals the presence of two insignificant contributions overlooked by the unsteady analysis (based on the impulsive Green's function), but which for an extended source may become of the same order as the main contribution. Among those is an upstream columnar disturbance associated with blocking.

Internal gravity waves propagate away from a localized monochromatic disturbance inside beams, which develop around a St Andrew's Cross in two dimensions and around a double cone in three dimensions. The structure of the beams depends on three mechanisms, which couple together the different directions of propagation of the waves within the fluid. These mechanisms are associated with the size of the disturbance, the start-up of the motion and the viscosity of the fluid, respectively. The present paper considers each mechanism in isolation, for three-dimensional generation. The analysis is asymptotic and relies on far-field and large-time approximations. For each mechanism, three expressions of the waves are found: one, exact for an extended disturbance, that involves all the wavenumber vectors satisfying the dispersion relation; and two others, respectively uniform and non-uniform asymptotic expansions, that involve only the wavenumber vectors associated with group velocity vectors pointing toward the observer. For each mechanism, profiles of pressure and velocity are presented. A new time-independent characterization of the waves is introduced, in terms of the intensity or average energy flux; it is applied to the definition of the beam width. For an extended disturbance this width is a constant, the diameter of the disturbance. For an impulsive start-up the width increases linearly with the distance from the disturbance, and decreases in inverse proportion to the time elapsed since the start-up. For a viscous fluid the width increases as the one-third power of the distance. In all three cases, for a disturbance of multipolar order $2^n$, at constant strength, the power output varies in inverse proportion to the $(2n+1)$th power of the beam width

International audienceA joint theoretical and experimental study is performed on the generation of internal gravity waves by an oscillating sphere, as a paradigm of the generation of internal tides by barotropic tidal flow over three-dimensional supercritical topography. The theory is linear and three-dimensional, applies both near and far from the sphere, and takes into account viscosity and the unsteadiness arising from the interference with transients generated at the start-up. The waves propagate in conical beams, evolving with distance from a bimodal to unimodal wave profile. In the near field, the profile is asymmetric with its major peak towards the axis of the cones. The experiments involve horizontal oscillations and develop a cross-correlation technique for the measurement of the deformation of fluorescent dye planes to sub-pixel accuracy. At an oscillation amplitude of one fifth of the radius of the sphere, the waves are linear and the agreement between experiment and theory is excellent. As the amplitude increases to half the radius, nonlinear effects cause the wave amplitude to saturate at a value that is 20% lower than its linear estimate. Application of the theory to the conversion rate of barotropic tidal energy into internal tides confirms the expected scaling for flat topography, and shows its transformation for hemispherical topography. In the ocean, viscous and unsteady effects have an essentially local role, in keeping the wave amplitude finite at the edges of the beams, and otherwise dissipate energy on such large distances that they hardly induce any decay

Age is a risk factor for cardiovascular disease (CVD), however the effect of age on platelet function remains unclear. Ideally, platelet function should be assayed under flow and shear conditions that occur in vivo. Our study aimed to characterise the effect of age on platelet translocation behaviour using a novel flow-based assay that measures platelet function in less than 200 μl of blood under conditions of arterial shear. Blood from males (n = 53) and females (n = 56), ranging in age from 19–82 and 21–70 respectively were perfused through custom-made parallel plate flow chambers coated with immobilised human von Willebrand Factor (VWF) under arterial shear (1,500s−1). Platelet translocation behaviour on VWF was recorded by digital-image microscopy and analysed. The study showed that aging resulted in a significant decrease in the number of platelet tracks, translocating platelets and unstable platelet interactions with VWF. These age related changes in platelet function were more profound in women than in men indicating that age and gender significantly impacts on platelet interactions with VWF.

International audienceTwo asymptotic analyses of the generation of lee waves by horizontal flow at velocity U of a stratified fluid of buoyancy frequency N past a sphere of radius a are presented, for either weak or strong stratification, corresponding to either large or small internal Froude number F=U/(Na), respectively. For F >> 1, the fluid separates into two regions radially: an inner region of scale a with three-dimensional irrotational flow unaffected by the stratification, and an outer region of scale U/N with small-amplitude lee waves generated by the O(1) vertical motion in the inner region. For F << 1, the fluid separates into five layers vertically: from the lower dividing streamsurface situated at a distance U/N above the bottom of the sphere to the upper dividing streamsurface situated at a distance U/N below the top, there is a middle layer with two-dimensional horizontal irrotational flow; from the upper dividing streamsurface to the top of the sphere, and from the lower dividing streamsurface to the bottom, there are top and bottom transition layers, respectively, with three-dimensional flow; above the top and below the bottom, there are upper and lower layers, respectively, with small-amplitude lee waves generated by the O(F) vertical motion in the transition layers. The waves are calculated where they have small amplitudes. The forcing is represented by a source of mass: for F >> 1, the surface distribution of singularities equivalent to the sphere in three-dimensional irrotational flow; for F << 1, the horizontal distribution of singularities equivalent, in the upper (resp. lower) layer, to the flat cut-off obstacle made up of the top (resp. bottom) portion of the sphere protruding above (resp. below) the upper (resp. lower) dividing streamsurface. The analysis is validated by comparison of the theoretical wave drag with existing experimental determinations. For F >> 1, the drag coefficient decreases as $(\ln F+7/4-\gamma)/(4F^4)$, with γ the Euler constant; for F << 1, it increases as $(32\sqrt{2})/(15\pi)F^{3/2}$. The waves have the crescent shape of the three-dimensional lee waves from a dipole, modulated by interferences associated with the finite size of the forcing. For strong stratification, the hydrostatic approximation is seen to produce correct leading-order drag, but incorrect waves

International audienceAn experimental study is presented on the spatial structure of the internal wave field emitted by a horizontally oscillating sphere in a uniformly stratified fluid. The limits of linear theory and the nonlinear features of the waves are considered as functions of oscillation amplitude. Fourier decomposition is applied to separate first harmonic waves at the fundamental frequency and higher harmonic waves at multiples of this frequency. For low oscillation amplitude, of 10% of the sphere radius, only the first harmonic is significant and the agreement between linear theory and experiment is excellent. As the oscillation amplitude increases up to 30% of the radius, the first harmonic becomes slightly smaller than its linear theoretical prediction and the second and third harmonics become detectable. Two distinct cases emerge depending on the ratio Ω between the oscillation frequency and the buoyancy frequency. When Ω > 0.5, the second harmonic is evanescent and localized near the sphere in the plane through its centre perpendicular to the direction of oscillation, while the third harmonic is negligible. When Ω < 0.5, the second harmonic is propagative and appears to have an amplitude that exceeds the amplitude of the first harmonic, while the third harmonic is evanescent and localized near the sphere on either side of the plane through its centre perpendicular to the direction of oscillation. Moreover, the propagative first and second harmonics have radically different horizontal radiation patterns and are of dipole and quadrupole types, respectively

To cite this version:Nathanaël Machicoane, Pierre-Philippe Cortet, Bruno Voisin, Frédéric Moisy. Influence of the multipole order of the source on the decay of an inertial wave beam in a rotating fluid. Physics of Fluids, American Institute of Physics, 2015, 27 (6) We analyze theoretically and experimentally the far-field viscous decay of a twodimensional inertial wave beam emitted by a harmonic line source in a rotating fluid. By identifying the relevant conserved quantities along the wave beam, we show how the beam structure and decay exponent are governed by the multipole order of the source. Two wavemakers are considered experimentally, a pulsating and an oscillating cylinder, aiming to produce a monopole and a dipole source, respectively. The relevant conserved quantity which discriminates between these two sources is the instantaneous flow rate along the wave beam, which is non-zero for the monopole and zero for the dipole. For each source, the beam structure and decay exponent, measured using particle image velocimetry, are in good agreement with the predictions. C 2015 AIP Publishing LLC.[http://dx