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A hard landing incident in Pico Aerodrome (LPPI) involving an Airbus A320-200 aircraft is investigated using airborne observations and forecasts of the AROME (Applications of Research to Operations at Mesoscale) model. A second flight is also analyzed. The severity of the wind shear during both flights is quantified using the intensity factor “I” that is based on aerial data and recommended by ICAO (International Civil Aviation Organization). During Flight 1, 36% of the landing phase (below 2100 ft) occurred under “severe” wind shear conditions and 16% occurred under “strong” conditions. Upstream characteristics included southwest winds, stable stratification and a Froude number close to 1. According to the AROME model, these circumstances triggered the development of vertically propagating mountain waves, with maximum vertical velocities above 400 ft/min and exceeding 200 ft/min in the flight path. These conditions, together with the severe wind shear, may have caused the incident. During the second flight, a wake with lee vortices and reversed flow developed in the region of the flight path, which is consistent with a low upstream Froude number and/or with the flow regime diagram of previous studies. During the approach phase of this flight, “severe” wind shear conditions were absent, with “strong” ones occurring 4% of the time. It predominantly displayed “light” conditions during 68% of this phase. As a result of the comparison between “I” and the AROME turbulence indicators, preliminary thresholds are proposed for these indexes. Lastly, this study provides an objective verification of AROME wind forecasts, showing a good agreement with airborne observations for wind speeds above 10 kt, but a poor skill for weaker winds.

A wave propagating in a non-uniform flow can have a critical layer where it is absorbed, amplified, reflected, or converted to another mode, possibly exchanging energy with the mean flow. Two examples are the propagation of: (i) fan noise in the shear flow in the air inlet of a jet engine; (ii) turbine noise in the swirling flow in the jet exhaust. Both situations (i) and (ii) are included by considering wave propagation in an axisymmetric isentropic non-homentopic mean flow allowing for the simultaneous existence of shear, swirl, temperature and density gradients. This corresponds to coupled acoustic-vortical modes that have both continuous and discrete spectra. It is shown that a critical layer exists where the Doppler shifted frequency vanishes. A stability condition is obtained for the continuous spectrum for all frequencies, axial and azimuthal wavenumbers generalizing previous results from the homentropic to the isentropic non-isentropic case. The wave fields are calculated and plotted for a case of non-rigid body rotation, namely angular velocity of swirl proportional to the radius; this demonstrates the mode conversion between acoustic and vortical waves across the critical layer where the waves are absorbed because the pressure spectrum vanishes. case of acoustic-shear waves for four velocity profiles: (i) linear 8-12 ; (ii) exponential for a boundary layer 13 ; (iii) hyperbolic tangent for a shear layer 14 ; (iv) parabolic for a ducted flow 15 . The case of an homenergetic shear flow with a linear velocity profile, that is isentropic but non-homentropic and leads to acoustic-shear waves, and has been considered without 16 and with 17 sound sources. The wave equation in an axisymmetric rotating flow that is for acoustic-swirl waves 5,18 has two simplest cases: (i) rigid body rotation 18 ; (ii) potential vortex swirl 19-21 . The present paper concerns an axisymmetric mean flow with shear and swirl, that has been considered in the homentropic case, corresponding to acoustic-vortical waves 22,23 using a velocity potential 24 . The extension to acoustic-vortical waves in an isentropic non-homentropic mean flow is discussed in the present paper, based on the wave for the pressure (section 2.1). This provides an extension of the stability condition 22,23 for the continuous spectrum of acoustic-vortical waves in an axisymmetric sheared and swirling mean flow to the non-homentropic case (section 2.2) allowing for entropy as well as pressure, density and temperature gradients that are adiabatically related.The Doppler shifted frequency is constant for uniform axial flow and rigid body swirl, excluding the existence of a critical layer. A critical layer exists in all other cases, for which the Doppler shifted frequency can vanish, leading to a singularity of the wave equation in: (i) a sheared axial flow as in an engine air intake; (ii) a rotating flow with non-rigid body swirl; (iii) both together (Figure 1). There are few studies of non-rigid body swirl as in a jet exhaust downstream of a turbine, with the excep...

The present paper considers the transmission of sound from a source distribution inside a jet to a receiver or observer outside; the source can be represented by a combination of multipoles moving relative to the jet. The shear layer has a random shape with a plane mean position, and entrains a region of turbulence. The transmission across the plane shear layer involves: (i) scattering by the convected, irregular and unsteady interface across which occurs the transition from the jet to the ambient medium; (ii) refraction in the region of low Mach number turbulence entrained by the shear layer. If the jet Mach number does not exceed two the local turbulence can be taken as incompressible. The transmission involves: (i) a deterministic amplitude factor due to the difference in sound speed, mass density and velocity between the jet and ambient medium; (ii) a random phase shift due to the scattering of sound by the irregular interface and the convection of sound by the turbulence entrained with the shear layer. Since there is a random phase shift for the acoustic pressure, the acoustic power, which is quadratic in the acoustic pressure, involves the statistics of interference between two waves. The latter specify the spectral directivity, defined as the acoustic power radiated per unit solid angle and unit frequency band, i.e. either the spectrum received in each direction or the directivity of sound received outside the jet at each frequency. The statistics of sound scattering by irregular interfaces and convection by turbulence are subject to assumptions and constraints which affect critically the directivity and spectra. The evaluation of radiation integrals without low-or high-frequency approximations is also essential to reproduce experimental results on the noise of cold or hot jets. An accuracy of 3 dB can be expected for directivities and 6 dB for spectra, for directions not too far away from the vertical, (i.e perpendicular to the jet). ACOUSTIC MODEL OF THE SHEAR LAYER The present model (Figure 1) assumes that the mean position of the shear layer is the plane x 3 = 0, and the coordinates x ជ * = (x 1 , x 2) lie on this plane. Thus the model applies to the sides of a rectangular jet; it applies locally to the tangent plane of a circular jet if the wavelength is small compared with the radius. There are four relevant velocities of which the first three are horizontal: (i) the velocity u ជ 0 of the sound source; (ii) the velocit v ជ a of the Dr. Dennis K. McLaughlin served as guest editor for this paper jet; (iii) the velocity of convection of the shear layer v ជ 0 = αv ជ a , which is typically a fraction α ∼ 0.6 of the jet velocity; (iv) the velocity of turbulence in the shear layer u ជ, whose magnitude is typically a fraction β ∼ 0.15 of the jet velocity |u ជ| ~ βv a. The coordinates convected by the shear layer in the plane of the mean position of the shear layer are y ជ = x ជ * − v ជ 0 t; the turbulent velocity u ជ(y ជ,x 3 ,t) is a random function of the convected coordinate in the plane of the shear layer...