On the optimaL response of q-vortex

Wingtip vortices represent a hazard for the stability of the following airplane in airport highways. These flows have been usually modeled as swirling jets/wakes, which are known to be highly unstable and susceptible to breakdown at high Reynolds numbers for certain flow conditions, but different to the ones present in real flying airplanes. A very recent study based on Direct Numerical Simulations (DNS) shows that a large variety of helical responses can be excited and amplified when a harmonic inlet forcing is imposed. In this work, the optimal response of q-vortex (both axial vorticity and axial velocity can be modeled by a Gaussian profile) is studied by considering the time-harmonically forced problem with a certain frequency ω. We first reproduce Guo and Sun’s results for the Lamb-Oseen vortex (no axial flow) to validate our numerical code. In the axisymmetric case m = 0, the system response is the largest when the input frequency is null. The axial flow has a weak influence in the response for any axial velocity intensity. We also consider helical perturbations |m| = 1. These perturbations are excited through a resonance mechanism at moderate and large wavelengths as it is shown in Figure 1. In addition, Figure 2 shows that the frequency at which the optimal gain is obtained is not a continuous function of the axial wavenumber k. At smaller wavelengths, large response is excited by steady forcing. Regarding the axial flow, the unstable response is the largest when the axial velocity intensity, 1/q, is near to zero. For perturbations with higher azimuthal wavenumbers |m| > 1, the magnitudes of the response are smaller than those for helical modes. In order to establish an alternative validation, DNS has been carried out by using a pseudospectral Fourier formulation finding a very good agreement.

Heat fluxes between the Guadalquivir river and the Gulf of Cádiz Continental Shelf

An 18-year time series of daily sea surface temperature of Gulf of Cadiz and an 18-month time series of temperature collected in the vicinity of the Guadalquivir estuary mouth have been analyzed to investigate the heat exchange between the estuary and the adjacent continental shelf. The first time identifies a continental shelf area where seasonal thermal oscillation signal (amplitudes and phase) changes abruptly. In order to explain this anomaly, the second data set allows a description of thermal fluctuations in a wide range of frequencies and an estimation of the upstream heat budget of the Guadalquivir estuary. Results show that high frequency thermal signal, diurnal and semidiurnal, and water flux signal through Guadalquivir mouth, mainly semidiurnal, apparently interact randomly to give a small exchange of thermal energy at high frequency. There is no trace, at the estuary's mouth, of daily heat exchanges with intertidal mudflats probably because it tends to cancel on daily time scales. Results also show that fluctuations of estimated air-sea fluxes force fluctuations of temperature in a quite homogeneous estuarine, with a delay of 20 days. The along-channel thermal energy gradient reaches magnitudes of 300-400 J m-4 near the mouth during the summer and winter and drives the estuary-shelf exchange of thermal energy at seasonal scale. Particularly, the thermal heat imported by the estuary from the shelf area during late fall-winter-early spring of 2008/2009 is balanced by the thermal heat that the estuary exports to the shelf area during late spring-summer of 2008. In summary, Guadalquivir river removes/imports excess of thermal energy towards/from the continental shelf seasonally, as a mechanism to accommodate excess of heat from one side respect to the other side.