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The DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Sat, 02 Mar 2024 17:06:50 GMT2024-03-02T17:06:50ZOptimal perturbation for two-dimensional vortex systems: route to non-axisymmetric state
http://hdl.handle.net/10985/14216
Optimal perturbation for two-dimensional vortex systems: route to non-axisymmetric state
NAVROSE; JOHNSON, Author H. G.; BRION, Véronique; JACQUIN, Laurent; ROBINET, Jean-Christophe
We investigate perturbations that maximize the gain of disturbance energy in a two-dimensional isolated vortex and a counter-rotating vortex pair. The optimization is carried out using the method of Lagrange multipliers. For low initial energy of the perturbation ( ), the nonlinear optimal perturbation/gain is found to be the same as the linear optimal perturbation/gain. Beyond a certain threshold , the optimal perturbation/gain obtained from linear and nonlinear computations are different. There exists a range of for which the nonlinear optimal gain is higher than the linear optimal gain. For an isolated vortex, the higher value of nonlinear optimal gain is attributed to interaction among different azimuthal components, which is otherwise absent in a linearized system. Spiral dislocations are found in the nonlinear optimal perturbation at the radial location where the most dominant wavenumber changes. Long-time nonlinear evolution of linear and nonlinear optimal perturbations is studied. The evolution shows that, after the initial increment of perturbation energy, the vortex attains a quasi-steady state where the mean perturbation energy decreases on a slow time scale. The quasi-steady vortex state is non-axisymmetric and its shape depends on the initial perturbation. It is observed that the lifetime of a quasi-steady vortex state obtained using the nonlinear optimal perturbation is longer than that obtained using the linear optimal perturbation. For a counter-rotating vortex pair, the mechanism that maximizes the energy gain is found to be similar to that of the isolated vortex. Within the linear framework, the optimal perturbation for a vortex pair can be either symmetric or antisymmetric, whereas the structure of the nonlinear optimal perturbation, beyond the threshold, is always asymmetric. No quasi-steady state for a counter-rotating vortex pair is observed.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10985/142162018-01-01T00:00:00ZNAVROSEJOHNSON, Author H. G.BRION, VéroniqueJACQUIN, LaurentROBINET, Jean-ChristopheWe investigate perturbations that maximize the gain of disturbance energy in a two-dimensional isolated vortex and a counter-rotating vortex pair. The optimization is carried out using the method of Lagrange multipliers. For low initial energy of the perturbation ( ), the nonlinear optimal perturbation/gain is found to be the same as the linear optimal perturbation/gain. Beyond a certain threshold , the optimal perturbation/gain obtained from linear and nonlinear computations are different. There exists a range of for which the nonlinear optimal gain is higher than the linear optimal gain. For an isolated vortex, the higher value of nonlinear optimal gain is attributed to interaction among different azimuthal components, which is otherwise absent in a linearized system. Spiral dislocations are found in the nonlinear optimal perturbation at the radial location where the most dominant wavenumber changes. Long-time nonlinear evolution of linear and nonlinear optimal perturbations is studied. The evolution shows that, after the initial increment of perturbation energy, the vortex attains a quasi-steady state where the mean perturbation energy decreases on a slow time scale. The quasi-steady vortex state is non-axisymmetric and its shape depends on the initial perturbation. It is observed that the lifetime of a quasi-steady vortex state obtained using the nonlinear optimal perturbation is longer than that obtained using the linear optimal perturbation. For a counter-rotating vortex pair, the mechanism that maximizes the energy gain is found to be similar to that of the isolated vortex. Within the linear framework, the optimal perturbation for a vortex pair can be either symmetric or antisymmetric, whereas the structure of the nonlinear optimal perturbation, beyond the threshold, is always asymmetric. No quasi-steady state for a counter-rotating vortex pair is observed.On the linear receptivity of trailing vortices
http://hdl.handle.net/10985/19657
On the linear receptivity of trailing vortices
BÖLLE, Tobias; BRION, Vincent; SIPP, Denis; JACQUIN, Laurent; ROBINET, Jean-Christophe
The present work investigates the excitation process by which free-stream disturbances are transformed into vortex-core perturbations. This problem of receptivity is modelled in terms of the resolvent in frequency space as the linear response to forcing. This formulation of receptivity suggests that non-normality of the resolvent is necessary to allow free-stream disturbances to excite the vortex core. Considering a local (in frequency) measure of non-normality, we show that vortices are frequency-selectively non-normal in a narrow frequency band of retrograde perturbations while the rest of the range is governed by an effectively normal operator, thus not contributing to receptivity. Canonical decomposition of the resolvent reveals that vortices are most susceptible to coiled filaments localised about the critical layer that induce bending waves on the core. Considering Lamb–Oseen, Batchelor and Moore–Saffman vortices as reference-flow models, we find free-stream receptivity to be essentially generic and independent of the axial wavelength on the considered range. A stochastic interpretation of the results could be a model for trailing-vortex meandering.
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/10985/196572020-01-01T00:00:00ZBÖLLE, TobiasBRION, VincentSIPP, DenisJACQUIN, LaurentROBINET, Jean-ChristopheThe present work investigates the excitation process by which free-stream disturbances are transformed into vortex-core perturbations. This problem of receptivity is modelled in terms of the resolvent in frequency space as the linear response to forcing. This formulation of receptivity suggests that non-normality of the resolvent is necessary to allow free-stream disturbances to excite the vortex core. Considering a local (in frequency) measure of non-normality, we show that vortices are frequency-selectively non-normal in a narrow frequency band of retrograde perturbations while the rest of the range is governed by an effectively normal operator, thus not contributing to receptivity. Canonical decomposition of the resolvent reveals that vortices are most susceptible to coiled filaments localised about the critical layer that induce bending waves on the core. Considering Lamb–Oseen, Batchelor and Moore–Saffman vortices as reference-flow models, we find free-stream receptivity to be essentially generic and independent of the axial wavelength on the considered range. A stochastic interpretation of the results could be a model for trailing-vortex meandering.Optimal perturbation for two-dimensional vortex systems: route to non-axisymmetric state
http://hdl.handle.net/10985/17877
Optimal perturbation for two-dimensional vortex systems: route to non-axisymmetric state
NAVROSE; JOHNSON, Author H. G.; BRION, Véronique; JACQUIN, Laurent; ROBINET, Jean-Christophe
We investigate perturbations that maximize the gain of disturbance energy in a two-dimensional isolated vortex and a counter-rotating vortex pair. The optimization is carried out using the method of Lagrange multipliers. For low initial energy of the perturbation (E.0/), the nonlinear optimal perturbation/gain is found to be the same as the linear optimal perturbation/gain. Beyond a certain threshold E.0/, the optimal perturbation/gain obtained from linear and nonlinear computations are different. There exists a range of E.0/ for which the nonlinear optimal gain is higher than the linear optimal gain. For an isolated vortex, the higher value of nonlinear optimal gain is attributed to interaction among different azimuthal components, which is otherwise absent in a linearized system. Spiral dislocations are found in the nonlinear optimal perturbation at the radial location where the most dominant wavenumber changes. Long-time nonlinear evolution of linear and nonlinear optimal perturbations is studied. The evolution shows that, after the initial increment of perturbation energy, the vortex attains a quasi-steady state where the mean perturbation energy decreases on a slow time scale. The quasi-steady vortex state is non-axisymmetric and its shape depends on the initial perturbation. It is observed that the lifetime of a quasi-steady vortex state obtained using the nonlinear optimal perturbation is longer than that obtained using the linear optimal perturbation. For a counter-rotating vortex pair, the mechanism that maximizes the energy gain is found to be similar to that of the isolated vortex. Within the linear framework, the optimal perturbation for a vortex pair can be either symmetric or antisymmetric, whereas the structure of the nonlinear optimal perturbation, beyond the threshold E.0/, is always asymmetric. No quasi-steady state for a counter-rotating vortex pair is observed.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10985/178772018-01-01T00:00:00ZNAVROSEJOHNSON, Author H. G.BRION, VéroniqueJACQUIN, LaurentROBINET, Jean-ChristopheWe investigate perturbations that maximize the gain of disturbance energy in a two-dimensional isolated vortex and a counter-rotating vortex pair. The optimization is carried out using the method of Lagrange multipliers. For low initial energy of the perturbation (E.0/), the nonlinear optimal perturbation/gain is found to be the same as the linear optimal perturbation/gain. Beyond a certain threshold E.0/, the optimal perturbation/gain obtained from linear and nonlinear computations are different. There exists a range of E.0/ for which the nonlinear optimal gain is higher than the linear optimal gain. For an isolated vortex, the higher value of nonlinear optimal gain is attributed to interaction among different azimuthal components, which is otherwise absent in a linearized system. Spiral dislocations are found in the nonlinear optimal perturbation at the radial location where the most dominant wavenumber changes. Long-time nonlinear evolution of linear and nonlinear optimal perturbations is studied. The evolution shows that, after the initial increment of perturbation energy, the vortex attains a quasi-steady state where the mean perturbation energy decreases on a slow time scale. The quasi-steady vortex state is non-axisymmetric and its shape depends on the initial perturbation. It is observed that the lifetime of a quasi-steady vortex state obtained using the nonlinear optimal perturbation is longer than that obtained using the linear optimal perturbation. For a counter-rotating vortex pair, the mechanism that maximizes the energy gain is found to be similar to that of the isolated vortex. Within the linear framework, the optimal perturbation for a vortex pair can be either symmetric or antisymmetric, whereas the structure of the nonlinear optimal perturbation, beyond the threshold E.0/, is always asymmetric. No quasi-steady state for a counter-rotating vortex pair is observed.