Journal of Fluid Mechanics Webinar Series: Adrian Lozano-Duran, USA and Adrian Lozano-Duran, USA

Speaker: Adrian Lozano-Duran, MIT, USA

Date/Time: Friday 21st May 2021 4:00pm BST/11am EST

Title: Cause-and-effect of linear mechanisms sustaining in wall turbulence

Abstract: Despite the nonlinear nature of turbulence, there is evidence that part of the energy-transfer mechanisms sustaining wall turbulence can be ascribed to linear processes. The different scenarios stem from linear stability theory and comprise exponential instabilities, neutral modes, transient growth from non-normal operators, and parametric instabilities from temporal mean-flow variations, among others. These mechanisms, each potentially capable of leading to the observed turbulence structure, are rooted in simplified physical models. Whether the flow follows any or a combination of them remains elusive. Here, we evaluate the linear mechanisms responsible for the energy transfer from the streamwise-averaged mean-flow U to the fluctuating velocities u’. To that end, we use cause-and-effect analysis based on interventions: manipulation of the causing variable leads to changes in the effect. This is achieved by direct numerical simulation of turbulent channel flows at low Reynolds number, in which the energy transfer from U to u’ is constrained to preclude a targeted linear mechanism. We show that transient growth is sufficient for sustaining realistic wall turbulence. Self-sustaining turbulence persists when exponential instabilities, neutral modes, and parametric instabilities of the mean flow are suppressed. We further show that a key component of transient growth is the Orr/push-over mechanism induced by spanwise variations of the base flow.

Click here to read Lozano-Duran's recent paper, published in the JFM Special Volume in celebration of the George Batchelor centenary.

Speaker: Debasish Das, Strathclyde University, UK

Date/Time: Friday 21st May 2021 4:30pm BST/11:30am EST

Title: A three-dimensional small-deformation theory for electrohydrodynamics of dielectric drops

Abstract: Electrohydrodynamics of drops is a classic fluid mechanical problem where deformations and microscale flows are generated by application of an external electric field. In weak fields, electric stresses acting on the drop surface drive quadrupolar flows inside and outside and cause the drop to adopt a steady axisymmetric shape. This phenomenon is best explained by the leaky-dielectric model under the premise that a net surface charge is present at the interface while the bulk fluids are electroneutral. In the case of dielectric drops, increasing the electric field beyond a critical value can cause the drop to start rotating spontaneously and assume a steady tilted shape. This symmetry-breaking phenomenon, called Quincke rotation, arises due to the action of the interfacial electric torque countering the viscous torque on the drop, giving rise to steady rotation in sufficiently strong fields. Here, we present a small-deformation theory for the electrohydrodynamics of dielectric drops for the complete Melcher–Taylor leaky-dielectric model in three dimensions. Our theory is valid in the limits of strong capillary forces and highly viscous drops and is able to capture the transition to Quincke rotation. A coupled set of nonlinear ordinary differential equations for the induced dipole moments and shape functions are derived whose solution matches well with experimental results in the appropriate small-deformation regime. Retention of both the straining and rotational components of the flow in the governing equation for charge transport enables us to perform a linear stability analysis and derive a criterion for the applied electric field strength that must be overcome for the onset of Quincke rotation of a viscous drop.

Enjoy free access to papers in support of Das' webinar, courtesy of the Journal of Fluid Mechanics.