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Second-mode Waves in Hypersonic Transition: Energy Balance, Kinematics and Mechanics

AMS Seminar Series

Speaker: Carlo Scalo, Program Manager, Defense Sciences Office, DARPA

Presentation

Seminar Slide Deck (PDF-8.1MB)

Abstract

This seminar presents recent advances in the understanding of the fundamental structure of second-mode waves in hypersonic transition published by Roy & Scalo, J. Fluid Mech. (2025-2026). Reference flow conditions are taken from a Mach 6 boundary layer over a 3◦ cone at zero angle of attack, with varying degrees of wall-to-adiabatic temperature ratios, ranging from strongly cooled, Tw/Tad = 0.25, to highly heated, Tw/Tad =1.75.

It was found that second-mode instabilities comprise two decks, separated by the pressure node location, i.e., the point of zero pressure fluctuation, y=y_π. The upper deck (y > y_π) is characterised by temperature and density fluctuations sustaining the bulk of the second-mode energy production, peaking between the critical layer, y=y_c, and the generalised inflection point, y=y_i. The nature of the wave at this location is NOT acoustic, but rather akin to a vortical roll-up of density gradients, ultimately visible in Schlieren imaging as the famous rope waves.

Slightly below the inflection point, a downward-oriented energy flux develops, sustaining acoustic energy accumulation in the lower deck, i.e., y < y_π, ultimately leading to the fluctuating pressure footprint of second-mode waves that is measured by experimental techniques such as wall-mounted PCBs or pressure sensitive paints (PSP). Colder walls (Tw/Tad << 1) enhance the temperature gradient in the second-mode energy production term, strengthening the flux from the upper to the lower deck. Ray tracing also reveals that colder walls, entailing stronger base flow velocity gradients, are more effective at kinematically trapping acoustic wave paths emanating from the wall, hence enabling eigenmode growth.

Biography

Photo of Carlo Scalo
Carlo Scalo, Ph.D., joined the Defense Advanced Research Projects Agency (DARPA) as a program manager in the Defense Sciences Office (DSO) in November 2025. He previously supported the U.S. Navy as a subject matter expert in hypersonic aerothermodynamics, where he contributed to the design of basic and applied research programs, and workforce training initiatives. In 2014, he joined the School of Mechanical Engineering at Purdue University. His research interests focus on numerical and theoretical modeling of high-speed boundary layer physics, linear and nonlinear acoustics, vortex dynamics, and turbulence. He was a recipient of Young Investigator Program (YIP) awards from the U.S. Air Force, Navy, and Army. He is also the founder of HySonic Technologies, LLC. Founded in 2017, HySonic is a Purdue-affiliated startup specializing in passive enhancement of aerodynamic and propulsive performance for hypersonic vehicles. At DARPA, he aims to advance the foundational science of extreme-scale hydrodynamics, multiphase chemistry, underwater communications, acoustic and shock wave propagation in water, and quantum-based methods for encryption, data transfer, and solution of partial differential equations.