Despite decades of research, thermoacoustic instability continues to hinder the development of rocket engines and gas turbines. The phenomenon arises primarily through interactions between unsteady heat release and sound, potentially leading to high-amplitude self-excited flow oscillations in a combustor. If not detected early enough and controlled, such oscillations can cause thermal and mechanical damage, resulting in long commissioning times, reduced operating limits and, in severe cases, even catastrophic system failure. Much progress has been made since the 1930s, but there is still insufficient understanding of the physical processes involved for them to be reliably predicted and designed out.

The traditional approach to analysing a thermoacoustic system is to treat it as an acoustic field driven by local fluctuations in the rate of heat release. Such fluctuations are typically modelled with a function that encapsulates the flame response to incident flow perturbations at different amplitudes and frequencies. Despite its simplicity, this approach has provided valuable insight over the years and has been successfully used to predict limit-cycle amplitudes, hysteresis and even mode switching. However, one of its key quasi-linear assumptions is that the acoustics are harmonic in time. Recent research has shown that thermoacoustic oscillations can often be much more elaborate than that, with multiple dominant modes interacting to produce a complex nonlinear dynamics such as intermittency, quasi-periodicity and chaos. Crucially, the traditional acoustic-based approach is intrinsically rooted in reductionism, a ‘divide and conquer’ paradigm where the goal is to understand the behaviour of a complete system by dividing it into multiple subsystems for detailed individual analysis. Although reductionism has greatly improved our understanding of the physics of thermoacoustic oscillations, it is by no means the only viable approach. Practical thermoacoustic systems are inherently complex, with multiple components – acoustics, turbulent hydrodynamics, chemical reactions and more – interacting, often nonlinearly, over a wide range of spatial and temporal scales. For such systems, a complex systems approach that focuses on the phenomena emerging from the collective behaviour of the interacting components of a system has obvious relevance.

In Thermoacoustic Instability, Sujith & Pawar take us on a fascinating journey through the application of dynamical systems theory and complex systems theory to the analysis and control of thermoacoustic oscillations. Their book consolidates more than a decade of research in this important and still-emerging field – research that, owing to its interdisciplinary nature, has lain scattered across journals specializing in subjects such as combustion, fluid mechanics, acoustics, vibration, nonlinear dynamics and aerospace propulsion.

Sujith & Pawar begin their book by reviewing the most important physical processes in both laminar and turbulent combustors and by providing a clear and detailed explanation of why it is important to adopt the dynamical and complex systems approaches in thermoacoustic analysis. They use examples from real combustors to illustrate the advantages and disadvantages of these approaches, before moving on to a general introduction to dynamical systems theory. Bifurcations, attractors, routes to chaos, phase space reconstruction and recurrence plots are all discussed, but this gentle yet effective introduction to the field assumes no prior knowledge of nonlinear dynamics.

The application of dynamical systems theory to laminar thermoacoustic systems is then presented in some detail. A wide variety of phenomena are covered, starting with bifurcations that take the system from a fixed point to a limit cycle, and progressing from there to more complex dynamics such as quasi-periodicity, frequency locking, intermittency, strange non-chaos and chaos. The key message is that even simple thermoacoustic systems can exhibit remarkably complex nonlinear dynamics.

Sujith & Pawar go on to explain through a series of well-presented examples how complex systems theory has been used in recent years to advance our understanding of thermoacoustic instability in turbulent combustors. For example, the long-held assumption that combustion noise is purely stochastic has been overturned. The intermittency route to thermoacoustic instability from a low-amplitude chaotic state has been elucidated and then reinterpreted in terms of pattern formation. Synchronization concepts have been used to unravel the intricate coupling between reactive flow and acoustic fields, and reduced-order models have been derived to capture the temporal dynamics of such synchronization based on vortex–acoustic interactions. The use of the Hurst exponent to forecast the onset of thermoacoustic instability and flame blowout is also explained, as is the use of complex networks to reveal hidden properties of thermoacoustic systems such as scale-free and small-world behaviour.

The final chapters apply those fundamental concepts to practical strategies for the early detection and control of thermoacoustic oscillations. This includes novel suppression techniques based on amplitude death and asynchronous quenching, as well as precursors based on recurrence quantification analysis, multi-fractal analysis and complex networks. This is followed by an intriguing discussion of the generality of the intermittency route to self-excited instability across various turbulent flows in thermoacoustic, aeroacoustic and aeroelastic systems.

Rocket and jet engines offer unrivalled power-to-weight ratios. Land-based gas turbines will continue to play a prominent role as the power industry moves away from coal and towards intermittent renewables. Thermoacoustics will therefore remain an active area of research for the foreseeable future. Sujith & Pawar's in-depth treatment of thermoacoustic instability fills a critical need by consolidating pioneering research on the application of dynamical systems theory and complex systems theory to the analysis and control of this damaging phenomenon. Thermoacoustic Instability promises to serve as a valuable reference for many years to come, particularly for those trying to use these theoretical tools without an advanced degree in mathematics. I would highly recommend the book to graduate students and established researchers alike – not just those working in thermoacoustics and combustion, but those working in any field where oscillatory instabilities are important. At the same time, thermoacoustic systems can serve as an ideal context for developing and testing concepts from dynamical systems theory and complex systems theory, so physicists too may find the book useful.