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Large-amplitude axisymmetric waves on columnar vortices, thought to be related to flow structures observed in vortex breakdown, are found as static bifurcations of the Bragg–Hawthorne equation. Solutions of this equation satisfy the steady, axisymmetric, Euler equations. Non-trivial solution branches bifurcate as the swirl ratio (the ratio of azimuthal to axial velocity) changes, and are followed into strongly nonlinear regimes using a numerical continuation method. Four types of solutions are found: multiple columnar solutions, corresponding to Benjamin's ‘conjugate flows’, with subcritical–supercritical pairing of wave characteristics; solitary waves, extending previously known weakly nonlinear solutions to amplitudes large enough to produce flow reversals similar to the breakdown transition; periodic wavetrains; and solitary waves superimposed on the conjugate flow that emerge from the periodic wavetrain as the wavelength or amplitude becomes sufficiently large. Weakly nonlinear soliton solutions are found to be accurate even when the perturbations they cause are fairly strong.

The flow in volumetric absorbers is investigated using a simple mathematical model. It is found that there are several restrictions and failure mechanisms that are inherent to the volumetric absorber, regardless of the precise structural details, material properties, etc. The heat that the absorber can extract safely is limited by flow-related constraints. Multiple steady solutions exist for certain parameter values: a “fast” solution corresponding to a low exit temperature, a “slow” solution which is unstable, and a “choked” solution for which the absorber is near to stagnation temperature. The existence of multiple solutions may lead to abrupt local “switching” and absorber failure. For a given irradiance applied to the absorber, the existence and the character of the solutions are determined by a single dimensionless parameter, the Blow parameter B. Neglecting the variation of the hydraulic resistivity with temperature may lead to a dangerous overestimate of the receiver’s ability to sustain irradiation. For reasonable efficiencies control of mass flow or outlet temperature of the absorber, rather than pressure control, may be required.

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