3.1. The flow regimes and topological characteristics

In the present study, we identified four distinct stable flow regimes: FC, LS, SS and RS, as illustrated in table 2 and figure 4. The RS regime represents a distinct topological state observed in condensable vapour ventilation, characterised by intense interfacial fluctuations. Intermediate transitional states (FC-LS, LS-SS and SS-RS) were also observed, which are morphologically characterised by unstable re-entrant jets, cavity-length fluctuations near the tail fins, and regular interfacial waves, respectively.

Figure 5.

Flow regime map. The central axis defines the natural cavitation baseline (increasing $U$ ). The upper and lower panels map the regime transitions driven by ventilation flow rate ( $Q_{\textit{in}}$ , group A) and temperature ( $T$ , group B), respectively.

To delineate the operational envelope, figure 5 maps these regimes against the control parameters: freestream velocity ( $U$ ), ventilation flow rate ( $Q_{\textit{in}}$ ) and ventilation temperature ( $T$ ). Along the natural cavitation baseline ( $U$ -axis), the flow evolves sequentially from FC to LS and finally to SS. Consistent with classical cavitation theory (Franc & Michel Reference Franc and Michel2004), the interface of these natural supercavities remains stable and glassy once fully formed. In contrast, active vapour ventilation generally promotes cavity formation but at the cost of enhanced interfacial instability; consequently, the stable range of the quiescent SS regime is significantly contracted. To facilitate an intuitive understanding of the three full-length supercavity regimes, a systematic qualitative comparison of high-speed images is provided in Appendix A (figure 18), corresponding to group A3. This morphological evidence reveals the interfacial evolution from a smooth state (SS) to regular waves (SS-RS) and finally to chaotic fluctuations (RS).

The regime transition is non-monotonic, with cavitation suppression at both excessively low and high ventilation flow rates. At minimal ventilation flow rates, the injection increases the local pressure, thereby suppressing natural cavitation; however, since the vapour supply remains below the effective threshold required for sustained vapour-ventilated supercavitation, the overall effect is an inhibition of cavity growth. In a distinct mechanism, the suppression observed at excessively high ventilation flow rates stems from intense interfacial instabilities. In this regime, the ventilation significantly enhances interfacial heat and mass transfer, which accelerates the condensation rate. This leads to a ‘regime regression’ where the supercavity collapses back into the FC regime. For non-condensable gas ventilation, even minimal injection rates promote cavity formation. Furthermore, excessive gas injection typically induces over-expansion and pulsation, characterised by the shedding of large-scale gas pockets driven by buoyancy and large-amplitude oscillations of the cavity geometry, without the same regime regression. These comparative phenomena are further illustrated in Appendix B (figure 19), which also indicates that the ventilation threshold for suppression in steam ventilation is significantly higher than that for non-condensable gas.

To elucidate the internal flow structure, we adopt a four-region conceptual framework (figure 6 $a$ ): the natural cavitation region, the ventilation influence region, the internal boundary layer, and the reverse flow region. The natural cavitation region (between the cavitator and the orifice) remains largely independent of ventilation, maintaining a smooth interface. Upon injection, the vapour forms the ventilation influence region. In the internal boundary layer, the hot vapour engages in heat/momentum transfer with the cavity fluid, while adverse pressure gradients at the tail drive the reverse flow region.

Figure 6.

Schematic diagrams of flow structure and instability mechanisms: ( $a$ ) four-region internal flow model; ( $b$ ) evolution of the vapour jet near the orifice; ( $c$ ) amplification of interfacial disturbances via K–H and R–T instabilities.

Figure 7.

High-speed visualisation of flow characteristics near the ventilation orifice and the ventilation influence region. ( $a$ ) Evolution of the cavity driven by increasing freestream velocity ( $U$ ) from 2.54 to 3.07 m s⁻¹, under constant ventilation parameters $Q_{\textit{in}} = 120$ SLPM and $T=523.15$ K. ( $b$ ) Evolution of the cavity driven by increasing ventilation flow rate $Q_{\textit{in}}$ from 100 to 180 SLPM under fixed freestream velocity $U=3.38$ m s⁻¹ and vapour temperature $T=523.15$ K. Supplementary movie 1 provided for reference is available at https://doi.org/10.1017/jfm.2026.11897.

Compared to natural or gas ventilation, the phase change introduces complex thermo-hydrodynamics. The injected steam originates as high-enthalpy superheated vapour. As it converges into the narrow orifice, it undergoes rapid acceleration and cooling (figure 6 $b$ ). At lower injection rates, this cooling forms discrete condensate droplets (figure 7 $b$ ). With increasing ventilation flow rates, the vapour flow becomes choked at the orifice pore, and forms an under-expanded jet upon exiting (Kerney et al. Reference Kerney, Faeth and Olson1972). Consequently, the vapour undergoes explosive radial expansion and temperature drop, crossing the saturation line to form observable mist flows (figure 7( $b$ ), also see supplementary movie 1). Based on previous literature (Wu et al. Reference Wu, Katayama, Nariai, Ishizuka, Widyatmoko and Yabe2007), we postulate the existence of internal expansion–compression waves, although direct visual evidence of these condensation shock structures was not captured due to experimental limitations. Nevertheless, the interaction between this high-speed multiphase jet and the water interface is obvious. This interaction, coupled with droplet impact and latent heat release, creates severe local density gradients and pressure pulsations. These thermodynamic disturbances are then convected by shear-driven K–H-type dynamics, and shaped by gravity-related R–T-type selection, culminating in the macroscopic roughness of the RS regime (figure 6 $c$ ). At extremely high ventilation flow rates ( $Q_{\textit{in}} \gt 400$ SLPM), the supercavity collapses back into a pseudo-FC regime, indicating that excessive interfacial instability can overcome the supplied vapour volume. Distinct from classical FC, the natural cavitation region remains smooth and transparent (see supplementary movie 1), indicating that the natural cavity is sustained while the ventilated portion is stripped away.

Figure 7 provides comparative visualisations of the flow evolution along different parameter regulation paths. First, regarding the interaction with natural cavitation (figure 7 $a$ ), increasing freestream velocity ( $U$ ) in the FC regime reveals that the injected vapour initially behaves as a submerged plume undergoing rapid condensation. As $U$ increases, natural cavitation nuclei grow and coalesce. Eventually, a coherent smooth interface establishes from the cavitator edge, creating a distinct stratification from the rough ventilated cavity. Second, for ventilation within a fully formed cavity (figure 7 $b$ ), at lower ventilation flow rates ( $Q_{\textit{in}}=100$ SLPM), discrete condensate droplets impinge on the interface, generating localised ripples. At moderate ventilation flow rates ( $Q_{\textit{in}}=180$ SLPM), the random small-scale disturbances induced by mist flow impact are rapidly amplified downstream, evolving into coherent quasi-two-dimensional interfacial waves. Detailed quantitative analysis of these dynamic mechanisms follows in § 3.3.

3.2. Quantitative dependence of cavity dimensions on ventilation parameters

In this section, we quantify the thermo-hydrodynamic response of the supercavity dimensions to ventilation parameters ( $Q_{\textit{in}}$ and $T$ ). As defined in figure 8, the cavity length ( $L_s$ ) and maximum diameter ( $L_d$ ) were extracted directly from the high-speed imagery. Given the periodic interfacial fluctuations characteristic of the RS regime, a time-averaged approach was adopted: statistical means were computed over 900 consecutive frames (approximately 0.1 s) to ensure convergence, with error bars representing the standard deviation of temporal fluctuations.

Figure 8.

Definition of supercavity dimensional parameters. The length ( $L_s$ ) is measured as the axial distance from the cavitator to the re-attachment point, while the maximum diameter ( $L_d$ ) is extracted at a fixed station 10 cm downstream of the cavitator.

Figure 9 illustrates the non-monotonic evolution of supercavity length $L_s$ with ventilation flow rate $Q_{\textit{in}}$ . The overall trend aligns well with the flow regime map (figure 5), generally correlating with the transition sequence from FC to LS, SS and RS. At low-to-moderate freestream velocities ( $U=3.07$ and 3.38 m s⁻¹), vapour injection acts as a mass source, generally promoting supercavity growth. However, a distinct suppression interval is observed in the initial ventilation stage. Small amounts of ventilation cause $L_s$ to shrink, although gas addition would usually be expected to enlarge a ventilated cavity. We attribute this to a competition between hydrodynamic disruption and thermodynamic mass loss.

1. (i) Hydrodynamically, the low-flux injection disrupts the coherent low-pressure vortex core in the wake, and weakens the local low-pressure support for natural cavitation. A comparable hydrodynamic disturbance can also occur for ambient-air ventilation. However, in the Appendix B comparison, low air injection promotes cavity formation because the injected air can remain as a gas phase inside the cavity and provide an effective gas-volume source. Thus non-condensable ventilation is governed primarily by the competition between imposed gas supply and closure-region leakage (Spurk Reference Spurk2002; Karn et al. Reference Karn, Arndt and Hong2016). This interpretation is also consistent with three-component numerical models of ventilated cavitation, in which the liquid, vapour and non-condensable-gas phases are solved separately (Ji et al. Reference Ji, Luo, Peng, Zhang, Wu and Xu2010; Hasani Malekshah et al. Reference Hasani Malekshah, Wróblewski and Majkut2024). These simulations show that gas ventilation can reduce the vapour-cavity component associated with natural cavitation, while the injected non-condensable gas still provides an effective gas-volume source over a suitable range of ventilation flow rates.

2. (ii) Thermodynamically, due to the low enthalpy flux at low $Q_{\textit{in}}$ , the injected vapour is rapidly depleted by condensation before it can effectively sustain the internal pressure. For vapour ventilation, direct-contact condensation therefore introduces an internal volume sink, while early condensation and near-orifice mixing reduce the effective source fraction. At low vapour flow rates, the imposed vapour source may be too weak to compensate for the weakened natural-cavitation support and condensation loss. Only when $Q_{\textit{in}}$ exceeds a transition threshold does the mass supply compensate for these losses, driving a qualitative transition from the FC to the supercavity regime. For instance, at $U=3.07$ m s⁻¹, increasing $Q_{\textit{in}}$ from 120 to 180 SLPM causes $L_s$ to nearly double. In contrast, the high-velocity case ( $U=3.51$ m s⁻¹) exhibits a smoother transition as it initiates from a fully developed supercavity.

Figure 9.

Variation of supercavity length ( $L_s$ ) with ventilation flow rate ( $Q_{\textit{in}}$ ) under different freestream velocities (groups A1–A3). Error bars represent the standard deviation of temporal fluctuations over 900 frames. Supplementary movie 2 is provided to demonstrate the cavity collapse under high $Q_{\textit{in}}$ .

Figure 10.

Variation of supercavity diameter ( $L_d$ ) with ventilation flow rate ( $Q_{\textit{in}}$ ). Error bars denote the standard deviation over 900 frames. The dashed line indicates the reference diameter $2d_c$ . Note that unlike length, the diameter exhibits strong inertial constraint.

Further analysis reveals a second suppression interval even within the fully formed supercavity regime (e.g. 60–120 SLPM at $U=3.51$ m s⁻¹). This interval coincides strictly with the shrinkage in diameter ( $L_d$ ) shown in figure 10. We hypothesise that this secondary suppression is due to ventilation disturbances amplifying interfacial pulsations, which correspondingly increase the effective vapour–liquid contact area and heat transfer coefficient. This creates a thermodynamic penalty where the enhanced condensation rate temporarily outweighs the increase in ventilation supply.

The same source–sink interpretation also explains the high-flow regression. As $Q_{\textit{in}}$ increases further, the imposed vapour supply is larger. At the same time, the interface becomes fragmented, and the closure region becomes more unstable. The resulting increase in effective contact area, interfacial renewal and closure loss can raise the sink side of the balance faster than the effective vapour source. Ultimately, at extreme ventilation flow rates ( $Q_{\textit{in}}=420$ SLPM), all three $L_s$ curves exhibit a sharp drop, the dynamic evolution of which is captured in supplementary movie 2. The high-momentum vapour stream impinges strongly on the interface, enhancing turbulent mixing and heat transfer rates. Consequently, the condensation rate surges and overwhelms the mass supply, stripping away the ventilated portion of the cavity. The flow topology following the collapse differs from the classic FC regime. As highlighted in the insets, the interface remains fully transparent across the natural cavitation region, standing in stark contrast to the opaque, foamy texture characteristic of low-ventilation states. This observation implies that while the high-momentum injection suppresses the ventilated supercavity via enhanced condensation, the natural cavitation region at the leading edge remains hydrodynamically stable.

Figure 11.

Evolution of cavity morphology with ventilation temperature $T$ . Experimental parameters correspond to groups B1–B4 (see table 1) from top to bottom, respectively. The supercavity length $L_s$ and diameter $L_d$ are annotated for fully developed cases. Note the collapse-to-recovery transition in group B1.

In contrast to the sensitive response of cavity length, the maximum diameter $L_d$ (figure 10) remains relatively insensitive to ventilation variations. While minor fluctuations correlate with the length suppression intervals, the overall magnitude of $L_d$ remains effectively clamped near $2d_c$ . This observation aligns with classical Logvinovich principle of independence of cavity expansion (Logvinovich Reference Logvinovich1973), indicating that the radial expansion is primarily governed by the inertial constraint, and is less sensitive to thermodynamic parameters. Even with active vapour injection, the cavity cannot break the hydrodynamic limit imposed by the oncoming flow momentum.

The independent influence of ventilation temperature $T$ is illustrated in figure 11. A pronounced thermal effect is evident in group B1, where injecting 423.15 K vapour destabilises the LS regime into a collapse; however, elevating $T$ to 473.15 K triggers a dramatic recovery, establishing a stable SS-RS flow. For other groups, the effect of $T$ exhibits a saturation trend. Temperature elevation initially drives significant length extension, but saturates once the cavity morphology is established. We attribute this to two mechanisms: (i) higher vapour enthalpy reduces the content of condensed droplets, mitigating impact disturbances; and (ii) elevated internal temperature increases the local saturation vapour pressure $P_v(T_c)$ , effectively lowering the local cavitation number. A similar saturation trend in diameter was reported by Jiang et al. (Reference Jiang, Hong, Pham and Ahn2023) using heated nitrogen, although their study did not observe the dramatic collapse–recovery transition seen in our group B1 due to the absence of phase change. However, the saturation trend implies a limit to these thermal benefits, likely associated with the nonlinear relationship between the source temperature and the actual internal cavity temperature.

Figure 12.

Comparison of interfacial characteristics between natural cavitation and vapour ventilation under identical flow conditions ( $U = 3.51$ m s⁻¹, $T = 523.15$ K). Supplementary movie 3 is provided for reference.

To illustrate the non-monotonic dimensional evolution observed above, we introduce a time-averaged source–sink balance for the ventilation cavity. The retained vapour volume is supplied by the residual natural-cavitation source and by the imposed vapour flow that survives near-orifice expansion, mixing and early condensation. It is depleted by closure-region leakage and by condensation at the gas–liquid interface. Appendix C derives this balance from a gas-phase control volume, and gives the reduced source–sink ordering

(3.1) \begin{align} \frac {1}{U d_c^2}\frac {\mathrm{d} V_c}{\mathrm{d} t} =\alpha C_{\mathit{nat}}+\beta C_Q-C_{\ell }-\varTheta _{\textit{cond}}, \end{align}

where $V_c$ is the cavity volume, $C_Q=Q_{\textit{in}}/(U d_c^2)$ is the imposed ventilation coefficient, $C_{\mathit{nat}}$ is the dimensionless source associated with the natural-cavitation state at the same freestream speed, $\alpha$ is its retained fraction after ventilation is introduced, $\beta$ is the effective fraction of imposed vapour supply, $C_{\ell }$ is the dimensionless closure leakage coefficient, and $\varTheta _{\textit{cond}}$ is the dimensionless potential condensation-sink capacity. The corresponding sink-to-source ratio is

(3.2) \begin{align} \varPi _{\textit{net}} = \frac {C_{\ell }+\varTheta _{\textit{cond}}} {\alpha C_{\mathit{nat}}+\beta C_Q}. \end{align}

Values $\varPi _{\textit{net}}\lt 1$ indicate that the retained natural-cavitation source plus the effective imposed supply is sufficient to maintain or enlarge the vapour-filled cavity. Values $\varPi _{\textit{net}}\gt 1$ indicate that leakage and condensation have overtaken the combined source, giving a tendency towards length reduction or regime regression. This parameter is used here as a physical ordering relation, since $\alpha$ , $\beta$ , $C_{\ell }$ , $S_i$ and $\textit{Nu}_i$ are closure parameters in the present measurements.

This ordering is consistent with the measured trend in figure 9. For group A, $Q_{\textit{in}}=120$ – $420$ SLPM corresponds to ventilation coefficients of order 1–4. The intermediate SS range has a relatively smooth interface and a weak condensation capacity, so representative parameter ranges give $\varPi _{\textit{net}}\lt 1$ , and the cavity length grows. At high ventilation flow rates, the RS regime exhibits interface fragmentation, droplet impingement, and a broadened misty interface in figures 9 and 18. These features increase the effective contact area and interfacial renewal, allowing the condensation and leakage sink to rise enough for $\varPi _{\textit{net}}$ to exceed unity. This explains why the cavity length can regress even though the imposed vapour flow rate is larger. The detailed parameter choices, arithmetic estimates and sensitivity checks supporting this semi-quantitative ordering are provided in the supplementary material (Estimation for the source–sink criterion).

3.3. The interfacial instabilities caused by vapour ventilation

The interfacial dynamics of supercavitation change markedly under active vapour ventilation. As visualised in figure 12 and supplementary movie 3, compared with the quiescent and glassy interface characteristic of natural cavitation, the introduction of high-temperature vapour results in a marked increase in surface roughness. The interface becomes highly unsteady, characterised by the continuous formation and break-up of irregular ripples and gas clusters.

We propose a conceptual model of the instability mechanisms, with the sequence schematised in figure 13, to explain the transition from a smooth to a rough interface leading up to cavity collapse. The dominant instability source evolves distinctly with the ventilation flow rate. (i) At low injection rates, the primary disturbance arises from the impingement of condensate droplets, which acts as a discrete excitation source on the cavity surface. (ii) In the RS regime, the formation of an under-expanded jet and contact condensation generates continuous thermodynamic pulsations. These perturbations are then convected and amplified by shear-driven K–H dynamics, while gravity and surface tension select the long-wave upper-interface disturbances through an R–T-type mechanism (Chandrasekhar Reference Chandrasekhar1961; Drazin & Reid Reference Drazin and Reid2004). (iii) Under very high ventilation, the mechanism shifts to rapid heat transfer. Strong mixing triggers a surge in condensation that overwhelms the mass supply, stripping the cavity rear and causing collapse.

To quantify the spatial evolution of these interfacial disturbances, we extracted the temporal envelopes of the upper cavity interface. Figure 14 presents the amplitude distribution $\Delta Y$ along the streamwise direction, where the origin is defined at the cavity detachment point. It is observed that the interfacial fluctuation amplitude grows linearly downstream ( $X/d_c \gt 2$ ). Comparing the envelopes for $Q_{\textit{in}}=120$ and 360 SLPM, it is evident that increasing the ventilation flow rate significantly enhances both the initial perturbation magnitude in the ventilation influence region and the spatial growth rate. The 95 % confidence intervals (grey shaded regions) confirm the statistical significance of this linear amplification.

Figure 13.

Schematic illustration of the interfacial instability mechanisms. ( $a$ ) Low ventilation flow rate: impingement of condensate droplets. ( $b$ ) Medium-to-high ventilation flow rate: thermodynamic pulsations with K–H/R–T instabilities. ( $c$ ) Very high ventilation flow rate: strong mixing and rapid condensation.

Figure 14.

Envelope contours of the upper supercavity interface and interfacial wave amplitudes at different axial positions under different ventilation flow rates: ( $a$ ) $Q_{\textit{in}} = 120$ SLPM, ( $b$ ) $Q_{\textit{in}} = 360$ SLPM.

Figure 15.

The FFT spectra of greyscale variations in the ventilation influence region under different ventilation flow rates. The vertical axis $\bar {G}$ represents the time-integrated spectral amplitude of the normalised greyscale fluctuations.

Figure 16.

Spatiotemporal analysis of interfacial instabilities at $Q_{\textit{in}}=360$ SLPM. ( $a$ ) Spatiotemporal diagram of the dimensionless surface displacement $\eta ^{*}$ , visualising the downstream convection of wave packets. Streamwise evolution of the Hilbert energy density spectra $E_{\mathit{H}}$ resolved in ( $b$ ) the dimensionless frequency domain ( $St = f d_c / U$ ) and ( $c$ ) the dimensionless wavelength domain ( $\lambda ^* = \lambda / d_c$ ). ( $d$ ) Dispersion spectrum $S_{\mathit{H}}(St, k^*)$ in the frequency–wavenumber plane, where $k^* = d_c / \lambda$ denotes the dimensionless wavenumber.

We further investigated the spectral characteristics of the excitation source by performing a fast Fourier transform (FFT) on the greyscale fluctuations within the ventilation influence region (figure 15). The ventilation influence region is selected as the monitoring region because the high-temperature flow interacts with the cavity interface and produces strong thermo-hydrodynamic coupling. These processes induce significant greyscale fluctuations that characterise the core dynamic properties of the excitation source. A dominant fundamental frequency, denoted as $f_0$ , is identified, which shifts from approximately 55 Hz to 146 Hz as $Q_{\textit{in}}$ increases. This suggests that the ventilation jet acts as a thermodynamic self-excited oscillator. However, a counter-intuitive drop in the peak amplitude is observed at intermediate ventilation flow rates ( $Q_{\textit{in}}=180{-}240$ SLPM). This attenuation can be attributed to the transition mechanism of interfacial instabilities: the under-expanded jet at these rates generates a mist flow containing very fine condensate droplets. The random impingement of this mist on the interface, and the unsteady contact condensation of the cooled jet at the cavity surface, introduce broadband thermodynamic pulsations instead of a single tonal excitation, thereby distributing the spectral energy and suppressing the dominant peak amplitude.

Figure 16 visualises the spatiotemporal evolution of the travelling waves. The trajectory of the dimensionless wave elevation $\eta ^{*}=\eta /d_c$ in figure 16( $a$ ) indicates a clear convection velocity, where $\eta$ denotes the instantaneous interface displacement extracted from the cavity boundaries. More importantly, the Hilbert–Huang transform spectra (Huang et al. Reference Huang, Shen, Long, Wu, Shih, Zheng, Yen, Tung and Liu1998) in figures 16( $b$ ) and 16( $c$ ) reveal a distinct frequency downshifting and wavelength dilation trend along the streamwise direction. This evolution is consistent with vortex pairing in a K–H-type shear-layer instability. As the interfacial waves propagate downstream, small-scale vortices in the shear layer merge into larger coherent structures, leading to an increase in the spatial wavelength ( $\lambda ^*$ ) and a consequent decrease in the characteristic frequency ( $St$ ).

Furthermore, the dispersion spectrum in figure 16( $d$ ) presents the energy distribution in the $(St,k^*)$ plane. The energy concentration along the linear ridge reveals the convective nature of the interfacial instabilities, where the slope represents the dimensionless phase velocity $C_{\!p}/U$ :

(3.3) \begin{align} \frac {C_{\!p}}{U} = \frac {\omega /k}{U} = \frac {2\pi f \lambda }{U} \approx 1.04. \end{align}

Theoretically, for a classical K–H instability at a gas–liquid interface, the phase velocity is a density-weighted average of the two stream velocities (Brennen Reference Brennen2014):

(3.4) \begin{align} C_{\mathit{K-H}} = \frac {\rho _l U_l + \rho _v U_v}{\rho _l + \rho _v}, \end{align}

where $\rho _l$ and $\rho _v$ are the densities of the liquid and vapour phases, respectively. Given that $\rho _l \gg \rho _v$ , the theoretical phase velocity should conform to the local liquid velocity ( $C_{\mathit{K-H}} \approx U_{l}$ ). Considering the model blockage ratio $B \approx 4.5\,\%$ (calculated in § 2.1), the accelerated local liquid velocity around the cavity can be estimated as $U_{l} \approx U / (1 - B) \approx 1.05 U$ . The close agreement between the measured phase velocity ( $C_{\!p} = 1.04 U$ ) and the estimated local velocity ( $C_{\mathit{K-H}}\approx 1.05 U$ ) supports a K–H-type convective mechanism for the interfacial waves. In this context, the pulsation of the cavity surface is organised as a source-convection process: the thermodynamic pulsations at the orifice provide the source excitation, which then undergoes downstream convection and amplification along the shear layer.

Although the K–H mechanism effectively explains the convective nature of the interfacial waves, the classical shear-layer picture implies a quasi-symmetric growth of disturbances on both interfaces (Wang et al. Reference Wang, Huang, Zhang, Wang and Zhao2018; Zou & Zhang Reference Zou and Zhang2021). Our high-speed imaging reveals a pronounced vertical asymmetry during the RS regime: the upper interface undergoes large-amplitude undulation and break-up, whereas the lower interface remains relatively stable. Previous studies have noted that the gravity-induced hydrostatic pressure gradient causes the cavity axis to migrate upwards, leading to significant disparities in the pressure and velocity distributions between the upper and lower interfaces (Ceccio Reference Ceccio2010; Liu et al. Reference Liu, Xiang, Xie and Zhang2023a ). Consequently, the interfacial evolution is likely shaped by K–H-type convection together with gravity-related R–T-type selection. Near the closure region, pressure recovery and re-entrant-flow impingement may also provide a local dynamic contribution by decelerating the interface and increasing the effective normal acceleration. To quantify this vertical asymmetry, we analyse the streamwise evolution of the fluctuation energy.

Figure 17.

Streamwise evolution of interfacial instability intensity at $Q_{\textit{in}}=360$ SLPM. The cumulative energy $E$ is calculated by integrating the Hilbert energy spectrum within the effective frequency band ( $5 {-} 3000$ Hz). The ratio $\xi _E = E_{up}/E_{low}$ quantifies the energetic asymmetry between the upper and lower interfaces. The vertical dashed line at $X/d_c \approx 7.2$ marks the approximate axial location of the cavity closure region.

The instability evolution is quantified by the cumulative energy intensity $E$ , as depicted in figure 17. In the near-field region ( $X/d_c \lt 2.5$ ), the fluctuation energies of the upper and lower interfaces are nearly equivalent, yielding energy ratio $\xi _E \approx 1$ . This symmetry indicates that the initial disturbances are mainly convected by K–H-type shear-layer dynamics. A significant divergence emerges in the mid-field region ( $2.5 \lt X/d_c \lt 7.2$ ). Here, the upper-surface fluctuation energy increases much more rapidly than that on the lower surface. This divergence is attributed to the superposition of shear-driven convection and gravity-related R–T-type amplification on the upper interface. On the lower interface, gravity acts as a restoring force, creating a stable stratification that inhibits the growth of large-scale fluctuations. At the intersection of the lower interface and the body surface ( $X/d_c \approx 7.2$ ), a localised surge in fluctuation energy is observed. This spike is correlated with flow separation and the vigorous impact of the re-entrant jet, both of which are driven by the severe adverse pressure gradient present in this region. Following this surge, the fluctuations on the lower interface undergo a sharp attenuation. This decay coincides with the cavity closure onto the sidewall of the test model, where the three-phase contact line effectively constrains and damps the interfacial oscillations. In the far-field region ( $X/d_c \gt 7.2$ ), the fluctuation energy of the upper interface continues to increase slightly before reaching saturation, resulting in a peak energy ratio $\xi _E$ exceeding 120.

Notably, the spectral evolution shown in figure 16( $c$ ) indicates that the dominant wavelength of the disturbances increases along the flow direction. This wavelength dilation can be physically explained by the filtering effect of surface tension against the R–T-type mechanism. According to the linear stability theory (Charru Reference Charru2011), the interface becomes unstable only when the perturbation wavelength exceeds a critical threshold $\lambda _{\mathit{R-T}}$ determined by the competition between surface tension and gravity:

(3.5) \begin{align} \lambda _{\mathit{R-T}} = 2\pi \sqrt {\frac {\gamma }{g(\rho _l - \rho _v)}}, \end{align}

where $\gamma$ is the surface tension, and $g$ is the gravitational acceleration. Under the reference experimental conditions ( $T = 298.15$ K, $P = 12.25$ kPa), the thermophysical properties derived from the IAPWS-95 formulation (Wagner & Pruß Reference Wagner and Pruß2002) are surface tension $\gamma = 0.072$ N m⁻¹, liquid density $\rho _l = 997.05$ kg m⁻³, and vapour density $\rho _v = 0.09$ kg m⁻³ (evaluated at the cavity reference pressure $12.25$ kPa; the source–sink condensation estimate in Appendix C and the supplementary material adopts a smaller representative density for the lower-pressure condensing region inside the cavity). These parameters yield $\lambda _{\mathit{R-T}} \approx 17.05$ mm. Theoretically, perturbations with wavelengths shorter than this threshold are damped by surface tension, while longer wavelengths are selectively amplified by gravity. Notably, in the case of high-temperature ventilation, although superheated vapour is injected, the effective interfacial temperature ( $T_{\textit{in}}$ ) remains only slightly above the ambient water temperature (298.15 K). This is attributed to the vast heat capacity disparity between the two phases, and the intense latent heat exchange during condensation. Even if $T_{\textit{in}}$ shifts to 303.15 K, the resulting deviations in $\gamma$ , $\rho _l$ and $\rho _v$ are minimal, leading to a negligible reduction in $\lambda _{\mathit{R-T}}$ (approximately 0.47 %). This quantitative stability of $\lambda _{\mathit{R-T}}$ suggests that the observed transition towards larger coherent structures in the far field is better attributed to the selective gravity-driven amplification of long-wave perturbations than to temperature-induced property changes.

In summary, the distinct interfacial dynamics of the RS regime are associated with a coupled thermo-hydrodynamic mechanism. In contrast to the predominantly inertial instabilities observed in non-condensable gas ventilation, the instability here originates from thermodynamic self-excitation at the ventilation orifice. This self-excitation is characterised by a feedback loop in which rapid condensation and latent-heat exchange generate local thermodynamic and pressure fluctuations near the ventilation orifice. These fluctuations can modulate the near-orifice vapour discharge and interfacial condensation, thereby sustaining the disturbance source. The resulting disturbances are convected downstream through a K–H-type shear-layer mechanism. The subsequent topological evolution is shaped by gravitational differentiation. On the lower surface, gravity suppresses fluctuations through stable stratification. On the upper surface, gravity selectively amplifies long-wave perturbations through an R–T-type mechanism. In this process, short-wave disturbances are effectively damped by surface tension. This physical progression explains the RS regime by tracing the evolution from thermo-hydrodynamic pulsations and shear-driven convection to gravity-selected interfacial amplification.