Abstract
The present model geometry is a recent iteration of the Joubert (Defence Science and Technology, Tech. Rep. TR1920, 2006) generic conventional submarine design and is known as the “BB2”. Windtunnel testing of the model at 10\(^\circ \) yaw, by Chinaclay visualisation and by ensembleaveraged measurements using highresolution stereoscopic particle image velocimetry, shows a similar wake flow at the modellength Reynolds numbers \(Re_\mathrm{L} = 4 \times 10^6\) and \(8 \times 10^6\). The most significant flow feature is on the model upper hull. It is a system of three corotating vortices produced by a cruciform appendage which consists of a vertical fin (or sail in American terminology) and two horizontal hydroplanes. Circulation is strongest from the fin tip followed by the windward hydroplane, then the leeward hydroplane. Vortex tracking shows a downwash of the fintip vortex, where the windward and leewardhydroplane vortices spiral in the rotation direction of the fintip vortex. The interpreted flow includes a Ushaped vortex line around the leeward hydroplane, where this vortex line connects the fintip vortex and a surface vortex on the leeward side of the fin.
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Acknowledgements
Model manufacturing and SPIV traverse automation by QinetiQ and the financial support by DST Maritime Division are acknowledged. Our thanks go to fellow DST colleagues and the anonymous referees for providing helpful feedback on this work.
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Appendix 1: Bias error in experimental technique
Appendix 1: Bias error in experimental technique
For SPIV, the bias error \(\langle u \rangle _\mathrm{b}/U_{\infty }\) is approximated by the uncertainties in the lengthscale conversion \((\delta _\mathrm{l})\), the laser timing \((\delta _t)\), the inplane displacement \((\delta _{yz})\) and the outofplane displacement \((\delta _x)\), viz.,
The terms on the right side of Eq. 15 are described as follows.

For the uncertainty in lengthscale conversion, \(\delta _\mathrm{l} / (r_\mathrm{m} / (R_\mathrm{l} \, r_\mathrm{s})) \simeq 4 \,\text {pixels} / (137\,\text {mm} / (10 \times 5.5\,\mu \text {m/pixel})) \simeq {\pm }\,0.002\), where \(r_s\) is the spatial resolution of the camera sensor or chargecoupled device and \(R_l\) is the reproduction ratio. The reference length \(r_\mathrm{m}\) is the maximum radius of the bare hull.

For the uncertainty in laser timing due to electronics jitter, \(\delta _t / \Delta t \simeq {\pm }\,0.001\), where \(\Delta t \simeq 11\,\upmu \)s to \(22\,\upmu \)s is the time interval applied between laser pulses.

For the uncertainty in the inplane (yz) displacement, \(\delta _{yz}/\langle \mathbf {s}_{yz} \rangle \,\simeq \)\(0.125\,\text {pixels} / 7\,\text {pixels} \simeq {\pm }\,0.018\), where \(\langle \mathbf {s}_{yz} \rangle \simeq 0.6U_{\infty } \times \Delta t / (R_l \, r_s\)) is the resolvable particleimage displacement based on a maximum swirl velocity of \(\simeq 0.6U_{\infty }\). The uncertainty \(\delta _{yz} = f \{ \langle \mathbf {s}_{yz} \rangle \}\) is effectively a lower limit on resolvable displacement as a function of \(\langle \mathbf {s}_{yz} \rangle \)—it is taken from the digital particleimagevelocimetry analysis (fig. 6b) of [35]; the uncertainty is for a seeding density of \(\simeq \) 6 particles per \(32 \times 32\) pixels interrogation window.

For a symmetrical arrangement of SPIV cameras at oblique angles of 45\(^\circ \) from the laser sheet, the ratio between the inplane and the outofplane particleimage displacement uncertainties is unity based on thinlens raytracing analysis [27, 36]. Assuming that the field of view is not affected by optical aberrations or vignetting, and the measurement uncertainty is approximately homogeneous and isotropic, the uncertainty in the outofplane (x) displacement may be written as
$$\begin{aligned} \frac{\delta _{x}}{\langle \mathbf {s}_x \rangle } \simeq \frac{\delta _{yz}}{\langle \mathbf {s}_{yz} \rangle }. \end{aligned}$$(16)
To summarise, the inplane and the outofplane displacement uncertainties are approximately the same \((\delta _{x}/\langle \mathbf {s}_x \rangle \simeq \delta _{yz}/\langle \mathbf {s}_{yz} \rangle \simeq {\pm }\,0.018)\), and are larger than the uncertainties in the lengthscale conversion \(( \delta _l / (r_\mathrm{m} / (R_l \, r_s)) \simeq {\pm }\,0.002)\) and the laser timing \((\delta _t / \Delta t \simeq {\pm }\,0.001)\). Overall, by substituting Eq. 16 into Eq. 15, this gives the bias error \(\langle u \rangle _\mathrm{b}/U_{\infty } \simeq {\pm }\,0.026\).
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Lee, SK., Manovski, P. & Kumar, C. Wake of a cruciform appendage on a generic submarine at 10\(^\circ \) yaw. J Mar Sci Technol 25, 787–799 (2020). https://doi.org/10.1007/s0077301900680x
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Keywords
 Generic submarine
 Windtunnel testing
 Flow visualisation
 Particle image velocimetry