Route survival and spectral modification of finite-depth salt-finger plume forests under imposed mean shear

Salt-finger plume forests in a finite layer can differ in strength and in the route by which interfacial activity becomes vertically connected. We use direct three-dimensional simulations to test whether such a route is a short-lived realization-specific transient or a persistent route family under an added mean-shear perturbation. The baseline route atlas holds density ratio, diffusivity ratio, Prandtl number, interface thickness, roughness amplitude, domain, and resolution fixed while varying the imposed interfacial roughness spectrum. Low-mode roughness forms a broad connecting endpoint, high-annulus roughness forms a localized route-memory endpoint, and mixed roughness forms a delayed scale-transfer route. A second mixed realization preserves continuous active-width, spectral, and transport measures after $t=45$, with mean absolute differences of $3.1\mathrm{\%}$ in $w$-active width, $1.6\mathrm{\%}$ in salinity-active width, $2.8\mathrm{\%}$ in broad spectral fraction, and $3.6\mathrm{\%}$ in salt flux, while shifting the binary scalar-contact label. We then impose an initial tanh mean shear on the mixed route. The full-resolution shear case reaches $t=60$ and preserves finite-depth reach: first velocity contact occurs at $t=57.75$, first salinity contact occurs at $t=59.5$, and both times match the unsheared mixed reference. The spectral branch is redistributed. At $t=60$, the broad fraction is $1.116$ times the mixed value, the intermediate fraction is $0.530$ times the mixed value, and the short-wave fraction is $1.278$ times the mixed value. In this finite-depth configuration, route survival means preserved reach and contact timing with a changed spectral pathway.