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 \(3.1\%\) in \(w\)-active width, \(1.6\%\) in salinity-active width, \(2.8\%\) in broad spectral fraction, and \(3.6\%\) 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.