Abstract

Finite amplitude numerical calculations are made for a completely unbounded salt finger domain whose overall vertical "property" gradients (Tz and Sz) are uniform and remain unaltered in time. For diffusivity ratio τ = κS/κT = O (1), Prandtl number ν/κT >> 1, and density ratio R = Tz/Sz > 1 this regime corresponds to a "double gradient" sugar (S)—salt (T) experiment. Two-dimensional pseudo-spectral calculations are made in the vicinity of the minimum critical condition for salt finger instability, viz., small ε ≡ (Rτ)-1 - 1 > 0; the allowed spectrum includes the fastest growing wave of linear theory. When the vertical wavelength of the fundamental Fourier component is systematically increased the solution changes from a single steady vertical mode to a multi-modal statistically steady chaotic state. Each of the long vertical modes can be amplified by the (unchanging overall) gradient Sz, and can be stabilized by the induced vertical T, S gradients on the same scale as the modes; nonlinear triad interactions in the T - S equations can also lead to amplitude equilibration even though ε, κT/ν, and the Reynolds number are extremely small. When subharmonics of the horizonal wavelength of maximum growth are introduced into the numerical calculations the new wave amplifies (via Sz) and produces a quantitative change in the time average fluxes. Experimentally testable values of heat flux and rms horizontal T-fluctuations are computed in the range 2.8 > R >1.6 for τ = 1/3. Asymptotic similarity laws ε → 0 are also presented.

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