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Free Content The salt finger amplitude in unbounded T-S gradient layers

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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  = S/T = O (1), Prandtl number /T >> 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  ≡ (R)-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 , T/, 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  = 1/3. Asymptotic similarity laws  → 0 are also presented.

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Document Type: Research Article

Publication date: January 1, 1998

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  • The Journal of Marine Research, one of the oldest journals in American marine science, publishes peer-reviewed research articles covering a broad array of topics in physical, biological and chemical oceanography. Articles that deal with processes, as well as those that report significant observations, are welcome. Biological studies involving coupling between ecological and physical processes are preferred over those that report systematics. The editors strive always to serve authors and readers in the academic oceanographic community by publishing papers vital to the marine research in the long and rich tradition of the Sears Foundation for Marine Research. We welcome you to the Journal of Marine Research.
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