Skip to main content

Free Content Salt fingers in three dimensions

Download Article:
 Download
(PDF)
 

Abstract:

Three dimensional (3D) numerical calculations are made for a vertically unbounded fluid with initially uniform vertical gradients of sugar ( S ) and salt ( T ), where  = S/T = 1/3 is the diffusivity ratio, and the molecular viscosity is  >> T. The latter inequality allows us to neglect the nonlinear term in the momentum equation, while retaining such terms in the T-S equations. The discrete 3D Fourier spectrum resolves the fastest growing horizontal wavelength, as well as the depth independent Fourier component. Unlike previous calculations for the pure 2D case the finite amplitude equilibration in 3D is primarily due to the instability of the lateral S-gradients in the fingers, and the consequent transfer of energy to vertical scales comparable with the finger width. It is shown that finite amplitude two-dimensional disturbances are unstable and give way to three dimensional fingers with much larger fluxes. Calculations are also made for rigid boundary conditions at z = (0,L) in order to make a rough quantitative comparison with previous lab experiments wherein a finger layer of finite thickness is sandwiched between two well-mixed (T,S) reservoirs. The flux ratio is in good agreement, and the fluxes agree within a factor of two even though the thin interfacial boundary layer between the reservoir and the fingers is not quite rigid because sheared fingers pass through it. It is suggested that future experiments be directed toward the much simpler unbounded gradient model, for which flux and variance laws are given herein.

Document Type: Research Article

DOI: https://doi.org/10.1357/002224099764805165

Publication date: 1999-05-01

More about this publication?
  • The Journal of Marine Research 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. In the area of biology, studies involving coupling between ecological and physical processes are preferred over those that report systematics. Authors benefit from thorough reviews of their manuscripts, where an attempt is made to maximize clarity. The time between submission and publication is kept to a minimum; there is no page charge.
  • Editorial Board
  • Information for Authors
  • Subscribe to this Title
  • Ingenta Connect is not responsible for the content or availability of external websites
  • Access Key
  • Free ContentFree content
  • Partial Free ContentPartial Free content
  • New ContentNew content
  • Open Access ContentOpen access content
  • Partial Open Access ContentPartial Open access content
  • Subscribed ContentSubscribed content
  • Partial Subscribed ContentPartial Subscribed content
  • Free Trial ContentFree trial content
Cookie Policy
X
Cookie Policy
Ingenta Connect website makes use of cookies so as to keep track of data that you have filled in. I am Happy with this Find out more