On the helical nature of neutral trajectories in the ocean
Abstract
A neutral tangent plane is defined so that small isentropic and adiabatic displacements of a fluid parcel in this plane do not produce bouyant restoring forces on the parcel. This local stability argument can also be used to trace a neutral trajectory in space along some predetermined path in latitude and longitude. If one integrates laterally around an entire ocean basin on a neutral trajectory, one can arrive at a different depth than that of the starting point on the original CTD cast. This means that the definition of a neutral surface is pathdependent. This is a real effect; it results from the complicated equation of state of seawater, and is not an artifact of errors in the lateral integration procedure. Dyed patches of fluid are mixed laterally by mesoscale eddies along these neutral helices, and at the same time they are smoothed and advected in the vertical direction by smallscale mixing processes. It is shown that, while a neutral surface is formally illdefined mathematically (in the above pathdependent sense), this is of little importance for the purpose of constructing lateral maps of properties in the ocean, since the ambiguity in constructing a neutral surface is often less than the measurement accuracy of modern oceanographic instruments (≈0.003 kg m ^{3} in density). Pathdependence in the definition of a neutral surface occurs because α/β is a function of pressure (where α and β are the thermal expansion and haline contraction coefficients respectively). The local contribution to pathdependence is proportional to ▽p· ▽Sx▽Sxθ , representing the angle between an isobaric surface and the line of intersection of an isohaline surface and a surface of constant potential temperature. This, in turn, is proportional to ▽_{n}px▽_{n}θ where ▽_{n} is the epineutral gradient operator for properties measured in a neutral tangent plane. That is, unless isobars and potential isotherms drawn in a neutral tangent plane are parallel, a neutral trajectory around this point will not lie in the plane, but will describe a helix in space. Although complete surfaces with the “neutral property” do not exist, the neutral tangent plane is everywhere welldefined. The lateral motion along helical neutral trajectories produces vertical advection in the ocean. A method is described in this paper of taking an approximately neutral surface and distributing the pathdependent effects over the surface in a leastsquares sense. At each point in the ocean an error vector is found that represents the difference between the “bestfit” surface (which is a mathematically welldefined surface) and the local slope of the neutral tangent plane, providing a rational way of distributing the pathdependent vertical velocity on the surface. The vertical fluxes of heat, salt or tracer produced by the pathdependence of neutral surfaces do not have a signature in the dissipation rate of mechanical energy that can be measured with microstructure instrumentation.
 Publication:

Progress in Oceanography
 Pub Date:
 1988
 DOI:
 10.1016/00796611(88)900018
 Bibcode:
 1988PrOce..20..153M