The thermal and hydrodynamic response of a Sea-Bird unpumped CTD
SBE 41, is numerically modeled to assess the biases occurring at the
slow flushing rates typical of glider operations. Based on symmetry
considerations, the sensor response is approximated by coupling the
incompressible Navier-Stokes and the thermal advection-diffusion equations
in two dimensions. Numerical results illustrate three regimes in the
thermal response of the SBE 41 sensor, when crossing water layers with
different thermal signatures. A linear decay in time of the bulk
temperature of the conductivity cell is initially found. This is induced
by the transit of the inflow through the conductivity cell in the form
of a relatively narrow jet. Water masses with new thermal signatures do
not immediately fill the sensor chambers, where the cross-section
widens. Thermal equilibrium of these water masses is then achieved, in a
second regime, via a cross-flow thermal diffusion between the boundary of the jet and the walls. Consequently, the evolution of the bulk temperature scales
with the square root of time. In a third regime, the evolution of the
bulk temperature depends on the thermal gradient between the fluid and
the coating material. This results on an exponential decay of the bulk
temperature with time. A comprehensive analytical model of the time
evolution of the bulk temperature inside a cell is proposed based on
these results.