Momentum, mass, heat, and vorticity balances from oceanic measurements of current and temperature
Bryden, Harry L.
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The local dynamics of low-frequency motions in the MODE region are investigated from three arrays of moored measurements of current and temperature. Tests for lowest-order balances of horizontal momentum, mass, heat, heat and vorticity within established errors are carried out. Geostrophic comparisons of four-day averaged observed and geostrophic current differences from the MODE-l array indicate that ageostrophic balance within estimated errors is the lowest-order horizontal momentum balance. The discrepancy between observed and geostrophic current differences has a standard deviation of 1.9 cm/see which is 26% as large as the standard deviation of the current differences. In the mass balance comparisons of estimates of δυ/δχ and δν/δγ from the MODE-O Array l indicate that within estimated errors the low frequency currents are horizontally nondivergent. The standard deviation of horizontal divergence, which is the discrepancy from horizontal nondivergence, is .22 x 10 6 sec 1 which is 36% as large as the standard deviation of the estimates of horizontal derivatives of velocity. These tests significantly increase the observational basis for geostrophy and horizontal nondivergence and confirm the validity of the error estimates. In the heat balance, estimates of horizontal advection of temperature balance local time changes of temperature within estimated errors for the IWEX observations. These estimates have small errors because a representation of horizontal advection of temperature in terms of the speed and turning about the vertical of the horizontal current is used. The errors are so small that from future measurements it may be possible to estimate the sum of local change plus horizontal advection of temperature and from this sum it may be possible to estimate vertical velocity. This balance between local change and horizontal advection demonstrates that horizontal advection of spatially varying features is an important cause of local time changes. The horizontal advection could not be explained in terms of advection by the long time-averaged flow field. This suggests that the local dynamics of low-frequency motions in the MODE region are strongly nonlinear. An indication of energy transfer, which occurs in nonlinear processes, is found in a phase lag such that estimates of horizontal advection lead local changes of temperature. In the context of the baroclinic instability model this phase lag is consistent with the growth of perturbation wave energy by conversion of potential energy contained in the forty-day averaged flow field. In the vorticity balance, estimates of planetary advection account for only half the local time change of vorticity for MODE-0 Array 1 measurements. Within estimated errors these two terms do not balance, so these observations cannot be explained as manifestations of barotropic Rossby waves alone. Estimates of vortex stretching and horizontal advection of relative vorticity could not be made. A phase lag such that estimates of planetary advection lead local changes of vorticity is consistent in the context of the instability model with an increase in perturbation wave enstrophy, which must occur when the perturbation wave grows, due to the conversion of planetary enstrophy. Because of the importance of the vorticity balance for understanding the dynamics of low-frequency motions an experiment is suggested to estimate accurately all terms in the lowest-order vorticity balance. From such measurements the energy transfer and enstrophy conversion could also be estimated.
Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution July, 1975
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