Horizontal advection of temperature for low-frequency motions

Estimates of low-frequency horizontal advection of temperature are made with small errors by using a representation of horizontal advection of temperature as a function of the speed and turning about the vertical of the horizontal current. Within these errors the horizontal advection of temperature accounts for the observed local time changes of temperature during the 40-day Internal Wave Experiment (IWEX) period. The importance of horizontal advection indicates the dominant heat balance is not that of local time change of temperature balanced by vertical advection of temperature as assumed in wave models linearized about a mean stratification. These estimates suggest that a more appropriate linear model should be based on a mean state including mean horizontal gradients of temperature and hence a mean vertical shear of horizontal velocity. The mean state is not that of the long-term mean, however, but one associated with motions of time-scale longer than the measurement period of 40 days. Using this linearization, comparisons are made with a baroclinic instability model to investigate energy transfer between motions of different time-scales. In the context of this model, the direction of potential energy transfer between the mean and perturbation fields can be determined from the sign of the temporal phase lag between negative horizontal advection and local change of temperature. For these estimates negative horizontal advection leads local change suggesting that mean potential energy is increasing at the expense of perturbation potential energy. This phase lag, however, is not significantly different from zero so that a longer record is needed to establish the direction of potential energy transfer.