Local Inertial Period Research Articles

Baroclinic Tsunami Generation

An analytical and experimental study of the baroclinic waves generated by a monopole dislocation of the sea floor is presented. Analytical results are based on a two-dimensional and linearized description of motion using a two-layer approximation for density variation; experiments utilize a stratification with finite (nonzero) pycnocline thickness. Scaling parameters which characterize the generation process and the potential role of nonlinear effects are discussed. It is shown that the barotropic modes are not affected by the small differences in potential density typical of ocean stratifications and all previous results for these waves are applicable. The two-layer approximation is found to provide an accurate representation of the (long) baroclinic waves typical of tsunamis. Like the barotropic response, baroclinic generation is impulsive and linear resulting in wave amplitudes proportional to the vertical offset of the sea floor. Near the generation region barotropic waves have amplitudes of one-half the sea floor displacement while the baroclinic waves are attenuated further by the ratio h1/h, where h is the total fluid depth and h1, the upper layer thickness. Although Coriolis effects are not included in either the analytical or experimental models, these effects may often be significant for baroclinic waves. In general, the potential role of Coriolis forces is both earthquake and site specific. Regardless, the analysis herein remains applicable for times smaller than the local inertial period.

A Numerical Study of Time-Dependent Turbulent Ekman Layers over Horizontal and Sloping Bottoms

A numerical study is made of a time-dependent turbulent Ekman bottom boundary layer. Parameters for the model were chosen to simulate conditions near the bottom of the Florida Current in the Straits of Florida. The model used is that of Lykosov and Gutman. It allows the coefficient of turbulent viscosity v to vary with time t and height z and permits the effects of an imposed stable stratification and sloping bottom to be included. The variation of v with t and z is not preset but is determined in the course of solving the problem subject to the turbulent energy equation, the similarity arguments of Komolgoroff, and a mixing length hypothesis of Zilitinkevich and Laykhtman. The results of this preliminary study are compared to the author's observations. The agreement is good for the friction velocity values as well as for the mean total Ekman veering. However, most of the computed Ekman veering occurred above the logarithmic layer while most of the measured veering occurred within the logarithmic layer. The results suggest, as do the observations, that turbulent Ekman bottom layers varying on time scales of order the local inertial period are not quasi-stationary. Allowing the bottom to be inclined at a small angle transverse to the flow is found to modify significantly the temperature profile near the bottom, leading at times either to the formation of a homogeneous layer of depth order 10 m or to conditions marginally suitable for the formation of convectively mixed layer of comparable depth.

Dispersion of Floatables in Lake Currents

A group of ten sub-surface drogues were released in a cluster in the epilimnion 15 km offshore near Oshawa, Lake Ontario, and the subsequent drift and horizontal spread were followed for 72 h using the radar/decca navigation system of the Canadian Survey Ship Limnos. Experimental data suggest periodic shrinking and expansion of the drogue group at approximately 16–18 h corresponding to the local inertial period. This is attributed to the generation of convergence and divergence flow fields as the inertial currents are modified by the sloping shore line or a sloping thermocline. Thus, mesoscale motions such as convergence and divergence of the flow field as well as turbulent dispersion due to random eddies are important considerations in the kinematics of floatables.

Vertical motions in a region of deep water formation

To study natural convection and deep water formation, in the open ocean, direct measurements of vertical motions and of the hydrological structure have been made during winter in the northern part of the Western Mediterranean Sea. The measurements were made in the winters of 1969, 1970 and 1972, using neutrally buoyant rotating floats described by Webb, Dorson and Voorhis (1970). Vertical profiles of the potential density and salinity in the vicinity of the floats were computed from in situ measurements of electrical conductivity, temperature and pressure. The 1972 measurements show that, in conditions characterized by a weak density stratification, there is no vertical motion at the local inertial period. The dominant carriers of energy are stability waves ( Gascard, 1972), i.e. gravity-inertial waves, probably induced by bursts of wind at the surface and generated in the sloping region of the continental shelf. Then, the 1969 and 1970 measurements ( Stommel, Voorhis and Webb, 1970, 1971) suggest that, in conditions of no density stratification, winds, the Earth's rotation and tides have a great influence on the stability waves and may result in natural convection and subsequent deep water formation. Both were observed in 1969 and 1970.

Synoptic time and length scales of motion in the north equatorial current system of the Pacific Ocean

In the summer of 1967 two deep-moored buoys measured subsurface temperature data for nearly 2 months in the North Equatorial countercurrent near 119°W. The power spectral density functions calculated from these time series indicate that most of the variance in temperature of the thermocline occurred near three principal time periods corresponding to the semidiurnal and diurnal tidal motions and to the inertial oscillation. The inertial periodicity is thought to be a manifestation in the sensors of the mooring motion induced by horizontal inertial currents. In the spring of 1969 two more buoys were moored near the location of the 1967 stations; the power spectral density functions from the newer buoys show approximately the same concentration of variance in temperature as the earlier observations did. The cross-correlation function between the two buoys provided phase information from which the zonal wavelength L of the inertial motion was calculated to have been approximately 110 km. In all the moored power spectra the inertial spectral peak was consistently at a frequency significantly higher than the local inertial frequency f. However, drogue measurements obtained during the 1969 expedition suggest an inertial frequency substantially closer to the local inertial period, though still higher. The finiteness of L was found to induce in the dispersion relation for inertial waves a frequency shift that can account for the observed frequency shift between the theoretical inertial frequency and the observed frequency obtained by drogue (Lagrangian) measurements. However, the frequency shift of the inertial wave as measured in the moored power spectra (a Eulerian measurement) could not be accounted for by the finiteness of L, this result suggesting that the inertial wave was Doppler shifted by the mean flow past the fixed moorings.

Measurements of vertical motion and the partition of energy in the New England slope water

Direct measurements of vertical motion have been made over a period of days in the slope water off New England using neutrally-buoyant rotating floats. From these measurements frequency spectra of potential and vertical kinetic energy have been computed for periods of several minutes to approximately half a day. They are compared with spectra of horizontal kinetic energy from nearby moored current meters. A frequency range exists between the local inertial period (18·9 hr) and the local Väisälä period in which there is approximate equipartition between potential and kinetic energy. In this range the vertical kinetic energy is maximum. It is suggested that the dominant carriers of energy in the range are internal waves. In the region of the Väisälä frequency the potential energy spectrum undergoes a transition and its level decrease very rapidly.