Ocean Dissipation Research Articles

Tidal Dissipation on Titan

Tidal dissipation may constrain the nature of the surface and interior of Titan. Provided the surface of Titan is covered by satellite-wide hydrocarbon seas and oceans, the solid body of Titan would have to respond not only to the external tidal disturbance potential but also to the loading and shifting weights of liquids on the surface. To estimate the tidal response of Titan's interior which is assumed to be differentiated into a crust-mantle-core structure, several endmember-type models have been considered, each of them constrained by Titan's mass and radius and consistent with either a volatile-rich or a volatile-poor evolution of the satellite. The dissipation rates as a consequence of the inelastic response of Titan's interior to body and loading tides have been computed from the imaginary parts of complex Love numbers and mass load coefficients. Additionally, a new analytical model of bottom frictional dissipation as a consequence of tidal currents in a global ocean is presented and is shown to compare well with a numerical model for both the radial and libration components of the ocean tide. In contrast to the solid volatile-poor interior structure, the volatile-rich interior contains an internal liquid ammonia-water region overlain by an icy shell, thereby mechanically decoupled from the deep interior. While the latter produces higher tidal dissipation rates than the former due to greater shell flexibility, the greater motion of the ocean floor accordingly induces smaller ocean currents, and hence much lower ocean dissipation rates for the volatile-rich scenario. The resultant total dissipation rates have been compared to those required to damp Titan's orbital eccentricity over the age of the Solar System. While the highly dissipative volatile-rich interior requires a time constant of orbit circularization of only about half this time period, the volatile-poor interior structure would allow restrictions on the minimum ocean depth and on ocean composition. Consequently, the volatile-rich scenario seems inconsistent with a primordial origin of the orbit eccentricity. This suggests Titan's interior may be rigid and that there is no global ocean. Alternatively, the eccentricity of the orbit may have a more recent origin. It is, however, also conceivable that the thermal history could have been governed by more rapid interior cooling in the past, thereby notably diminishing the amount of solid dissipation in the deep interior.

The Application of Internal-Wave Dissipation Models to a Region of Strong Mixing

Abstract Several models now exist for predicting the dissipation rate of turbulent kinetic energy, ϵ, in the oceanic thermocline as a function of the large-scale properties of the internal gravity wave field. These models are based on the transfer of energy toward smaller vertical scales by wave-wave interactions, and their predictions are typically evaluated for a canonical internal wave field as described by Garrett and Munk. Much of the total oceanic dissipation may occur, however, in regions where the wave field deviates in some way from the canonical form. In this paper simultaneous measurements of the internal wave field and ϵ from a drifting ice camp in the eastern Arctic Ocean are used to evaluate the efficacy of existing models in a region with an anomalous wave field and energetic mixing. By explicitly retaining the vertical wavenumber bandwidth parameter, β*, models can still provide reasonable estimates of the dissipation rate. The amount of data required to estimate β*, is, however, substanti...

Eddy-viscosity and drag-law models for random ocean wave dissipation

Eddy-viscosity and drag-law models for random ocean wave dissipation

Kolmogorov similarity hypotheses for scalar fields: sampling intermittent turbulent mixing in the ocean and galaxy

Kolmogorov’s three universal similarity hypotheses are extrapolated to describe scalar fields like temperature mixed by turbulence. The analogous first and second hypotheses for scalars include the effects of Prandtl number and rate-of-strain mixing. Application of velocity and scalar similarity hypotheses to the ocean must take into account the damping of active turbulence by density stratification and the Earth’s rotation to form fossil turbulence. By the analogous Kolmogorov third hypothesis for scalars, temperature dissipation rates X averaged over lengths r > L K should be lognormally distributed with intermittency factors σ 2 that increase with increasing turbulence energy length scales L O as σ 2 ln<x> r ≈ μ θ ln( L O / r ). Tests of kolmogorovian velocity and scalar universal similarity hypotheses for very large ranges of turbulence length and timescales are provided by data from the ocean and the galactic interstellar medium. These ranges are from 1 to 9 decades in the ocean, and over 12 decades in the interstellar medium. The universal constant for turbulent mixing intermittency μ θ is estimated from oceanic data to be 0.44 ± 0.01, which is remarkably close to estimates for Kolmogorov’s turbulence intermittency constant μ of 0.45 ± 0.05 from galactic as well as atmospheric data. Extreme intermittency complicates the oceanic sampling problem, and may lead to quantitative and qualitative undersampling errors in estimates of mean oceanic dissipation rates and fluxes. Intermittency of turbulence and mixing in the interstellar medium may be a factor in the formation of stars.

Evolution of the lunar orbit with temperature‐ and frequency‐dependent dissipation

The coupled thermal‐dynamical evolution of the Earth‐Moon system is modeled. The lunar orbit is assumed noncircular and inclined to Earth's equator plane. Solid planet dissipation in the Earth and Moon is assumed to occur by temperature‐ and frequency‐dependent solid friction. The dissipative response of Earth's oceans is represented as an equilibrium ocean with constant phase lag. Subsolidus convection cools the Earth and Moon, removing primordial, radioactive, and (in the Moon) tidal heating. A model without oceanic dissipation results in the Moon moving out to about 50 RE (Earth radii) in less than about 1.5 b.y. Thereafter, dynamic evolution slows considerably because the Earth has cooled and become less dissipative. A model that includes oceanic dissipation shows that about 700 m.y. of large oceanic dissipation (equivalent phase lag equals 1/11) is required to move the Moon to 60 RE. In one interpretation of this result, consistent with variable ocean basin configuration, several episodes of large oceanic dissipation have occurred since the end of the Archean with a cumulative time span of about 700 m.y. In our model, about 90% of the lunar angular momentum received from the Earth is the result of solid friction. Uncertainties in the thermal evolution and dissipation law preclude an unequivocal partitioning of tidal dissipation into solid Earth and oceanic parts. Our model likely underestimates solid Earth dissipation, however, and so emphasizes the proposition that solid Earth tidal friction might have been the main energy sink in the Earth‐Moon system and that oceanic dissipation may have been relatively much less important than solid Earth dissipation over geologic time.

Causes and implications of noise in oceanic dissipation measurements

Measurements of the rate of dissipation of turbulent kinetic energy using airfoil probes mounted on Camel profilers show a constant lower limit of about <3 × 10 −7 W m −3. A series of experiments conducted in Jervis Inlet, British Columbia, indicated that this value represents the noise in the measurement and is attributed to vehicular accelerations from hydrodynamically induced forces on the instrument body. Because a large fraction of observations are at the noise level, ambient dissipation rates in the ocean must be <3 × 10 −7 W m −3.

The role of Earth tides in the balance of tidal energy

The main role of earth tides in the planetary balance of tidal energy is to dispose elastically of energy transmitted to the solid earth from the ocean. This is accomplished by negative correlations between body tide and load tide transports and forces. The correlations arise from ocean dissipation. They are illustrated here in a model that has an elastic lithosphere and a rigid mantle.