Bottom Drag Research Articles

Comparing three conventional penaeid-trawl otter boards and the new batwing design

Three experiments were conducted to compare the engineering and catching performances of a hydrodynamic otter board termed the ‘batwing’ (comprising a sled-and-sail assembly, configured to operate at 20° angle of attack – AOA and with minimal bottom contact) against three conventional designs (termed the ‘flat-rectangular’, ‘kilfoil’ and ‘cambered’ otter boards) with AOAs between ∼30 and 40°. Experiments involved paired penaeid trawls (7.35-m headlines). The first experiment compared the batwing otter boards against all other designs (using 41-mm mesh trawls). In experiment 2, the batwing was tested against the flat-rectangular design (with 32-mm mesh trawls). In experiment 3, the batwing and flat-rectangular otter boards were towed without trawls to facilitate estimates of their partitioned drag. Overall, compared to the conventional otter boards, the batwings had up to ∼86 and ∼18% less bottom contact and drag, respectively. Among the conventional otter boards, the trawls spread by the cambered design caught up to 13% more school prawns Metapenaeus macleayi attributed to their greater solid profile. No significant differences were detected among catches of fish in the trawls spread by the various otter boards. The results reaffirm that because otter boards contribute towards a large proportion of total system drag (estimated here at up to ∼56%), their appropriate configuration is essential to maximise the fuel efficiency of penaeid-trawl systems.

Energy Cascades and Loss of Balance in a Reentrant Channel Forced by Wind Stress and Buoyancy Fluxes

AbstractA large fraction of the kinetic energy in the ocean is stored in the “quasigeostrophic” eddy field. This “balanced” eddy field is expected, according to geostrophic turbulence theory, to transfer energy to larger scales. In order for the general circulation to remain approximately steady, instability mechanisms leading to loss of balance (LOB) have been hypothesized to take place so that the eddy kinetic energy (EKE) may be transferred to small scales where it can be dissipated. This study examines the kinetic energy pathways in fully resolved direct numerical simulations of flow in a flat-bottomed reentrant channel, externally forced by surface buoyancy fluxes and wind stress in a configuration that resembles the Antarctic Circumpolar Current. The flow is allowed to reach a statistical steady state at which point it exhibits both a forward and an inverse energy cascade. Flow interactions with irregular bathymetry are excluded so that bottom drag is the sole mechanism available to dissipate the upscale EKE transfer. The authors show that EKE is dissipated preferentially at small scales near the surface via frontal instabilities associated with LOB and a forward energy cascade rather than by bottom drag after an inverse energy cascade. This is true both with and without forcing by the wind. These results suggest that LOB caused by frontal instabilities near the ocean surface could provide an efficient mechanism, independent of boundary effects, by which EKE is dissipated. Ageostrophic anticyclonic instability is the dominant frontal instability mechanism in these simulations. Symmetric instability is also important in a “deep convection” region, where it can be sustained by buoyancy loss.

Scaling of Off-Equatorial Jets in Giant Planet Atmospheres

Abstract In the off-equatorial region of Jupiter’s and Saturn’s atmospheres, baroclinic eddies transport angular momentum out of retrograde and into prograde jets. In a statistically steady state, this angular momentum transfer by eddies must be balanced by dissipation, likely produced by magnetohydrodynamic (MHD) drag in the planetary interior. This paper examines systematically how an idealized representation of this drag in a general circulation model (GCM) of the upper atmosphere of giant planets modifies jet characteristics, the angular momentum budget, and the energy budget. In the GCM, Rayleigh drag at an artificial lower boundary (with mean pressure of 3 bar) is used as a simple representation of the MHD drag that the flow on giant planets experiences at depth. As the drag coefficient decreases, the eddy length scale and eddy kinetic energy increase, as they do in studies of two-dimensional turbulence. Off-equatorial jets become wider and stronger, with increased interjet spacing. Coherent vortices also become more prevalent. Generally, the jet width scales with the Rhines scale, which is of similar magnitude as the Rossby radius in the simulations. The jet strength increases primarily through strengthening of the barotropic component, which increases as the drag coefficient decreases because the overall kinetic energy dissipation remains roughly constant. The overall kinetic energy dissipation remains roughly constant presumably because it is controlled by baroclinic conversion of potential to kinetic energy in the upper troposphere, which is mainly determined by the differential solar radiation and is only weakly dependent on bottom drag and barotropic flow variations. For Jupiter and Saturn, these results suggest that the wider and stronger jets on Saturn may arise because the MHD drag on Saturn is weaker than on Jupiter, while the thermodynamic efficiencies of the atmospheres are not sensitive to the drag parameters.

Field observations of wave‐driven circulation over spur and groove formations on a coral reef

AbstractSpur and groove (SAG) formations are found on the forereefs of many coral reefs worldwide. Modeling results have shown that SAG formations together with shoaling waves induce a nearshore Lagrangian circulation pattern of counter‐rotating circulation cells, but these have never been observed in the field. We present results from two separate field studies of SAG formations on Palmyra Atoll which show their effect on waves to be small, but reveal a persistent order 1 cm/s depth‐averaged Lagrangian offshore flow over the spur and onshore flow over the grooves. This circulation was stronger for larger, directly incident waves and low alongshore flow conditions, consistent with predictions from modeling. Favorable forcing conditions must be maintained on the order of 1 h to accelerate and develop the SAG circulation cells. The primary cross and alongshore depth‐averaged momentum balances were between the pressure gradient, radiation stress gradient, and nonlinear convective terms, and the bottom drag was similar to values found on other reefs. The vertical structure of these circulation cells was previously unknown and the results show a complex horizontal offshore Lagrangian flow over the spurs near the surface driven by alongshore variability in radiation stress gradients. Vertical flow was downward over the spur and upward over the groove, likely driven by alongshore differences in bottom stress and not by vortex forcing.

Tide and Mixing Characteristics in Sundarbans Estuarine River System

Sundarbans Estuarine System (SES, 21.25°-22.5° N and 88.25°-89.5° E), comprising the southernmost part of the Indian portion of the Ganga-Bramhaputra delta bordering the Bay of Bengal, is India’s largest monsoonal, macrotidal delta front system. Sundarbans Estuarine Programme (SEP), the first comprehensive observational programme to study tidal as well as salinity features was conducted during 18-21 March, 2011 (Equinoctial spring phase). The main objective of this program was to monitor tides and salinity characteristics within the SES. Out of 30 observation stations, spread over more than 3,600 sq km covering seven inner estuaries, we have chosen river Jagaddal, which is connected with Saptamukhi East Gulley (SEG) in the West and river Thakuran in the East, due to the fact that the station Indrapur situated on this river at location very close to Bay of Bengal represents the condition at the mouth of all seven estuaries. Tidal elevation, salinity, bathymetry and vertical profile of salinity using CTD were measured during the observation period. Observed current data collected from different sources have been used for comparison with computed tidal current. Finally, the estuarine current, bottom drag coefficient and gradient Richardson number have also been computed. Computed values of these parameters have analyzed for interpreting variations for tidal, current and mixing feature prevailing in the estuary.

Analysis of mean velocity and turbulence measurements with ADCPs

The present study examines the vertical structure of the coastal current in the inner part of the Gulf of Taranto, located in the Ionian Sea (Southern Italy), including both the Mar Grande and Mar Piccolo basins. To this aim, different measuring stations investigated by both a Vessel Mounted Acoustic Doppler Current Profiler (VM-ADCP) and a bottom fixed ADCP were taken into consideration. Two surveys were carried out in the target area on 29.12.2006 and on 11.06.2007 by the research unit of the Technical University of Bari (DICATECh Department), using a VM-ADCP to acquire the three velocity components along the water column in selected stationing points. The measurements were taken in shallow waters, under non-breaking wave conditions, offshore the surf zone. Due to the recording frequency of the instrument time-averaged vertical velocity profiles could be evaluated in these measuring stations. Water temperature and salinity were also measured at the same time and locations by means of a CTD recorder. A rigidly mounted ADCP, located on the seabed in the North-Eastern area of the Mar Grande basin, provided current data relative to the period 10–20 February 2014. Set to acquire the three velocity components with higher frequency with respect to the VM-ADCP, it allowed us to estimate the turbulent quantities such as Reynolds stresses and turbulent kinetic energy by means of the variance method.Therefore, the present research is made up of two parts. The first part examines the current pattern measured by the VM-ADCP and verifies that, for each station, the classical log law reproduces well the vertical profile of the experimental streamwise velocities extending beyond its typical limit of validity up to the surface i.e. reaching great heights above the sea bed. This behavior is quite new and not always to be expected, being generally limited to boundary layers. It has been convincingly observed in only few limited experimental works. In the present study this occurred when two conditions were met: (i) the flow was mainly unidirectional along the vertical; (ii) the interested layer was non-stratified.The second part of the research studies the turbulent statistics derived from the beam signals of the fixed ADCP by means of the variance method. This technique had the advantage of being able to measure the time evolution of the turbulent mixing throughout the entire water column, thus making it possible to perform a detailed study on momentum transfer and turbulence. The deduced vertical profiles of the Reynolds stresses and of the turbulent kinetic energy TKE showed an increasing trend toward the surface, in agreement with previous results in literature.New data-sets of mean velocities and shear stresses, coming from field measurements, are always needed. In fact they represent the first step to derive reliable reference values of coefficients and parameters for the implementation and calibration of the used mathematical hydrodynamic models.Consequently, an effort was made to evaluate consistent bottom drag and wind drag coefficients, on the basis of the calculated bottom and surface shear stresses, respectively.

The US Navy Coupled Ocean-Wave Prediction System

A new coupled ocean-wave model has been developed and tested as a new component of the Coupled Ocean/Atmosphere Mesoscale Prediction System (COAMPS(circle)). The modeling system is comprised of the Simulating WAves Nearshore (SWAN) wave model and the Navy Coastal Ocean Model (NCOM). The models are two-way coupled using the Earth System Modeling Framework (ESMF). The ocean model has been modified to incorporate the effect of the Stokes drift current, wave radiation stresses due to horizontal gradients of the momentum flux of surface waves, enhancement of bottom drag in shallow water, and enhanced vertical mixing due to Langmuir turbulence. The wave model ingests surface currents (wave-current interaction) and water levels. The system is designed to support the Navy's ocean forecast requirements for regional and coastal domains. Validation studies for the Florida Straits and Virginia coastal area are presented. The system will run at the Naval Oceanographic Office and at the Fleet Numerical Meteorology and Oceanography Center.

Inferring deep ocean tidal energy dissipation from the global high‐resolution data‐assimilative HAMTIDE model

AbstractEnergy dissipation rates of eight major semidiurnal and diurnal tidal constituents are inferred using a barotropic data assimilative tide model with 7.5' spatial resolution. Dynamical residuals and dynamical residual power, estimated through the assimilation procedure as a correction for model uncertainties, constitute an essential contribution to deep‐ocean and shallow‐seas dissipation rates. Resulting total dissipation rates amount to 3.54 TW, of which 2.44 TW (69%) are accounted for by the component alone. Concentrating on the deep ocean (> 1000 m water depth), the dissipation by all eight constituents amounts to 1.42 TW, and 0.93 TW just for the component. These results are higher by 19% and 38% than dissipation rates estimated by Egbert and Ray (2003), respectively. Of the globally dissipated energy, 1.24 TW are estimated to arise from bottom drag and eddy turbulence, 1.20 TW from residual power. For just the deep ocean, respective numbers amount to 0.10 TW for bottom drag and eddy turbulence, 1.07 TW for barotropic‐to‐baroclinic energy conversion due to the internal wave drag. Interpreting negative residual power −0.24 TW as a potential tidal energy source, a net surface‐to‐internal tide energy conversion would amount to 0.83 TW.

Nonlinear Equilibration of Baroclinic Instability: The Growth Rate Balance Model

Abstract A theoretical model is developed, which attempts to predict the lateral transport by mesoscale variability, generated and maintained by baroclinic instability of large-scale flows. The authors are particularly concerned by the role of secondary instabilities of primary baroclinically unstable modes in the saturation of their linear growth. Theory assumes that the fully developed equilibrium state is characterized by the comparable growth rates of primary and secondary instabilities. This assumption makes it possible to formulate an efficient algorithm for evaluating the equilibrium magnitude of mesoscale eddies as a function of the background parameters: vertical shear, stratification, beta effect, and bottom drag. The proposed technique is applied to two classical models of baroclinic instability—the Phillips two-layer model and the linearly stratified Eady model. Theory predicts that the eddy-driven lateral mixing rapidly intensifies with increasing shear and weakens when the beta effect is increased. The eddy transport is also sensitive to the stratification pattern, decreasing as the ratio of upper/lower layer depths in the Phillips model is decreased below unity. Theory is successfully tested by a series of direct numerical simulations that span a wide parameter range relevant for typical large-scale currents in the ocean. The spontaneous emergence of large-scale patterns induced by mesoscale variability, and their role in the cross-flow eddy transport, is examined using a suite of numerical simulations.

Energy Fluxes in the Quasigeostrophic Double Gyre Problem

AbstractThe classic baroclinic, wind-driven, double gyre problem is considered over a range of deformation radii, wind stress amplitudes, and bottom friction coefficients with the aim of better understanding the transfer of energy across scales. In this β-plane basin setting, significant differences are found with respect to classic studies of geostrophic turbulence, which generally assume zonal periodicity and for which the β term does not play a direct role in the energy transfers. In a basin geometry, the β term can play a direct role in the transfers; for example, it can be the dominant term allowing for energy transfer between the basin scale and the baroclinic mesoscale. It is also found that barotropization of baroclinic energy forces the barotropic mode near scales at which bottom drag damps this mode. Associated with this, the barotropic, nonlinear, inverse energy cascade does not extend between mesoscale injection and large-scale dissipation wavenumbers, as is often assumed. Instead, it is part of a “double cascade” of barotropic energy in which the nonlinear inverse cascade is nearly offset by a forward cascade associated with the β term. This is particularly evident in weak bottom drag simulations, for which a time eddy-mean decomposition of the flow reveals the double cascade to be associated with the eddy-only terms.

The Dispersal of Dense Water Formed in an Idealized Coastal Polynya on a Shallow Sloping Shelf

Abstract This study examines the dispersal of dense water formed in an idealized coastal polynya on a sloping shelf in the absence of ambient circulation and stratification. Both numerical and laboratory experiments reveal two separate bottom pathways for the dense water: an offshore plume moving downslope into deeper ambient water and a coastal current flowing in the direction of Kelvin wave propagation. Scaling analysis shows that the velocity of the offshore plume is proportional not only to the reduced gravity, bottom slope, and inverse of the Coriolis parameter, but also to the ratio of the dense water depth to total water depth. The dense water coastal current is generated by the along-shelf baroclinic pressure gradient. Its dynamics can be separated into two stages: (i) near the source region, where viscous terms are negligible, its speed is proportional to the reduced gravity wave speed and (ii) in the far field, where bottom drag becomes important and balances the pressure gradient, the velocity is proportional to Hc[g′/(LCd)]1/2 in which Hc is the water depth at the coast, g′ the reduced gravity, Cd the quadratic bottom drag coefficient, and L the along-shelf span of the baroclinic pressure gradient. The velocity scalings are verified using numerical and laboratory sensitivity experiments. The numerical simulations suggest that only 3%–23% of the dense water enters the coastal pathway, and the percentage depends highly on the ratio of the velocities of the offshore and coastal plumes. This makes the velocity ratio potentially useful for observational studies to assess the amount of dense water formed in coastal polynyas.

Research of the Influential Factors on the Simulation of Storm Surge in the Bohai Sea

A hindcast of typical extratropical storm surge occurring in the Bohai Sea in Oct. 2003 is performed using a three-dimensional storm surge model system based on Finite-Volume Coastal Ocean Model (FVCOM). The surface winds are obtained from the WRF data set. Some preliminary sensitivity studies of the influential factors affecting the storm surge simulation in the Bohai Sea are conducted with the high revolution numerical model of storm surge. The factors of tide-surge interaction, the wind stress, the water depth, the bottom drag coefficient and the critical depth in the model are studied. After considering the tide-wind interaction and the severe wind, the most important influential factor affecting the storm surge in the Bohai Sea is the bottom drag coefficient. These sensitivity studies indicate that the storm surge simulations depend critically on the parameterizations. Hence additional experimental guidance is required on the bottom drag coefficient. This study is useful for the storm surge simulation in order to select the proper parameter to make possible a good conservation behavior of the storm surge model.

Improvements in LICOM2. Part I: Vertical Mixing

Abstract Better computational stability is achieved in an improved version of the National Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics (LASG)/Institute of Atmospheric Physics (IAP) Climate Ocean Model, version 2 (LICOM2, the standard version), after improvements to the implementations of the vertical mixing, mesoscale eddy parameterization, and bottom drag schemes. The large warm biases of LICOM2 in the western Pacific Ocean and eastern Indian Ocean warm pool and on the east coast of the Pacific Ocean are significantly improved. The salinity bias in the tropical Pacific Ocean related to the warm bias of the warm pool is also alleviated. The simulation of the Atlantic meridional overturning circulation is improved because of enhanced vertical mixing in the high latitudes of the North Atlantic Ocean. The new version also presents a stronger Deacon cell, and thus a more powerful Antarctic Circumpolar Current that is closer to the observation, due to weaker southward mesoscale eddy transport in the Southern Ocean.

Streamwise velocity profiles in coastal currents

The ability to model marine currents can be a powerful device for many planning activities, for which the knowledge of the velocity field is of pivotal importance, such as the evaluation of current-induced loading on maritime structures or the diffusion and dispersion of polluted flow discharges. Observations of time-averaged velocity profiles, taken with a vessel mounted acoustic Doppler current profiler during a monitoring survey program in the seas of Southern Italy, are analysed in this paper. The measurements were taken under non-breaking conditions, offshore the surf zone, with the aim of reproducing the vertical trends of the streamwise velocity by means of standard theoretical laws. To evaluate also the possible influence of stratification on the current velocity profile shape, together with velocity measurements water temperature and salinity were also measured at the same time and locations, by means of a CTD recorder. The examined surveys referred to different time periods and sites, to guarantee a general validity of deductions. On the basis of the experiments, we verified the actual existence of a log-layer and concluded that the upper limit of the region in which the log law is applicable extends well beyond the inner region. Moreover, the deviations of the measured velocity from the logarithmic profiles above the height of the log layer is consistent with the effects of stratification. The parameters of the log law were estimated, depending on both flow dynamics and stratification in the target area. As a second step, in the most superficial and stratified layer, the velocity profiles were modelled by means of a power law, which fitted the measured data well. According to previous studies, the power law parameters result Reynolds number dependent by means of a new proposed formulation. Finally, the bottom stress and the bottom drag coefficient were investigated.

The influence of channel deepening on estuarine turbidity levels and dynamics, as exemplified by the Ems estuary

Active deepening of tidal channels usually results in the alteration of the vertical and the horizontal tide. This may lead to concurrent significant increases in mean suspended matter concentrations (SPM) in coastal plain estuaries, the turbidity maximum (ETM) included. This is exemplified by an extensive analysis of the Ems estuary, a prototypical heavily stressed estuary in the Dutch-German border area. Measurements show that the SPM concentrations in the lower reaches of the estuary have increased an average of 2- to 3-fold between 1954 and 2005, with a 10-fold increase observed in the upper estuary (tidal river). Longitudinal profiles of surface SPM demonstrate that the ETM has moved upstream by up to 25 km and has broadened into a zone 30 km in length which extends into the freshwater tidal river. On an annual scale, variations in freshwater discharge significantly influence the formation and breakdown of the ETM: during low river discharge the ETM approaches equilibrium over 2–3 months, whilst elevated river discharges relocate the ETM downstream over several weeks.An exploratory, semi-analytical model is calibrated to simulate the equilibrium SPM distribution in the upper estuary during five time periods from 1965 to 2005, using archival bathymetric and tidal data. Results suggest that the deepening of tidal channels and a reduction in hydraulic drag have most likely resulted in a landward shift of the SPM trapping location. The measured increase in SPM concentrations and the development of fluid mud around the 1990s likely contributed to reduced mixing and bottom drag, creating a feedback loop that further altered tidal and SPM dynamics. It is argued that the removal of some non-erodible (consolidated) layers in the lower reaches of the estuary has created new internal sediment sources that may be responsible for feeding the observed high SPM concentrations, rather than increased sediment input from the boundaries. All findings are based on and supported by measured short-term seasonal fluctuations, as well as long-term developments of yearly averaged concentrations in the longitudinal SPM distribution.

Improvements in LICOM2. Part II: Arctic Circulation

Abstract A known issue of the National Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics/Institute of Atmospheric Physics Climate Ocean Model, version 2 (LICOM2, the standard version) is the use of an artificial island in the Arctic Ocean. The computational instability in the polar region seriously influences the model performance in terms of the Arctic circulation. The above-mentioned instability was originally attributed to the converging zonal grids in the polar region. However, this study finds that better computational stability could be achieved in an improved version of LICOM2 (i.e., LICOM2_imp) after four improvements on implementations of the vertical mixing, mesoscale eddy parameterization, and bottom drag schemes. LICOM2_imp is then able to reduce the aforesaid artificial island to a point (i.e., the North Pole). Two experiments of 650-yr integration by LICOM2_imp are carried out using different bathymetries: Exp IMPV0 with the artificial island (88°–90°N) and IMPV1 with only the single pole. The focus of this paper is on the Arctic circulation. Exp IMPV1 gives a more reasonable distribution of salinity and temperature in the Arctic Ocean, a more accurate location of the center of the Beaufort Gyre, and a better net volume flux of the transpolar drift. With more realistic bathymetry in the Arctic Ocean, the biases of net volume fluxes across the Fram Strait, Barents Sea Opening, and Barents Sea Exit are reduced from 1.71 to 1.56, from 0.23 to 0.10, and from 0.71 to 0.45 Sv (1 Sv ≡ 106 m3 s−1), respectively, closer to the observations. The large biases of the net volume fluxes at the Fram Strait in both experiments may be attributed to the closed Nares Strait and other straits/channels in the Canadian Arctic Archipelago.

Dynamics of the Leeuwin Current: Part 2. Impacts of mixing, friction, and advection on a buoyancy-driven eastern boundary current over a shelf

The boundary currents over the Western Australian continental shelf and slope consist of the poleward flowing Leeuwin Current (LC) and the equatorward flowing Leeuwin Undercurrent (LUC). Key properties of the LC are its poleward strengthening, deepening to the south, and shelfbreak intensification. The alongshore flow reverses direction below about 300m, forming the LUC at greater depths. To investigate the processes that cause these features, we obtain solutions to an idealized, regional ocean model of the South Indian Ocean. Solutions are forced by relaxing surface density to a prescribed, meridionally varying density profile ρ*(y) with a timescale of δt. In addition, vertical diffusion is intensified near the ocean surface. This diffusion establishes the minimum thickness over which density is well-mixed. We define this thickness as the “upper layer”. Solutions are obtained with and without a continental shelf and slope off Western Australia and for a range of values of δt and mixing parameters. Within this upper layer, there is a meridional density gradient that balances a near-surface, eastward geostrophic flow. The eastward current downwells near the eastern boundary, leading to westward flow at depth. The upper layer's meridional structure and zonal currents crucially depend on coastal processes, including the presence of topography near the eastern boundary. Kelvin waves inhibit the upper layer from deepening at the coast. Rossby waves propagate the coastal density structure offshore, hence modifying the interior currents. A comparison of the solutions with or without a continental shelf and slope demonstrate that topographic trapping of Rossby waves is a necessary process for maintaining realistic eastern boundary current speeds. Significant poleward speeds occur only onshore of where the upper layer intersects the slope, that is, at a grounding line. Its poleward transport increases when surface-enhanced vertical mixing is applied over a greater depth. When the timescale δt is sufficiently short, the poleward current is nearly barotropic. The current's spatial structure over the shelf is controlled by horizontal mixing, having the structure of a Munk layer. Increasing vertical diffusion deepens the upper layer thickness and strengthens the alongshore current speed. Bottom drag leads to an offshore flow along the bottom, reducing the net onshore transport and weakening the current's poleward acceleration. When δt is long, poleward advection of buoyancy forms a density front near the shelf break, intensifying poleward speeds near the surface. With bottom drag, a bottom Ekman flow advects density offshore, shifting the jet core offshore of the shelf break. The resulting cross-shelf density gradient reverses the meridional current's direction at depth, leading to an equatorward undercurrent.

Tidal heating in icy satellite oceans

Tidal heating plays a significant role in the evolution of many satellites in the outer Solar System; however, it is unclear whether tidal dissipation in a global liquid ocean can represent a significant additional heat source. Tyler (Tyler, R.H. [2008]. Nature 456, 770-772; Tyler, R.H. [2009]. Geophys. Res. Lett. 36, doi:10.1029/2009GL038300) suggested that obliquity tides could drive large-scale flow in the oceans of Europa and Enceladus, leading to significant heating. A critical unknown in this previous work is what the tidal quality factor, Q, of such an ocean should be. The corresponding tidal dissipation spans orders of magnitude depending on the value of Q assumed.To address this issue we adopt an approach employed in terrestrial ocean modeling, where a significant portion of tidal dissipation arises due to bottom drag, with the drag coefficient O (0.001) being relatively well-established. From numerical solutions to the shallow-water equations including nonlinear bottom drag, we obtain scalings for the equivalent value of Q as a function of this drag coefficient. In addition, we provide new scaling relations appropriate for the inclusion of ocean tidal heating in thermal–orbital evolution models. Our approach is appropriate for situations in which the ocean bottom topography is much smaller than the ocean thickness.Using these novel scalings, we calculate the ocean contribution to the overall thermal energy budgets for many of the outer Solar System satellites. Although uncertainties such as ocean thickness and satellite obliquity remain, we find that for most satellites it is unlikely that ocean tidal dissipation is important when compared to either radiogenic or solid-body tidal heating. Of known satellites, Triton is the most likely icy satellite to have ocean tidal heating play a role in its present day thermal budget and long-term thermal evolution.

Kelvin waves in Lake Geneva

The passage of Kelvin waves in Lake Geneva after strong wind events was experimentally investigated in 1987 and 2002 using thermistor chains, current meters and Acoustic Doppler Current Profilers (ADCP) probing the whole water column, including the bottom boundary layer. Characteristics of these internal waves such as period, amplitude, exponential decay with distance from the shore and damping were determined. A significant increase of shear was observed in the thermocline region during the passage of a Kelvin wave crest. The passage of a Kelvin wave crest also led to a well-mixed bottom boundary layer characterized by a logarithmic velocity profile, complying with the so-called “law of the wall” up to an average height of 11m. A bottom drag coefficient of 2.5×10−3 was determined from our measurements. We estimated that ~70% of the Kelvin wave energy is dissipated in the bottom boundary layer. This study shows that the passage of Kelvin waves energizes the thermocline and near bed region and that this process is of fundamental importance in the dynamics of the nearshore region of mid-latitude large lakes.

Impact of parameterized lee wave drag on the energy budget of an eddying global ocean model

The impact of parameterized topographic internal lee wave drag on the input and output terms in the total mechanical energy budget of a hybrid coordinate high-resolution global ocean general circulation model forced by winds and air-sea buoyancy fluxes is examined here. Wave drag, which parameterizes the generation of internal lee waves arising from geostrophic flow impinging upon rough topography, is included in the prognostic model, ensuring that abyssal currents and stratification in the model are affected by the wave drag.An inline mechanical (kinetic plus gravitational potential) energy budget including four dissipative terms (parameterized topographic internal lee wave drag, quadratic bottom boundary layer drag, vertical eddy viscosity, and horizontal eddy viscosity) demonstrates that wave drag dissipates less energy in the model than a diagnostic (offline) estimate would suggest, due to reductions in both the abyssal currents and stratification. The equator experiences the largest reduction in energy dissipation associated with wave drag in inline versus offline estimates. Quadratic bottom drag is the energy sink most affected globally by the presence of wave drag in the model; other energy sinks are substantially affected locally, but not in their global integrals. It is suggested that wave drag cannot be mimicked by artificially increasing the quadratic bottom drag because the energy dissipation rates associated with bottom drag are not spatially correlated with those associated with wave drag where the latter are small. Additionally, in contrast to bottom drag, wave drag is a non-local energy sink.All four aforementioned dissipative terms contribute substantially to the total energy dissipation rate of about one terawatt. The partial time derivative of potential energy (non-zero since the isopycnal depths have a long adjustment time), the surface advective fluxes of potential energy, the rate of change of potential energy due to diffusive mass fluxes, and the conversion between internal energy and potential energy also play a non-negligible role in the total mechanical energy budget. Reasons for the <10% total mechanical energy budget imbalance are discussed.