Aspects of Deep Ocean Mixing

The turbulent motions responsible for ocean mixing occur on scales much smaller than those resolved in numerical simulations of oceanic flows. Great progress has been made in understanding the sources of energy for mixing, the mechanisms, and the rates. On the other hand, we still do not have adequate answers to first order questions such as the extent to which the thermohaline circulation of the ocean, and hence the earth's climate, is sensitive to the present mixing rates in the ocean interior. Internal waves, generated by either wind or flow over topography, appear to be the principle cause of mixing. Mean and eddy flows over topography generate internal lee waves, while tidal flows over topography generate internal tides. The relative importance of these different internal wave sources is unknown. There are also great uncertainties about the spatial and temporal variation of mixing. Calculations of internal tide generation are becoming increasingly robust, but we do not know enough about the subsequent behavior of internal tides and their eventual breakdown into turbulence. It does seem, however, that most internal tide energy flux is radiated away from generation sites as low modes that propagate over basin scales. The mechanisms of wave-wave interaction and topographic scattering both act to transfer wave energy from low modes to smaller dissipative scales. This revised version was published online in August 2006 with corrections to the Cover Date.     

底地形变化对内潮产生影响的数值研究

本文结合南沙群岛海域出现内潮的水文背景,建立了一个两层数值模式,并通过数值试验来探讨由正压潮波作用下的内潮产生机制。结果表明：底形效庆是促使内潮产生的重要因子;内潮心要在大陆坡产生,然后分别沿着大陆架和深海平原两个方向传播;内潮斜压流速的量级可与正压流速的相比拟。     

基于数值模式评估细尺度参数化方案在南大洋背风波生成源地的适用性

验证基于GM(Garret-Munk)大洋内波普适谱的细尺度参数化方案在不同海域的适用性,对于湍流混合研究来说非常重要。包含背景GM内波场的高分辨率数值模式被用于评估细尺度参数化方案在背风波生成源地处的适用性。细尺度参数化方案主要包括基于剪切的G89 (Gregg 1989)方案、基于应变的W93 (Wijesekera 1993)方案、基于剪切和应变的GHP (Gregg-Henyey-Polzin)方案以及对GHP方案中的频率矫正项作出变换的IH (Ijichi-Hibiya)方案。计算结果显示,背风波的生成伴随着海底上方近惯性内波的增强,使得内波场的动能与势能的比值相较于GM内波场偏大。在这种情况下,基于剪切的G89方案会因为高估内波场的总能量而高估耗散率。反之,基于应变的W93方案会因为低估内波场的总能量而低估耗散率。计算结果还显示,已经考虑了内波谱变形的GHP方案仍然会高估耗散率,但IH方案能比较准确地估算耗散率。     

Transmission of wave energy through an offshore wind turbine farm

The transmission of wave energy passing an offshore wind farm is studied. Three effects that can change the wave field are analysed, which is the A) energy dissipation due to drag resistance, B) wave reflection/diffraction from structures, and C) the effect of a modified wind field inside and on the lee side of the wind farm. The drag dissipation, A), is quantified by a quadratic resistance law. The effect of B) is parameterised based on 1st order potential theory. A method to find the amount of reflected and transmitted wave energy is developed based on the panel method WAMIT™ and a radiation condition at infinity. From airborne and Satellite SAR (Synthetic Aperture Radar) a model has been derived for the change of the water surface friction C) inside and on the lee side of the offshore wind farm. The effects have been implemented in a spectral wind wave model, MIKE21 SW, and a parametric study to compare the 3 different processes has been carried out. The method to study reflection/diffraction can be used for any type of offshore structure, vessel or a number of structures, as long as the assumptions for the use of potential wave theory are valid, and the effect of the modified wind field on the water surface friction is known.     

Propagation and amplitude decay mechanisms of internal solitary waves

In this paper, a modified dynamic coherent eddy model (DCEM) of large eddy simulation is applied to study internal solitary waves in a numerical flume. The model was verified by physical experiment and applied to investigate the potential influence factors on internal wave amplitude. In addition, we discussed the energy loss of internal solitary wave as well as hydrodynamics in the propagation. The results of our study show that (1) Step-depth is the most sensitive factor on wave amplitude for the “step-pool” internal wave generation method and the wave amplitudes obey a linear increase with step depth, and the increase rate is about 0.4. (2) Wave energy loss obeys a linear decrease with the propagation distance and its loss rate of large amplitude waves is smaller than that of small amplitude waves. (3) Loss of kinetic energy in wave valley is larger than that near the interface due to relative high fluctuating frequency. (4) Discovered boundary jet-flow can intensify the bottom shear, which might be one of the mechanisms of substance transportation, and the boundary layers of jet flows are easily influenced by the adjacent waves.     

Energy balance of wind waves as a function of the bottom friction formulation

Four different expressions for wave energy dissipation by bottom friction are intercompared. For this purpose, the SWAN wave model and the wave data set of Lake George (Australia) are used. Three formulations are already present in SWAN (ver. 40.01): the JONSWAP expression, the drag law friction model of Collins and the eddy–viscosity model of Madsen. The eddy–viscosity model of Weber was incorporated into the SWAN code. Using Collins' and Weber's expressions, the depth- and fetch-limited wave growth laws obtained in the nearly idealized situation of Lake George can be reproduced. The wave model has shown the best performance using the formulation of Weber. This formula has some advantages over the other formulations. The expression is based on theoretical and physical principles. The wave height and the peak frequency obtained from the SWAN runs using Weber's bottom friction expression are more consistent with the measurements. The formula of Weber should therefore be preferred when modelling waves in very shallow water.     

The influence of tidal hydrodynamic conditions on the generation of lee waves at the main sill of the Strait of Gibraltar

The main sill of the Strait of Gibraltar (Camarinal Sill) is an area of very energetic internal wave activity. The highest amplitude internal wave is the well-known internal bore, generated at critical conditions over Camarinal Sill. A very energetic lee wave has recently been found and reported. This occurs in neap tides when favorable combination of the stratification, vertical profile of horizontal background velocity, and bottom topography determines its generation. When the lee wave is developed the manifestation of high-amplitude internal waves is observed at the sea surface as high-frequency chaotic oscillations, named boiling waters. We analyze the generation of the lee wave over the main sill of Gibraltar Strait on the basis of the data from a ship mounted ADCP, multi-probe CTD data taken during a survey carried out in November 1998, and the numerical solution of the Taylor–Goldstein equation for the prevailing hydraulic conditions previous to its generation. Stratification is computed from CTD data, and the tidal current prediction is made from the 2 years of ADCP hourly data at Camarinal Sill gathered during the Gibraltar Experiment 94-96. The main characteristic is that they happen during neap tides, and their magnitude is comparable to the internal bore generated during spring tides. The classical internal bore and the lee waves are different phenomena, and the presence of the latter is an indicator of minimum flow over Camarinal Sill. A prediction model for lee waves based on the tidal hydrodynamic conditions is also developed.     

Impacts of frontal stability and topography on cross-shelf exchange in the Northern Gulf of Mexico

The shelfbreak wintertime thermal front in the Northeastern Gulf of Mexico often exhibits meandering, eddy formation and warm-water intrusion. A high level of frontal variability plays an essential role in exchange processes across the shelf. This study examines the impacts of local frontal instability and bottom topography on turbulent heat exchange across the front using the results of two numerical models. Analysis of a series of numerical experiments reveals that the flow is baroclinically unstable. Predicted frontal instability contributes significantly to cross-frontal exchange and accounts for about 35% of the total eddy heat flux. Onshore eddy heat flux has the highest intensity at the frontal position. In addition, eddy activity and heat flux are sensitive to variation of bottom topography. For topographic features and frontal characteristics that are typical of the area, bottom steepness enhances the flux and is nearly proportional to the cross-frontal heat exchange. The study attempts to explain physical mechanisms that drive frontal circulation in the area and to quantify heat transport across the shelf. Estimated heat fluxes can provide important information for climate and ecosystem modeling of the Mississippi Bight.     

Energetics of lateral eddy diffusion/advection：Part Ⅰ. Thermodynamics and energetics of vertical eddy diffusion

Two important nonlinear properties of seawater thermodynamics linked to changes of water density, cabbeling and elasticity(compressibility), are discussed. Eddy diffusion and advection lead to changes in density; as a result, gravitational potential energy of the system is changed. Therefore, cabbeling and elasticity play key roles in the energetics of lateral eddy diffusion and advection. Vertical eddy diffusion is one of the key elements in the mechanical energy balance of the global oceans. Vertical eddy diffusion can be conceptually separated into two steps: stirring and subscale diffusion. Vertical eddy stirring pushes cold/dense water upward and warm/light water downward; thus, gravitational potential energy is increased. During the second steps, water masses from different places mix through subscale diffusion, and water density is increased due to cabbeling. Using WOA01 climatology and assuming the vertical eddy diffusivity is equal to a constant value of 2×103 Pa2/s, the total amount of gravitational potential energy increase due to vertical stirring in the world oceans is estimated at 263 GW. Cabbeling associated with vertical subscale diffusion is a sink of gravitational potential energy, and the total value of energy lost is estimated at 73 GW. Therefore, the net source of gravitational potential energy due to vertical eddy diffusion for the world oceans is estimated at 189 GW.     

北极薄冰-煎饼冰区域中不同重力波驱动形成海流的敏感性分析

A coupled ocean-ice-wave model is used to study ice-edge jet and eddy genesis during surface gravity wave dissipation in a frazil-pancake ice zone. With observational data from the Beaufort Sea, possible wave dissipation processes are evaluated using sensitivity experiments. As wave energy dissipated, energy was transferred into ice floe through radiation stress. Later, energy was in turn transferred into current through ocean-ice interfacial stress. Since most of the wave energy is dissipated at the ice edge, ice-edge jets, which contained strong horizontal shear, appeared both in the ice zone and the ocean. Meanwhile, the wave propagation direction determines the velocity partition in the along-ice-edge and cross-ice-edge directions, which in turn determines the strength of the along-ice-edge jet and cross-ice-edge velocity. The momentum applied in the along-ice-edge(cross-ice-edge)direction increased(decreased) with larger incident angle, which is favorable condition for producing stronger mesoscale eddies, vice versa. The dissipation rate increases(decreases) with larger(smaller) wavenumber, which enhances(reduces) the jet strength and the strength of the mesoscale eddy. The strong along-ice-edge jet may extend to a deep layer(> 200 m). If the water depth is too shallow(e.g., 80 m), the jet may be largely dampened by bottom drag, and no visible mesoscale eddies are found. The results suggest that the bathymetry and incident wavenumber(magnitude and propagation direction) are important for wave-driven current and mesoscale eddy genesis.     

The effect of dynamic–thermodynamic icebergs on the Southern Ocean climate in a three-dimensional model

Melting icebergs are a mobile source of fresh water as well as a sink of latent heat. In most global climate models, the spatio-temporal redistribution of fresh water and latent heat fluxes related to icebergs is parameterized by an instantaneous more or less arbitrary flux distribution over some parts of the oceans. It is uncertain if such a parameterization provides a realistic representation of the role of icebergs in the coupled climate system. However, icebergs could have a significant climate role, in particular during past abrupt climate change events which have been associated with armada’s of icebergs. We therefore present the interactive coupling of a global climate model to a dynamic thermodynamic iceberg model, leading to a more plausible spatio-temporal redistribution of fresh water and heat fluxes. We show first that our model is able to reproduce a reasonable iceberg distribution in both hemispheres when compared to recent data. Second, in a series of sensitivity experiments we explore cooling and freshening effects of dynamical icebergs on the upper Southern Ocean and we compare these dynamic iceberg results to the effects of an equivalent parameterized iceberg flux.In our model without interactive icebergs, the parameterized fluxes are distributed homogeneously South of 55°S, whereas dynamic icebergs are found to be concentrated closer to shore except for a plume of icebergs floating North–East from the tip of the Antarctic Peninsula. Compared to homogeneous fluxes, the dynamic icebergs lead to a 10% greater net production of Antarctic bottom water (AABW). This increased bottom water production involves open ocean convection, which is enhanced by a less efficient stratification of the ocean when comparing to a homogeneous flux distribution.Icebergs facilitate the formation of sea-ice. In the sensitivity experiments, both the fresh water and the cooling flux lead to a significant increase in sea-ice area of 12% and 6%, respectively, directly affecting the highly coupled and interactive air/sea/ice system. The consequences are most pronounced along the sea-ice edge, where this sea-ice facilitation has the greatest potential to affect ocean stratification, for example by heat insulation and wind shielding, which further amplifies the cooling and freshening of the surface waters.     

On the interaction of a solitary wave and a submerged dike

The unsteady, two-dimensional Navier–Stokes equations and the exact free surface boundary conditions were solved to study the interaction of a solitary wave and a submerged dike. A piston-type wavemaker was set up in the computational domain to produce the incident solitary waves. The incident wave and the associated boundary layer flow in a wave tank with a flat bed were compared with the analytical solutions to verify the accuracy of this numerical scheme. Effects of the incident wave height and the size of the dike on the wave transformation, the flow fields, and the drag forces on the dike were discussed. Our numerical results showed that even though the induced local shear stress on the top surface of the dike is large at some particular locations, the resultant pressure drag is much larger than the friction drag. The primary vortex generated at the lee side of the dike and the secondary vortex at the right toe of the dike may scour the bottom and cause a severe problem for the dike.     

Numerical modelling of the propagation of tsunami waves in the crimean peninsula shelf zone

The paper analyses the effect of non-linearity and bottom friction on propagation of tsunami-type surface waves from the abyssal part of the Black Sea towards the shelf zone. The study relies, on numerical solution of unidimensional non-linear equations for long waves, using the finite-difference technique. Numerical experiments have been conducted for the bottom profile continental slope and shelf, with the full wave reflection being prescribed at a 10-m depth contour. It has been shown that the major role in transforming solitary waves belongs to non-linear topographic factors rather than to dissipation. The reflected wave has been found to be non-linearly distorted, and wave heights in the Black Sea coastal zone have been found to increase by many times. Translated by Vladimir A. Puchkin.     

Concurrent simulation of the eddying general circulation and tides in a global ocean model

This paper presents a five-year global simulation of HYCOM, the HYbrid Coordinate Ocean Model, that simultaneously resolves the eddying general circulation, barotropic tides, and baroclinic tides with 32 layers in the vertical direction and 1/12.5° (equatorial) horizontal grid spacing. A parameterized topographic wave drag is inserted into the model and tuned so that the surface tidal elevations are of comparable accuracy to those in optimally tuned forward tide models used in previous studies. The model captures 93% of the open-ocean sea-surface height variance of the eight largest tidal constituents, as recorded by a standard set of 102 pelagic tide gauges spread around the World Ocean. In order to minimize the impact of the wave drag on non-tidal motions, the model utilizes a running 25-h average to approximately separate tidal and non-tidal components of the near-bottom flow. In contrast to earlier high-resolution global baroclinic tide simulations, which utilized tidal forcing only, the simulation presented here has a horizontally non-uniform stratification, supported by the wind- and buoyancy forcing. The horizontally varying stratification affects the baroclinic tides in high latitudes to first order. The magnitude of the internal tide perturbations to sea surface elevation amplitude and phase in a large box surrounding Hawai’i is quite similar to that observed in satellite altimeter data, although the exact locations of peaks and troughs in the modeled perturbations differ from those in the observed perturbations.     

Computations of the energy flux to mixing processes via baroclinic wave drag on barotropic tides

The geographical distribution of barotropic to baroclinic transfer of tidal energy by baroclinic wave drag in the abyssal ocean is estimated. Using tidal velocities from a state-of-the-art numerical tidal model, the total loss of barotropic tidal energy in the deep ocean (between 70°S and 70°N and at depths greater than 1000 m) is estimated to be about 0.7 TW (M₂) corresponding to a mean value of the energy flux (e) of 2.4×10⁻³ W/m². The distribution of e is however highly skewed with a median of about 10⁻⁶ W/m². Only 10% of the area is responsible for more than 97% of the total energy transfer.To assess the possible influence of the relatively coarse bathymetry representation upon the present estimate, complementary calculations using better resolved sea floor topography are carried out over a control area around the Hawaiian Ridge. There are no major differences between the results achieved using the two different bathymetry databases. Fluxes of about 16 GW or 6×10⁻³ W/m² are computed in both cases, and the main contributions to the total fluxes originate in the same range of e-values and cover equally large parts of the total area.It is not clear whether the present model is valid at flat or subcritical bottom slopes. However, for the Hawaiian region, only 2% of the total energy flux as calculated in the present study originates in areas of critical and subcritical slopes.     

内潮耗散与自吸-负荷潮对南海潮波影响的数值研究

利用非结构三角形网格的FVCOM海洋数值模式,在其传统二维潮波方程中加入参数化的内潮耗散项和自吸-负荷潮项,计算了南海及其周边海域的M_2、S_2、K_1和O_1分潮的分布。与实测值的比较表明,引入这两项对模拟准确度的提高有明显效果。根据模式结果本文计算分析了研究海域的潮能输入和耗散。能量输入计算表明,能通量是潮能输入的最主要构成部分,通过吕宋海峡断面进入南海的M_2和K_1分潮能通量分别为38和29GW;半日周期的自吸-负荷潮能量输入以负值居多,而全日周期的自吸-负荷潮能量输入以正值居多,因而自吸-负荷潮减弱了南海的半日潮,并加强了南海的全日潮。引潮力的作用也减弱了半日潮而加强了全日潮,但其作用要小于自吸-负荷潮。潮能耗散的分析显示底摩擦耗散在沿岸浅水区域起主导作用,内潮耗散则主要发生在深水区域。内潮耗散的最大值出现在吕宋海峡,且位于南海之外的海峡东部的耗散量大于位于南海之内的海峡西部的耗散量。对M_2和K_1分潮吕宋海峡的内潮耗散总值分别达到16和23GW。     

Numerical study of tide-induced mixing over rough bathymetry in the abyssal ocean

Locally enhanced turbulent mixing over rough bottom bathymetry is one of the candidates that might make up for the lack of diapycnal diffusivity in maintaining the global overturning circulation. In the present study, using a two-dimensional vertical numerical model for the Brazil Basin, we numerically examine the intensity and vertical structure of tide-induced mixing over multi-beam bottom bathymetry via the comparison with those over somewhat smoothed bottom bathymetry. Note that even this smoothed bottom bathymetry is finer than in commonly used datasets. In comparison to the response over the smoothed bottom bathymetry, energy dissipation rates are enhanced within a few hundred meters over the multi-beam bottom bathymetry. In spite of several limitations of the two-dimensional vertical numerical model, the magnitude and vertical distribution of the calculated dissipation rates agree well with those from microstructure measurements. We find that tidal interaction with fine-scale (≤2 km) bottom bathymetry efficiently generates high wavenumber internal waves, which are subject to local energy dissipation and hence strongly control the abyssal mixing; the most important finding is that the intensity and vertical decay scale of abyssal mixing are in a trade-off relationship with each other, which is not taken into account in the existing parameterizations.     

Bathymetric influence on mean currents in two high-resolution near-global ocean models

The question of whether mean flow generation by eddies interacting with sloping bathymetry significantly influences World Ocean circulation is approached by examining output from two near-global circulation models, OFES and the LANL/NPS POP model, having ∼1/10° lateral resolution. In each of these vigorously eddying models, the mean currents over sloping bathymetry tend preferentially to align with the direction of topographic Rossby wave propagation, in accordance with theories of eddy-topographic interaction. This tendency, which is particularly strong near the ocean bottom and at abyssal depths, prevails both globally and within a variety of circulation regimes including the subpolar and subtropical gyres and the extra-equatorial tropics. By contrast, two coarser (∼1–2°), non-eddying models exhibit flow alignments throughout much of the abyssal ocean that are oppositely directed. This result suggests that eddies play an essential role in determining the direction of mean circulation over slopes, and that non-eddying models could benefit from a parameterization of this effect.     

Vertical momentum transfer by internal waves when eddy viscosity and diffusion are taken into account

Free internal waves are considered in a Boussinesq approximation in the situation when horizontal eddy viscosity and diffusion in a vertically inhomogeneous flow are taken into account. The dispersion relation and wave damping factor are found in a linear approximation. The Stokes drift velocity is determined in the second order of smallness based on the wave amplitude. It has been indicated that the Stokes drift velocity, transverse with respect to the wave propagation direction, differs from zero if the flow-rate transverse component depends on the vertical coordinate. Vertical momentum fluxes differ from zero and can be comparable with or exceed the corresponding turbulent fluxes if eddy viscosity and diffusion are taken into account.     

Numerical Study of a Kyucho and a Bottom Intrusion in the Bungo Channel,Japan: Disturbances Generated by the Kuroshio Small Meanders

The generation and propagation mechanisms of a Kyucho and a bottom intrusion in the Bungo Channel, Japan, have been studied numerically using the hydrostatic primitive equations by assuming density stratification during summer. The experiments are designed to generate a Kuroshio small meander in Hyuga-Nada, which acts as a trigger for these disturbances. After the current speed of the Kuroshio is changed, a small meander is generated. At the head of the small meander, warm Kuroshio water is engulfed, and encounters the southwest coast of Shikoku. However, convergence of heat flux on the bump off Cape Ashizuri suppresses the generation of a warm disturbance, if the current speed is large. As the cold eddy associated with the small meander approaches Cape Ashizuri, the heat flux diverges on the bump. This heat source forces a warm disturbance, which intrudes along the east coast of the Bungo Channel as a baroclinic Kelvin wave (a Kyucho). After the cold eddy passes off Cape Ashizuri, the Kuroshio approaches the bump again. Strong convergence of heat flux then occurs on the bump, which forces a cold disturbance. This disturbance propagates as a topographic Rossby wave along the shelf break at the mouth of the channel. After the topographic wave reaches the west end of the shelf break, it intrudes along the bottom layer of the channel as a density current (a bottom intrusion). These results suggest that a Kyucho and a bottom intrusion are successive events associated with the propagation of the small meander.