Global estimates of wind energy input to subinertial motions in the Ekman-Stokes layer

By incorporating the wave-induced Coriolis-Stokes forcing into the classical Ekman model, the wind energy input to the Ekman-Stokes layer is investigated, with an emphasis on the surface wave effects when the direction of Stokes drift deviates from that of wind stress. Theoretical analysis of the kinetic energy balance of the Ekman-Stokes layer shows that the total wind energy input consists of the direct wind energy input and the wave-induced energy input. Details of the direct wind and wave-induced energy input are discussed. Based on the ECMWF ERA-40 Re-Analysis wind stress and surface wave data, the global total wind energy input to subinertial motions in the Ekman-Stokes layer is estimated at 2.19 TW, including 0.26 TW (12%) wave-induced energy input and 1.93 TW (88%) direct wind energy input. The effect of sea-ice coverage on the energy input to the Ekman-Stokes layer is also considered. It is shown that the global total energy input could be overestimated by 0.08 TW (about 4%) without taking the sea-ice coverage into account.     

Improving the estimate of wind energy input into the Ekman layer within the Antarctic Circumpolar Current

Based on the data and method offered by Liu et al. (2009), the direct wind and Stokes drift-induced energy inputs into the Ekman layer within the Antarctic Circumpolar Current (ACC) area are reestimated since the results of the former have been proved to be underestimated. And the result shows that the total rate of energy input into the Ekman-Stokes layer within the ACC area is 852.41 GW, including 649.75 GW of direct wind energy input (76%) and 202.66 GW of Stoke drift-induced energy input (24%). Total increased energy input, due to wave-induced Coriolis-Stokes forcing added to the classical Ekman model, is 52.05 GW, accounting for 6.5% of the wind energy input into the classical Ekman layer. The long-term variability of direct wind and Stokes drift-induced energy inputs into the Ekman layer within the ACC is also investigated, and the result shows that the Stokes drift hinders the decadal increasing trend of direct wind energy input. Meanwhile, there is a period of 4-5 a in the energy spectrums, as same as the Antarctic circumpolar wave.     

A wave averaged energy equation: Comment on “global estimates of wind energy input to subinertial motions in the Ekman-Stokes layer” by Bin Liu,Kejian Wu and Changlong Guan

In a recent paper, Liu et al. (2007) formulate an expression for how surface gravity waves modify the Ekman layer energy budget. They then diagnose the effect in the world oceans using available data. This comment addresses the formulation of the energy equation that is fundamental to their study.     

基于高分辨率风场的海洋近惯性能通量计算——时空特征及其影响因素

基于高分辨率CFSR(climate forecast system reanalysis)风场资料、气候态海洋混合层厚度资料和卫星高度计海面高度异常资料,本文估计了大气风场向全球海洋混合层的近惯性能通量和近惯性能量输入功率,并探究了混合层厚度、风场时间分辨率、经验衰减系数和中尺度涡旋涡度对近惯性能通量和能量输入功率的影响。浮标实测风场和流速表明,本文所用的风场和阻尼平板模型可用于估计风场向全球海洋的近惯性能通量。本文计算得到的大气向全球海洋输入近惯性能量的功率为0.56TW(1TW=10~(12)W),其中北半球贡献0.22TW,南半球贡献0.34TW。在时间上,风场的近惯性能通量呈现各个半球冬季最强、夏季最弱的特征,这和西风带风场的季节变化有关。在空间上,近惯性能通量的高值海域为南、北半球西风带海洋,尤其是南大洋。混合层厚度和风场空间不均匀性使得西风带近惯性能通量呈现纬向变化,即海盆西部强于海盆东部。风场时间分辨率对近惯性能通量的估计至关重要,低时间分辨率风场对近惯性能通量的低估达到13%—30%。阻尼平板模型中的经验衰减系数对近惯性能通量估计的影响不超过5%。中尺度涡旋涡度仅改变近惯性能通量的空间分布,而对全球近惯性能量输入功率的影响可以忽略。     

Energy budget of surface waves in the global ocean

Mechanical energy input from atmosphere and losses from wave-breaking dissipation of sea surface waves are estimated by a direct scheme. This scheme is based on the integration in the wavenumber space of the wind input and breaking dissipation source functions of the MASNUM wave model. The global amount of wind energy input, averaged in 2005, is about 57 TW, and the wave-breaking dissipation summed in deep-water is about 33 TW, over a half of the wind energy input. The residual may be dissipated by beach processes. Global distributions of the energy input and breaking dissipation concentrate in the westerlies of the Southern Hemisphere.     

Once again: once again—tidal friction

Topex/Poseidon (T/P) altimetry has reopened the problem of how tidal dissipation is to be allocated. There is now general agreement of a M₂ dissipation by 2.5 Terawatts (1 TW = 10¹² W), based on four quite separate astronomic observational programs. Allowing for the bodily tide dissipation of 0.1 TW leaves 2.4 TW for ocean dissipation. The traditional disposal sites since (1920) have been in the turbulent bottom boundary layer (BBL) of marginal seas, and the modern estimate of about 2.1 TW is in this tradition (but the distribution among the shallow seas has changed radically from time to time). Independent estimates of energy flux into the marginal seas are not in good agreement with the BBL estimates.T/P altimetry has contributed to the tidal problem in two important ways. The assimilation of global altimetry into Laplace tidal solutions has led to accurate representations of the global tides, as evidenced by the very close agreement between the astronomic measurements and the computed 2.4 TW working of the Moon on the global ocean. Second, the detection by and (1996) of small surface manifestation of internal tides radiating away from the Hawaiian chain has led to global estimates of 0.2 to 0.4 TW of conversion of surface tides to internal tides. Measurements of ocean microstructure yields 0.2 TW of global dissipation by pelagic turbulence (away from topography). We propose that pelagic turbulence is maintained by topographic scattering of barotropic into baroclinic tidal energy, via internal tides and internal waves. Previous estimates by (1974); , (1982)) of this conversion along 150,000 km of continental coastlines gave a negligible 0.02 TW; evidently the important conversion takes place along mid-ocean ridges.The maintenance of the abyssal global stratification requires a much larger expenditure of power. 2 TW versus 0.2 TW. This is usually attributed to wind forcing. If tidal power is to play a significant role here, then the BBL estimates need to be reduced. The challenge is to estimate dissipation from the energy flux divergence in the T/P adjusted tidal models, without prior assumptions concerning the dissipation processes.     

The wind field over wind-waves

The velocity fluctuations of wind over wind-waves in a wind tunnel are measured with a X-type hot-wire anemometer at some heights over the water surface.The observed vertical profiles of the wave-induced velocity fluctuations and the wave-induced Reynolds stress at the wave spectral peak frequency are different from those expected from the inviscid quasi-laminar model;i.e., the observed vertical profiles of the power spectral density of the wave-induced horizontal or vertical velocity fluctuations of wind have the minimum value at the height much heigher than the critical layer, and the value of the wave-induced Reynolds stress is negative at several heights over the water surface. From the comparison between the experimental results and the numerical solutions of a linear model of the turbulent shear flow over the wavy boundary, it is shown that the discrepancy described above can be attributed to the atmospheric turbulence.     

Prediction of ocean waves based on the single-parameter growth equation of wind waves (II) introduction of grid method

The present study is a modification of the wave prediction model presented in the first paper of this title (Kawai et al., 1979) based on the Toba's (1978) single parameter equation of the wind wave growth. The introduction of a grid method reduces the two defects pointed out inKawai et al., i.e., the absence of the prediction of certain instants at fixed points, and the concentration of wave energy at certain points in the wind direction, arising from the lack of treatment of the lateral spreading of wave energy around the wind direction. The new model is applied to the same set of data. The results shows overall improvements, such as the elimination of certain overestimate in the first study and the coincidence of the predicted maximum with the measured one. The swells are separately hindcasted and a very good agreement with measurement is obtained.     

基于CESM1.2.2模拟的浪致混合对末次冰盛期和工业革命前气候的影响

海洋上层垂向混合在模式中发挥重要的作用,以往的研究表明垂向混合的不足使得模拟的海洋温度和混合层深度与观测存在显著偏差。前人提出一种修正方案,考虑波浪产生的垂向混合,将由表面风作用下产生的波浪这样一个实际物理过程的湍混合进行参数化,其结果被证实能够显著提高模式模拟和预报的准确性。本文首次将浪致混合引入海气耦合的古气候模式,基于末次冰盛期和工业革命前2种不同的气候条件,探究浪致混合在海气耦合模式中的作用。在不同气候背景下,由于风场强度的不同,导致末次冰盛期浪致混合的强度小于工业革命前,但2个气候时期都体现出中纬度混合强度最大的特点。将浪致混合加入到气候模式中,模拟结果表明：中纬度海域2个时期都出现海表面降温而次表层升温的现象,但末次冰盛期的表面降温强度弱于工业革命前状态;不同月份下的模拟结果显示,在南北半球的夏季,海洋表层温度的降温最为显著。中纬度海域海洋上混合层深度在年平均条件下2个气候背景时期都出现加深现象,但末次冰盛期的加深程度弱于工业革命前;不同月份下的模拟结果显示,在南北半球的冬季,混合层加深的变化达到极值。另一方面,在高纬度海域,末次冰盛期的海表面温度出现了显著升高,这是由于浪...     

Turbulent structure of the subsurface layer of the sea according to the data of the <Emphasis Type="Italic">Sigma-1</Emphasis> measuring complex

We present the results of experimental investigations of the characteristics of turbulence in the layer of wave-induced mixing. The data on the fluctuations of velocity, temperature, and conductivity are obtained with the help of a Sigma-1 measuring complex. The computed values of the dissipation rate of turbulent energy are compared with different models proposed for the subsurface layer. It is shown that the available models fail to guarantee satisfactory agreement of the numerical results with the experimental data for the layer of active wave action and, in particular, in the presence of swell. This leads us to the conclusion concerning the necessity of parametrization and assimilation of more complete data on the state of the sea surface, the structure of currents, and the surface layer of the atmosphere in the models. __________ Translated from Morskoi Gidrofizicheskii Zhurnal, No. 2, pp. 15–28, March–April, 2007.     

Abyssal recipes II: energetics of tidal and wind mixing

Without deep mixing, the ocean would turn, within a few thousand years, into a stagnant pool of cold salty water with equilibrium maintained locally by near-surface mixing and with very weak convectively driven surface-intensified circulation. (This result follows from Sandström’s theorem for a fluid heated and cooled at the surface.) In this context we revisit the 1966 “Abyssal Recipes”, which called for a diapycnal diffusivity of 10^-4m²/s (1 cgs) to maintain the abyssal stratification against global upwelling associated with 25 Sverdrups of deep water formation. Subsequent microstructure measurements gave a pelagic diffusivity (away from topography) of 10^-5 m²/s — a low value confirmed by dye release experiments.A new solution (without restriction to constant coefficients) leads to approximately the same values of global upwelling and diffusivity, but we reinterpret the computed diffusivity as a surrogate for a small number of concentrated sources of buoyancy flux (regions of intense mixing) from which the water masses (but not the turbulence) are exported into the ocean interior. Using the Levitus climatology we find that 2.1 TW (terawatts) are required to maintain the global abyssal density distribution against 30 Sverdrups of deep water formation.The winds and tides are the only possible source of mechanical energy to drive the interior mixing. Tidal dissipation is known from astronomy to equal 3.7 TW (2.50±0.05 TW from M₂ alone), but nearly all of this has traditionally been allocated to dissipation in the turbulent bottom boundary layers of marginal seas. However, two recent TOPEX/POSEIDON altimetric estimates combined with dynamical models suggest that 0.6–0.9 TW may be available for abyssal mixing. A recent estimate of wind-driving suggests 1 TW of additional mixing power. All values are very uncertain.A surprising conclusion is that the equator-to-pole heat flux of 2000 TW associated with the meridional overturning circulation would not exist without the comparatively minute mechanical mixing sources. Coupled with the findings that mixing occurs at a few dominant sites, there is a host of questions concerning the maintenance of the present climate state, but also that of paleoclimates and their relation to detailed continental configurations, the history of the Earth–Moon system, and a possible great sensitivity to details of the wind system.     

Non-linear wave-induced transient response of soil around a trenched pipeline

Submarine pipelines are always trenched within a seabed for reducing wave loads and thereby enhancing their stability. Based on Biot's poroelastic theory, a two-dimensional finite element model is developed to investigate non-linear wave-induced responses of soil around a trenched pipeline, which is verified with the flume test results by Sudhan et al. [Sudhan, C.M., Sundar, V., Rao, S.N., 2002. Wave induced forces around buried pipeline. Ocean Engineering, 29, 533–544] and Turcotte et al. [Turcotte, B.R., Liu, P.L.F., Kulhawy, F.H., 1984. Laboratory evaluation of wave tank parameters for wave-sediment interaction. Joseph H. Defree Hydraulic Laboratory Report 84-1, School of Civil and Environmental Engineering, Cornell University]. Non-linear wave-induced transient pore pressure around pipeline at various phases of wave loading is examined firstly. Unlike most previous investigations, in which only a single sediment layer and linear wave loading were concerned, in this study, the influences of the non-linearity of wave loading, the physical properties of backfill materials and the geometry profile of trenches on the excess pore pressures within the soil around pipeline, respectively, were explored, taking into account the in situ conditions of buried pipeline in the shallow ocean zones. Based on the parametric study, it is concluded that the shear modulus and permeability of backfill soils significantly affect the wave-induced excess pore pressures around trenched pipeline, and that the effect of wave non-linearity becomes more pronounced and comparable with that of trench depth, especially at high wave steepness in shallow water.     

Effects of a cover layer on wave-induced pore pressure around a buried pipe in an anisotropic seabed

In engineering practice, a cover layer of coarser material has been used to protect a buried marine pipeline from wave-induced seabed instability. However, most previous investigations of the wave–seabed–pipe interaction problem have been concerned only with such a problem either in an isotropic single layer or a rigid pipe. This paper proposes a two-dimensional finite element model by employing the principle of repeatability to investigate the wave-induced soil response around a buried pipeline. The elastic anisotropic soil bahavior and geometry of cover layer are included in the present model, while the pipe is considered to be an elastic medium. This study focuses on the effects of a cover layer (including thickness B and width W of the cover layer) on the wave-induced pore pressure in the vicinity of a buried pipeline.     

A global wave parameter database for geophysical applications. Part 1: Wave-current–turbulence interaction parameters for the open ocean based on traditional parameterizations

Ocean surface mixing and drift are influenced by the mixed layer depth, buoyancy fluxes and currents below the mixed layer. Drift and mixing are also functions of the surface Stokes drift U_ss, volume Stokes transport T_S, a wave breaking height scale H_swg, and the flux of energy from waves to ocean turbulence Φ_oc. Here we describe a global database of these parameters, estimated from a well-validated numerical wave model, that uses traditional forms of the wave generation and dissipation parameterizations, and covers the years 2003–2007. Compared to previous studies, the present work has the advantage of being consistent with the known physical processes that regulate the wave field and the air–sea fluxes, and also consistent with a very large number of in situ and satellite observations of wave parameters. Consequently, some of our estimates differ significantly from previous estimates. In particular, we find that the mean global integral of Φ_oc is 68 TW, and the yearly mean value of T_S is typically 10–30% of the Ekman transport, except in well-defined regions where it can reach 60%. We also have refined our previous estimates of U_ss by using a better treatment of the high frequency part of the wave spectrum. In the open ocean, U_ss  0.013U₁₀, where U₁₀ is the wind speed at 10 m height.     

Modeling of the wind-driven circulation in the Japan Sea using a reduced gravity model

The surface circulation in the Japan Sea is investigated using a 1.5 layer reduced gravity model. Historical observations suggest strongly that an anti-clockwise circulation is dominant in the subpolar region north of the Polar Front as a general feature. This anti-clockwise circulation as well as the branching of the Tsushima Warm Current was simulated well by incorporating the Naet al. (1992)'s wind stress. The positive curl of the wind stress in the northern and the northwestern Japan Sea was found to play an important role in the formation of the subpolar gyre and the separation of the western boundary current (the East Korean Warm Current) in the Japan Sea.     

The effects of random surface waves on the steady Ekman current solutions

The response of near-surface current profiles to wind and random surface waves are studied based on the approach of Jenkins [1989. The use of a wave prediction model for driving a near surface current model. Dtsch. Hydrogr. Z. 42, 134–149] and Tang et al. [2007. Observation and modeling of surface currents on the Grand Banks: a study of the wave effects on surface currents. J. Geophys. Res. 112, C10025, doi:10.1029/2006JC004028]. Analytic steady solutions are presented for wave-modified Ekman equations resulting from Stokes drift, wind input and wave dissipation for a depth-independent constant eddy viscosity coefficient and one that varies linearly with depth. The parameters involved in the solutions can be determined by the two-dimensional wavenumber spectrum of ocean waves, wind speed, the Coriolis parameter and the densities of air and water, and the solutions reduce to those of Lewis and Belcher [2004. Time-dependent, coupled, Ekman boundary layer solutions incorporating Stokes drift. Dyn. Atmos. Oceans. 37, 313–351] when only the effects of Stokes drift are included. As illustrative examples, for a fully developed wind-generated sea with different wind speeds, wave-modified current profiles are calculated and compared with the classical Ekman theory and Lewis and Belcher's [2004. Time-dependent, coupled, Ekman boundary layer solutions incorporating Stokes drift. Dyn. Atmos. Oceans 37, 313–351] modification by using the Donelan and Pierson [1987. Radar scattering and equilibrium ranges in wind-generated waves with application to scatterometry. J. Geophys. Res. 92, 4971–5029] wavenumber spectrum, the WAM wave model formulation for wind input energy to waves, and wave energy dissipation converted to currents. Illustrative examples for a fully developed sea and the comparisons between observations and the theoretical predictions demonstrate that the effects of the random surface waves on the classical Ekman current are important, as they change qualitatively the nature of the Ekman layer. But the effects of the wind input and wave dissipation on surface current are small, relative to the impact of the Stokes drift.     

Discussion/comments regarding “Trends in<Emphasis Type="Italic"> p</Emphasis>CO<Subscript>2</Subscript> and sea–air CO<Subscript>2</Subscript> flux over the global open oceans for the last two decades” by Y. Iida,A. Kojima,Y. Takatani,T. Nakano,H. Sugimoto,T. Midorikawa,M. Ishii

A paper by Iida et al. that was recently published in this journal (J Oceanogr 17:637–661, 2015) presented trends in the partial pressure of carbon dioxide in surface seawater and the estimated sea–air carbon dioxide flux over the global open oceans for the last two decades. The purpose of the present discussion is to demonstrate that the formula used by Iida et al. in their assessments can also be employed to estimate the sea–air carbon dioxide flux based on long-term wind statistics, i.e., based on data showing how the mean wind speed 10 m above the sea surface has varied over a long period. Examples of the application of this approach are given here, based on long-term wind statistics for the northern North Sea and the North West Shelf of Australia.     

Examination of wind-wave interaction source term in WAVEWATCH III with tropical cyclone wind forcing

Results of drag coefficient(CD) from field observations and laboratory wave tank experiments indicate that the operational wave model can overestimate wind energy input under high wind conditions. The wind-wave interaction source term in WAVEWATCH Ⅲ has been modified to examine its behavior with tropical cyclone wind forcing. Using high resolution wind input,numerical experiments under idealized wind field and tropical cyclone Bonnie(1998) were designed to evaluate performance of the modified models. Both experiments indicate that the modified models with reduced CD significantly decrease wind energy input into the wave model and then simulate lower significant wave height(SWH) than the original model. However,the effects on spatial distribution of SWH,mean wavelength,mean wave direction,and directional wave spectra are insignificant. Due to the reduced wind energy input,the idealized experiment shows that the modified models simulate lower SWH than the original model in all four quadrants. The decrease in the front quadrants is significantly larger than that in the rear quadrants;it is larger under higher winds than lower winds. The realistic experiment on tropical cyclone Bonnie shows that the modified model with the various downward trends of CD in high winds creates a simulation that agrees best with scanning radar altimeter observations.     

A Numerical Modeling of the Upper and the Intermediate Layer Circulation in the East Sea

Circulation in the upper and the intermediate layer of the East Sea is investigated by using a fine resolution, ocean general circulation model. Proper separation of the East Korean Warm Current from the coast is achieved by adopting the isopycnal mixing, and using the observed heat flux (Hirose et al., 1996) and the realistic wind stress (Na et al., 1992). The simulated surface circulation exhibits a remarkable seasonal variation in the flow patterns of the Nearshore Branch, the East Korean Warm Current and the Cold Currents. East of the Oki Bank, the Nearshore Branch follows the isobath of shelf topography from late winter to spring, while in summer and autumn it meanders offshore. The Nearshore Branch is accompanied by cyclonic and anticyclonic eddies in a fully developed meandering phase. The meandering and the eddy formation of the Nearshore Branch control the interior circulation in the Tsushima Current area. A recirculation gyre is developed in the region of the East Korean Warm Current in spring and grown up to an Ulleung Basin scale in summer. A subsurface water is mixed with the fresh surface water by winter convection in the northeastern coastal region of Korea. The well-mixed low salinity water is transported to the south by the Cold Currents, forming the salinity minimum layer (Intermediate Water) beneath the East Korean Warm Current water. The recirculation gyre redistributes the core water of the salinity minimum layer in the Ulleung Basin. This revised version was published online in August 2006 with corrections to the Cover Date.