A note on a critical wind speed for air–sea boundary processes

Wind and wind-generated waves were measured in a wind-wave tank. A clear transition was found in the relation between the wind speed U ₁₀ and the wind friction velocity u _* near u _* = 0.2 m/s, where U ₁₀ is the wind speed at 10 m height extrapolated from the measured wind profile in a logarithmic layer, and u _* = 0.2 m/s corresponds roughly to U ₁₀ = 8 m/s in the present measurement. Quite a similar transition was found in the relation between the spectral density of high frequency wind waves and u _*. These results suggest the existence of the critical wind speed for air–sea boundary processes, which was proposed by Munk (J Marine Res 6:203–218, 1947) more than half a century ago. His original idea of the critical wind speed was based on the discontinuities in such phenomena as white caps, wind stress, and evaporation, which commonly appear at a wind speed near 7 m/s. On the basis of the results of our present study and those of earlier studies, we discuss the phenomena which are relevant to the critical wind speed for the air–sea boundary processes. The conclusion is that the critical wind speed exists and it is attributed to the start of wave breaking rather than the Kelvin–Helmholtz instability, but the air–sea boundary processes are not discontinuous at a particular wind speed; because of the stochastic nature of breaking waves, the changes occur over a range of wind speeds. Detailed discussions are presented on the dynamical processes associated with the critical wind speed such as wind-induced change of sea surface roughness and high frequency wave spectrum. Future studies are required, however, to clarify the dynamical processes quantitatively. In particular, there is a need to further examine the gradual change of breaking patterns of wind waves with the increase of wind speed, and the associated change of the structure of the wind over wind waves, such as separation of the airflow at the crest of wind waves, the turbulent stress, and wave-induced stress. Studies on the dynamical structure of the high frequency wave spectrum are also needed.     

Determining the influence of wind-wave breaking on the dissipation of the turbulent kinetic energy in the upper ocean and on the dependence of the turbulent kinetic energy on the stage of wind-wave development

New experimental data that make it possible to explain and predict the observed variability of turbulent-energy dissipation in the upper ocean are discussed. For this purpose, the dependence of the energy dissipation rate of breaking wind waves on their propagation velocity (see [1]) is used. The turbulent-energy dissipation values obtained earlier in [2, 3] by a direct method are compared to the results of radar measurements of individual breaking events presented in [1]. On the basis of this comparison, a strong dependence of the turbulent-energy dissipation value on the stage of wind-wave development, which is characterized by the ratio U _a /c _p (U _a is the wind speed and c _p is the phase speed of the peak of the wind-wave spectrum) is confirmed. This dependence was found earlier purely empirically. Moreover, it is shown that the theoretically obtained dependence (c _p /U _a )⁴, does not contradict the available empirical data. The results of this study opens possibilities for scientifically substantiated calculations of greenhouse-gas exchange (specifically, CO₂ exchange between the ocean and the atmosphere).     

Waves and diffusion on the sea surface

The frequency spectrum of surface elevations in the presence of wind waves is well known. On this basis, one can estimate the frequency spectrum of vertical velocities in sea-surface waves. Owing to liquid incompressibility, the spectrum of horizontal velocities should have the same frequency dependence. The use of the dispersion equation for waves on the surface of a heavy liquid allows one to obtain to the spatial spectrum of velocities. Therefore, one can estimate the spatial structure function of the velocity field. For short waves and large depths, the structure function increases as r ^1/2, where r is the distance between the points of observations. For long waves and shallow depths h, this increase is proportional to r. The coefficient of turbulent mixing K(r) of pollution spots of size r on the sea surface is now estimated as the product of the spot size and the rms difference of velocities. As a result, depending on r and h, the exponent in the r ⁿ dependence of K(r) may vary between 1.25 and 1.5. This outcome provides an explanation for a scatter in the values of the exponent n, a phenomenon that has been observed by many experimentalists.     

Wave Activity and Its Changes in the Troposphere and Stratosphere of the Northern Hemisphere in Winters of 1979–2016

An analysis of spectra of wave disturbances with zonal wave numbers 1 ≤ k ≤ 10 is carried out using winter (November to March) ERA-Interim reanalysis geopotential data in the troposphere and stratosphere for 1979–2016. Contributions of eastward-traveling (E), westward-traveling (W), and stationary (S) waves are estimated. The intensification of wave activity is observed in the tropical troposphere and stratosphere and in the upper stratosphere of the entire Northern Hemisphere. The intensification of wave activity in the tropics and subtropics is noted for waves of all types (E, W, and S), while in the middle and higher latitudes it is related mainly to stationary and eastward waves. Near the subtropical tropopause, the energy of stationary waves has increased in recent decades. In addition, in the tropical and subtropical troposphere and in the subtropical lower stratosphere, the energy of the eastward-traveling waves in El Niño years may be one and a half times or twice the energy in La Niña years. The spectrally weighted zonal wave numbers for waves of all types (E, W, and S) are the largest in the upper subtropical troposphere. The spectrally weighted zonal wave number for W and S waves is correlated with the Atlantic Multidecadal Oscillation index and varies by 15% in 1979–2016 (on an interdecadal time scale). The spectrally weighted wave period is larger in the stratosphere than in the troposphere. It is maximal in the middle extratropical stratosphere. The spectrally weighted wave periods correlate with the activity of sudden stratospheric warmings. The sign of this correlation depends on the latitude, atmospheric layer, and zonal wave number.     

Features of the atmospheric boundary layer block for three versions of the WAM wind wave model

The estimated characteristics of the atmospheric boundary layer, obtained by the simulation of wind wave fields using three versions of the WAM numerical model are compared with the well-known empirical dependences of drag coefficient C _d on wind speed U ₁₀ and wave age A, as well as with the dependence of dimensionless roughness height z _n on inverse wave age u*/с р. Calculations carried out for several years in the areas of the Pacific and Indian oceans, based on the ERA-interim and CFSR wind reanalyses have shown good agreement between the model and empirical dependences C _d (U ₁₀) and C _d (A). The range of estimated variability for z _n (u*/с _р ) has been found to be significantly less than empirical. It has been also found that estimated values of wind speed U _10W (t) are overestimated from 5 to 10% in all versions of WAM models compared with the input wind reanalysis U _10R (t) at the moments of appearance maximum values of wind U _10R (t). The reasons for the established features of the WAM model and their dependence on the model version are discussed.     

Experimental Study on Crescent Waves Diffracted by A Circular Cylinder

Crescent waves often observed on the sea surface are unusual wave pattern induced by the instability of Stokes wave. The paper presents the experimental results of the wave field around a circular cylinder generated by the diffraction of crescent wave in order to examine the difference of diffracted crescent waves from the commonly-used diffracted Stokes waves. The results show that with the existence of the cylinder, the crescent wave pattern can still get fully developed, and with the presence of this type of wave pattern, the symmetry breaking of the wave amplitude distribution occurs and there are extra wave components at the frequencies of 0.5ω₀, 1.5ω₀ and 2.5ω₀ (ω₀ is the frequency of Stokes waves) appearing in the wave amplitude spectrum.     

On the Development of Models for Height Profiles of the Wind Speed in the Atmospheric Surface Layer

The reliability of the known models of a height profile of the wind speed V(h) in the atmospheric boundary layer (ABL) and near-surface layer (NSL) is analyzed using the data of long-term ABL measurements accumulated in Russia in the state network of meteorological and aerological stations and the data of multilevel measurements at mast wind-measuring complexes. A new multilayer semiempirical model of V(h) is proposed which is based on aerodynamic and physical representations of the ABL vertical structure and relies on the hypothesis that wind-speed profiles providing the minimum wind friction on the ground and satisfying the conditions of profile smoothness are feasible in the ABL. This model ensures the best agreement with the data of meteorological, aerological, and mast wind measurements.     

Studying the sea surface slopes using an array of wave gauge sensors

The deviations of the marine surface slope spectra (measured using an array of wave gauge sensors) from the theoretical estimates obtained using the linear spectral model of the wave field are analyzed. It has been indicated that the average measured full slope spectra (the sum of the slope component spectra in the orthogonal directions) is higher than the theoretical estimates by 6% at frequencies from the surface wave spectral peak (f _m ) to 4.5 f _m . The difference between the measured and theoretical estimates of the full slope spectrum rapidly increases at frequencies of f < f _m . At f _m ≈ 0.75 f _m , the average measured full slope spectrum is higher than the theoretical estimate by a factor of more than 5.     

Application of importance sampling method in sliding failure simulation of caisson breakwaters

It is assumed that the storm wave takes place once a year during the design period, and N histories of storm waves are generated on the basis of wave spectrum corresponding to the N-year design period. The responses of the breakwater to the N histories of storm waves in the N-year design period are calculated by mass-spring-dashpot mode and taken as a set of samples. The failure probability of caisson breakwaters during the design period of N years is obtained by the statistical analysis of many sets of samples. It is the key issue to improve the efficiency of the common Monte Carlo simulation method in the failure probability estimation of caisson breakwaters in the complete life cycle. In this paper, the kernel method of importance sampling, which can greatly increase the efficiency of failure probability calculation of caisson breakwaters, is proposed to estimate the failure probability of caisson breakwaters in the complete life cycle. The effectiveness of the kernel method is investigated by an example. It is indicated that the calculation efficiency of the kernel method is over 10 times the common Monte Carlo simulation method.     

Negative correlations of variations in near-water wind and surface wind waves

The relationship between the intensity of surface wind waves and near-water wind is analyzed. The data of measuring wind waves and near-water wind under natural conditions in the Black Sea (July 2004) and Norwegian Sea (June 2003, 16th cruise of the R/V Akademik Sergei Vavilov) are used. A phenomenon of negative correlations has been found between the intensity of wind waves and near-water wind in regions of substantial restructuring of wind waves in the field of inhomogeneous flows: wind-wave amplification during wind decay and vice versa. Examples of such observations are presented, a theoretical model is constructed for the observed phenomenon, and a good agreement is obtained between theory and experiment.     

斜向波浪作用下双层水平板式防波堤波浪荷载试验研究

In this study, systematic physical model tests were performed to investigate the wave forces on the twin-plate breakwater under irregular waves. Based on the experimental results, the effects of the relative plate width B/L,wave height Hs/D and incident angle θ0 on the wave forces were analyzed and discussed. The results showed that:(1) The envelopes of the total wave pressure were generally symmetrical along the direction of plate width under the incident angles(θ0) being 0°, 15°, 30°, 45° and 60°. In particular, the envelopes of wave pressure atθ0=30° were larger than all other cases.(2) The synchronous pressure distribution of the breakwater under oblique wave action was more complicated comparing to the normal incident waves.(3) Based on data analysis, an empirical formula was obtained to estimate the total vertical force of the twin-plate breakwater.This empirical formula can be a good reference for the design basis of engineering applications under specified wave conditions.     

Simulating the Propagation of Infrasonic Waves and Estimating the Energy of the Chelyabinsk Meteoroid Explosion Observed on February 15, 2013

Results obtained from simulating the propagation of infrasonic waves from the Chelyabinsk meteoroid explosion observed on February 15, 2013, are given. The pseudodifferential parabolic equation (PDPE) method has been used for calculations. Data on infrasonic waves recorded at the IS31 station (Aktyubinsk, Kazakhstan), located 542.7 km from the likely location of the explosion, have been analyzed. Six infrasonic arrivals (isolated clearly defined pulse signals) were recorded. It is shown that the first “fast” arrival (F) corresponds to the propagation of infrasound in a surface acoustic waveguide. The rest of the arrivals (T1–T5) are thermospheric. The agreement between the results of calculations based on the PDPE method and experimental data is satisfactory. The energy E of the explosion has been estimated using two methods. One of these methods is based on the law of conservation of the acoustic pulse I, which is a product of the wave profile area S/2 of the signal under analysis and the distance to its source E _I [kt] = 1.38 × 10^–10 (I [kg/s])^1.482. The other method is based on the relation between the energy of explosion and the dominant period T of recorded signal E _T [kt] = 1.02 × (T [s]²/σ)^3/2, where σ is the dimensionless distance determining the degree of nonlinear effects during the propagation of sound along ray trajectories. According to the data, the explosion energy E _I,T ranges from 1.87 to 32 kt TNT.     

Generation mechanism of an alongshore bar on a sandy beach slope

A model explaining the mechanism of alongshore bar formation from the point of view of the sediment balance in the surf zone is considered. A cloud of suspended matter that appears during wave breaking is transported shoreward and simultaneously sediments forming a vertical material flux directed to the bottom (S). Simultaneously, an undertow generates a horizontal offshore flux of suspended matter q _x . Under these conditions, the sediment balance is determined by the equality of the flux -S and the gradient dq _x /dx. The bottom profile satisfying the balance equation is a bar profile with the crest at the point of the flux maximum -S. The model predicts a concave profile of the seaside slope and a concave-convex profile of the slope in the trough. A conclusion is reached on the basis of the calibration and verification of the model based on the field data that the suggested mechanism manifests itself differently in the outer and inner zones of the coastal zone. In the inner zone, the horizontal size of the bar is determined by the length of short wind waves, while, in the outer one, it is determined by the length of the infragravity waves related to the groups of short waves. It is shown that the model can be applied to estimate the parameters of the largest bar in the inner part of the coastal zone.     

Evaluation of spatial distribution of turbulent mixing in the central Pacific

A long-term mean turbulent mixing in the depth range of 200–1000 m produced by breaking of internal waves across the middle and low latitudes (40°S–40°N) of the Pacific between 160°W and 140°W is examined by applying fine-scale parameterization depending on strain variance to 8-year (2005–2012) Argo float data. Results show that elevated turbulent dissipation rate (ε) is related to significant topographic regions, along the equator, and on the northern side of 20°N spanning to 24°N throughout the depth range. Two patterns of latitudinal variations of ε and the corresponding diffusivity (K_ρ) for different depth ranges are confirmed: One is for 200–450 m with significant larger ε and K_ρ, and the maximum values are obtained between 4°N and 6°N, where eddy kinetic energy also reaches its maximum; The other is for 350–1000 m with smaller ε and K_ρ, and the maximum values are obtained near the equator, and between 18°S and 12°S in the southern hemisphere, 20°N and 22°N in the northern hemisphere. Most elevated turbulent dissipation in the depth range of 350–1000 m relates to rough bottom roughness (correlation coefficient?=?0.63), excluding the equatorial area. In the temporal mean field, energy flux from surface wind stress to inertial motions is not significant enough to account for the relatively intensified turbulent mixing in the upper layer.     

南极西北威德尔海上层海洋湍流混合研究

Turbulent mixing in the upper ocean(30-200 m) of the northwestern Weddell Sea is investigated based on profiles of temperature,salinity and microstructure data obtained during February 2014.Vertical thermohaline structures are distinct due to geographic features and sea ice distribution,resulting in that turbulent dissipation rates(ε) and turbulent diffusivity(K) are vertically and spatially non-uniform.On the shelf north of Antarctic Peninsula and Philip Ridge,with a relatively homogeneous vertical structure of temperature and salinity through the entire water column in the upper 200 m,both ε and K show significantly enhanced values in the order of O(10~(-7))-O(10~(-6)) W/kg and O(10~(-3))-O(10~(-2)) m~2/s respectively,about two or three orders of magnitude higher than those in the open ocean.Mixing intensities tend to be mild due to strong stratification in the Powell Basin and South Orkney Plateau,where s decreases with depth from O(10~(-8)) to O(10~(-9)) W/kg,while K changes vertically in an inverse direction relative to s from O(10~(-6)) to O(10~(-5)) m~2/s.In the marginal ice zone,K is vertically stable with the order of10~(-4) m~2/s although both intense dissipation and strong stratification occur at depth of 50-100 m below a cold freshened mixed layer.Though previous studies indentify wind work and tides as the primary energy sources for turbulent mixing in coastal regions,our results indicate weak relationship between K and wind stress or tidal kinetic energy.Instead,intensified mixing occurs with large bottom roughness,demonstrating that only when internal waves generated by wind and tide impinge on steep topography can the energy dissipate to support mixing.In addition,geostrophic current flowing out of the Weddell Sea through the gap west of Philip Passage is another energy source contributing to the local intense mixing.     

Using the acoustic-pulse conservation law in estimating the energy of surface acoustic sources by remote sounding

The atmospheric effect on the characteristics of infrasonic signals from explosions has been studied. New methods have been proposed to remotely estimate the energy of explosions using the data of infrasonic wave registration. One method is based on the law of conservation of acoustic pulse I, which is equal to the product of the wave profile area S/2 of the studied infrasonic signal and the distance to the source E_I [kt] = 1.38 × 10^–10 (I [kg/s])^1.482. The second method is based on the relationship between the explosion energy and the dominant period T of the recorded signal, EТ [kt] =1.02 × (Т [s]²/σ)^3/2, where σ is a dimensionless distance used for determining the degree of manifestation of nonlinear effects in the propagation of sound along ray trajectories. When compared to the conventional E_W (Whitaker’s) relation, the advantage of the EI relation is that it can be used for pulsed sources located at an arbitrary height over the land surface and having an arbitrary form of the initial-pulse profile and for any type of infrasonic arrivals. A distinctive feature of the expression for E_Т is that the atmospheric effect on the characteristics of recorded infrasonic signals is explicitly taken into account. These methods have been tested using infrasonic data recorded at a distance of 322 km from the sources (30 explosions caused by a fire that occurred at the Pugachevo armory in Udmurtia on June 2, 2011). For the same explosion, empirical relations have been found between energy values obtained by different methods: E_I = 1.107 × E _W , E _Т = 2.201 × E _I .     

Regional long-period magnitude scales and their capabilities for tsunami warning

The tsunami warning system in the Russian Far East employs the medium-period magnitude MS (BB) by Vaniek–Soloviev. However, its use may lead to inadequacies and underestimates for the tsunamigenic potential of an earthquake. Specifically, this can happen in the case of a so-called tsunami–earthquake. This kind of earthquakes with a nonstandard spectrum was revealed by H. Kanamori in 1972. This problem can be overcome by using a magnitude scale that deals with longer period seismic waves. This study develops a technique for determining the magnitudes at regional distances (from 70 to 4500 km) using the amplitudes of surface seismic waves of periods of 40 and 80 s. At distances of 70–250 km, the amplitude of the joint group of shear and surface waves is used. For the new magnitudes designated M _S(40) and M _S(80), experimental calibration curves are constructed using more than 1250 three-component records at 12 stations of the region. The magnitudes are calibrated so as to produce an unbiased estimate of the moment magnitude M _w in the critical range 7.5–8.8. The rms error of the single-station estimate M _w is around 0.27. At distances below 250 km and M _w ≥ 8.3, the estimate of M _w obtained by the proposed technique becomes saturated at the level of M _w ~ 8.3, which is acceptable for operative analysis because no missed alarms arise. The technique can be used in operational tsunami warning based on seismological data. This can markedly decrease the number of false alarms.     

使用参数化初猜测谱算法提取VV极化Sentinel-1 SAR图像的海浪要素并与ECMWF再分析数据以及浮标数据进行验证对比

The purpose is to study the accuracy of ocean wave parameters retrieved from C-band VV-polarization Sentinel-1Synthetic Aperture Radar(SAR) images, including both significant wave height(SWH) and mean wave period(MWP), which are both calculated from a SAR-derived wave spectrum. The wind direction from in situ buoys is used and then the wind speed is retrieved by using a new C-band geophysical model function(GMF) model,denoted as C-SARMOD. Continuously, an algorithm parameterized first-guess spectra method(PFSM) is employed to retrieve the SWH and the MWP by using the SAR-derived wind speed. Forty–five VV-polarization Sentinel-1 SAR images are collected, which cover the in situ buoys around US coastal waters. A total of 52 subscenes are selected from those images. The retrieval results are compared with the measurements from in situ buoys. The comparison performs good for a wind retrieval, showing a 1.6 m/s standard deviation(STD) of the wind speed, while a 0.54 m STD of the SWH and a 2.14 s STD of the MWP are exhibited with an acceptable error.Additional 50 images taken in China's seas were also implemented by using the algorithm PFSM, showing a 0.67 m STD of the SWH and a 2.21 s STD of the MWP compared with European Centre for Medium-range Weather Forecasts(ECMWF) reanalysis grids wave data. The results indicate that the algorithm PFSM works for the wave retrieval from VV-polarization Sentinel-1 SAR image through SAR-derived wind speed by using the new GMF C-SARMOD.     

A new formula for saturated water steam pressure within the temperature range −25 to 220°C

Instead of approximation formula ln(E(t)/E(0)) = [(a ? bt)t/(c + T)] commonly used at present for representing dependence of pressure of saturated streams of liquid water E upon temperature we suggested new approximation formula of greater accuracy in the form ln(E(t)/E(0)) = [(A ? Bt + Ct ²)t/T], where t and T are temperature in °C and K respectively. For this formula with parameters A = 19.846, B = 8.97 × 10^?3, C = 1.248 × 10^?5 and E(0) = 6.1121 GPa with ITS-90 temperature scale and for temperature range from 0°C to 110°C relative difference of approximation applying six parameter formula by W. Wagner and A. Pruß 2002, developed for positive temperatures, is less than 0.005%, that is approximately 15 times less than accuracy obtained with the firs formula. Increase of temperature range results in relative difference increasing, but for even temperature range from 0°C to 220°C it does not higher than 0.1%. For negative temperatures relative difference between our formula and a formula of D. M. Murphy and T. Koop, 2005, is less than 0.1% for temperatures higher than ?25°C. This paper also presents values of coefficients for approximation of Goff and Grach formula recommended by IMO. The procedure of finding dew point T _d for known water steam pressure e _n based on our formula adds up to solving an algebraic equation of a third degree, which coefficients are presented in this paper. For simplifying this procedure this paper also includes approximation ratio applying a coefficient A noted above, in the form T _d (e _n ) = \(\frac{{AT_0 }}{{A - \varepsilon }}\) + 0.0866?² + 0.0116?^10/3, where ? = ln(e _n /E(T ₀)). Error of dew point recovery in this ratio is less than 0.005 K within the range from 0 to 50°C.