The effects of topographically-controlled thermal tides in the martian upper atmosphere as seen by the MGS accelerometer

Mars Global Surveyor accelerometer observations of the martian upper atmosphere revealed large variations in density with longitude during northern hemisphere spring at altitudes of 130-160 km, all latitudes, and mid-afternoon local solar times (LSTs). This zonal structure is due to tides from the surface. The zonal structure is stable on timescales of weeks, decays with increasing altitude above 130 km, and is dominated by wave-3 (average amplitude 22% of mean density) and wave-2 (18%) harmonics. The phases of these harmonics are constant with both altitude and latitude, though their amplitudes change significantly with latitude. Near the South Pole, the phase of the wave-2 harmonic changes by 90° with a change of half a martian solar day while the wave-3 phase stays constant, suggesting diurnal and semidiurnal behaviour, respectively. We use a simple application of classical tidal theory to identify the dominant tidal modes and obtain results consistent with those of General Circulation Models. Our method is less rigorous, but simpler, than the General Circulation Models and hence complements them. Topography has a strong influence on the zonal structure.     

Tidally driven stress accumulation and shear failure of Enceladus's tiger stripes

Straddling the south polar region of Saturn's moon Enceladus, the four principal “tiger stripe” fractures are a likely source of tectonic activity and plume generation. Here we investigate tidally driven stress conditions at the tiger stripe fractures through a combined analysis of shear and normal diurnal tidal stresses and accounting for additional stress at depth due to the overburden pressure. We compute Coulomb failure conditions to assess failure location, timing, and direction (right- vs left-lateral slip) throughout the Enceladus orbital cycle and explore a suite of model parameters that inhibit or promote shear failure at the tiger stripes. We find that low coefficients of friction (μf=0.1-0.2) and shallow overburden depths (z=2-4 km) permit shear failure along the tiger stripe faults, and that right- and/or left-lateral slip responses are possible. We integrate these conditions into a 3D time-dependent fault dislocation model to evaluate tectonic displacements and stress variations at depth during a tiger stripe orbital cycle. Depending on the sequence of stress accumulation and subsequent fault slip, which varies as a function of fault location and orientation, frictional coefficient, and fault depth, we estimate resolved shear stress accumulation of ∼70 kPa prior to fault failure, which produces modeled strike-slip displacements on the order of ∼0.5 m in the horizontal direction and ∼5 mm in the vertical direction per slip event. Our models also indicate that net displacements on the order of 0.1 m per orbital cycle, in both right- and left-lateral directions, are possible for particular fault geometries and frictional parameters. Tectonic activity inferred from these analyses correlates with observed plume activity and temperature anomalies at Enceladus's south polar region. Moreover, these analyses provide important details of stress accumulation and the faulting cycle for icy satellites subjected to diurnal tidal stress.     

World-wide synthetic tide parameters for gravity and vertical and horizontal displacements

The response of the Earth’s crust to the direct effect of lunisolar gravitational forcing is known as the body tide. The body tide is superimposed by surface-loading forces due to the pressure of the periodically varying ocean tide acting on the Earth, called ocean tide loading (OTL). Both body tide and OTL can be decomposed into components of the same frequency known as tidal parameters. However, OTL is more complicated than body tides because of the dynamic effects of the ocean. Estimating OTL requires a model of the ocean tides and knowledge of the elastic properties of the solid Earth. Thus, synthetic tide parameters (amplitude factors and phase leads) have been developed here on a world-wide grid for gravity and positional displacements. The body tide contributions were added to the oceanic contribution to provide the Earth tide response. The accuracy and reliability of the synthetic tidal parameters have been estimated by comparing observed gravity and vertical-displacement tide parameters with those interpolated from our synthetic model, which shows good agreement. Tests also indicate that the synthetic tide parameters provide realistic gravimetric and displacements for practical use in tidal prediction.     

The interior structure of Mercury and its core sulfur content

Depth-dependent interior structure models of Mercury are calculated for several plausible chemical compositions of the core and of the mantle. For those models, we compute the associated libration amplitude, obliquity, tidal deformation, and tidal changes in the external potential. In particular we study the relation between the interior structure parameters for five different mantle mineralogies and two different temperature profiles together with two extreme crust density values. We investigate the influence of the core light element concentration, temperature, and melting law on core state and inner and outer core size. We show that a sulfur concentration above 10 wt% is unlikely if the temperature at the core-mantle boundary is above 1850 K and the silicate shell at least 240 km thick. The interior models can only have an inner core if the sulfur weight fraction is below 5 wt% for core-mantle boundary temperature in the 1850-2200 K range. Within our modeling hypotheses, we show that with the expected precision on the moment of inertia the core size can be estimated to a precision of about 50 km and the core sulfur concentration with an error of about 2 wt%. This uncertainty can only be reduced when more information on the mantle mineralogy of Mercury becomes available. However, we show that the uncertainty on the core size estimation can be greatly reduced, to about 25 km, if tidal surface displacements and tidal variations in the external potential are considered.     

Tidal pattern instabilities on multi-moon planets

The equilibrium tide-generating forces in the lunar orbital plane of a planet of radius R are calculated for the case of N moons of mass Mi orbiting the planet at instantaneous polar coordinates (Di, αi). For the case of a single moon, there are only two high tides. For the case of two moons, it is found that there can exist a critical lunar orbital distance at which two high tides become unstable with respect to formation of three high tides. Bifurcation diagrams are presented which depict how the angular positions of the high and low tides on the planet vary with the lunar distances and lunar separation angle. Tidal stability diagrams, which illustrate the stability regions for various tidal patterns as a function of lunar distances and lunar separation angle, are presented for various values of D₂/D₁ and M₂/M₁. Generally speaking, the aforementioned tidal instability, and hence the propensity for formation of three high tides on a two-moon planet, exists over a significant range of lunar distances and separation angles provided that M₂/M₁∼³(D₂/D₁). For the case of N>2 moons, the tidal stability diagram becomes more complex, revealing a diversity of potential tidal patterns.     

黄海绿潮应急溯源数值模拟初步研究

基于三维全动力POM 海洋模式, 根据2008 年6 月1 日海监飞机监测绿潮所在位置, 采用拉格朗日粒子追踪法反向积分, 追溯绿潮来源。数值模拟结果显示, 回溯至5 月中旬, 绿潮主要来源于黄海南部江苏连云港和盐城近海海域。黄海绿潮溯源数值模拟, 为政府相关部门了解绿潮的源头, 并采取相应的措施提供依据, 进而为保护生态环境、防灾减灾做贡献。     

渤、黄、东海三维潮波运动数值模拟

采用POM三维海流数值模式模拟渤、黄、东海潮波运动。所得潮汐调和常数与77个测站的观测值的平均绝对误差：m1振幅1．92cm,迟角4．39°;M2振幅4．70cm,迟角5．08°。模拟结果显示M2分潮流共存在8个圆流点,m1岁潮流共存在9个圆流点。其中,M2分潮流在舟山群岛附近与m1分潮流在黄海北部和台湾海峡谷存在一个圆流点,这三个圆流点是本文数值模拟所首次显示的,需进一步的观测验证它们实际存在与否。模式还得出湍流涡动系数分布。     

On topographic coupling of surface and internal tides

The problem of the generation of internal tides through the interaction of surface tides with oceanic bottom topography is re-examined, taking into account the horizontal components of the Earth's rotation. It is shown that previous models that have omitted these terms may be readily extended to include them, and changes in the magnitude and character of the barotropic to baroclinic conversion are estimated. For semi-diurnal tides the energy conversion is increased, but only by about 2%. However, the character of the waves differs at high latitudes, where the phase and location of the wave energy may change by as much as 14%. Accordingly, inclusion of these terms is recommended in future studies with these models.     

How tides and river flows determine estuarine bathymetries

For strongly tidal, funnel-shaped estuaries, we examine how tides and river flows determine size and shape. We also consider how long it takes for bathymetric adjustment, both to determine whether present-day bathymetry reflects prevailing forcing and how rapidly changes might occur under future forcing scenarios.Starting with the assumption of a 'synchronous' estuary (i.e., where the sea surface slope resulting from the axial gradient in phase of tidal elevation significantly exceeds the gradient in tidal amplitude ), an expression is derived for the slope of the sea bed. Thence, by integration we derive expressions for the axial depth profile and estuarine length, L, as a function of and D, the prescribed depth at the mouth. Calculated values of L are broadly consistent with observations. The synchronous estuary approach enables a number of dynamical parameters to be directly calculated and conveniently illustrated as functions of and D, namely: current amplitude Û, ratio of friction to inertia terms, estuarine length, stratification, saline intrusion length, flushing time, mean suspended sediment concentration and sediment in-fill times.Four separate derivations for the length of saline intrusion, L_I, all indicate a dependency on (U_o is the residual river flow velocity and f is the bed friction coefficient). Likely bathymetries for `mixed' estuaries can be delineated by mapping, against and D, the conditions L<sub>I</sub>/L<1,E<sub>X</sub>/L<1 (E<sub>X</sub> is the tidal excursion) alongside the Simpson-Hunter criteria D/U<sup>3</sup><50 m<sup>−2</sup> s<sup>3</sup>. This zone encompasses 24 out of 25 `randomly' selected UK estuaries.However, the length of saline intrusion in a funnel-shaped estuary is also sensitive to axial location. Observations suggest that this location corresponds to a minimum in landward intrusion of salt. By combining the derived expressions for L and L_I with this latter criterion, an expression is derived relating D_i, the depth at the centre of the intrusion, to the corresponding value of U_o. This expression indicates U_o is always close to 1 cm s⁻¹, as commonly observed. Converting from U_o to river flow, Q, provides a morphological expression linking estuarine depth to Q (with a small dependence on side slope gradients).These dynamical solutions are coupled with further generalised theory related to depth and time-mean, suspended sediment concentrations (as functions of and D). Then, by assuming the transport of fine marine sediments approximates that of a dissolved tracer, the rate of estuarine supply can be determined by combining these derived mean concentrations with estimates of flushing time, F_T, based on L_I. By further assuming that all such sediments are deposited, minimum times for these deposition rates to in-fill estuaries are determined. These times range from a decade for the shortest, shallowest estuaries to upwards of millennia in longer, deeper estuaries with smaller tidal ranges.     

Non-linear channel–shoal dynamics in long tidal embayments

The dynamics of finite-amplitude bed forms in a tidal channel is studied with the use of an idealized morphodynamic model. The latter is based on depth-averaged equations for the tidal flow over a sandy bottom. The model considers phenomena on spatial scales of the order of the tidal excursion length. Transport of sediment mainly takes place as suspended load. The reference state of this model is characterized by a spatially uniform M₂ tidal current over a fixed horizontal bed. The temporal evolution of deviations from this reference state is governed by amplitude equations: these are a set of non-linear equations that describe the temporal evolution of bed forms. These equations are used to obtain new morphodynamic equilibria which may be either static or time-periodic. Several of these bottom profiles show strong similarity with the tidal bars that are observed in natural estuaries. The dependence of the equilibrium solutions on the value of bottom friction and channel width is investigated systematically. For narrow channels (width small compared to the tidal excursion length) stable static equilibria exist if bottom friction is slightly larger than r_cr. For channel widths more comparable to the tidal excursion length, multiple stable steady states may exist for bottom friction parameter values below r_cr. Regardless of channel width, stable time-periodic equilibria seem to emerge as the bottom friction is increased.Responsible Editor: Jens Kappenberg