Effects of hydrostatic approximation and resolution on the simulation of convective adjustment

A two-dimensional non-hydrostatic ocean model and a hydrostatic version of the same model are used to simulate convective adjustment, without the use of an instantaneous adjustment parameterization. The model geometry is a domain on the vertical plane of width 40 km and depth 500 m. Model results for four cases are examined: hydrostatic and non-hydrostatic, at 0.1 and 1 km spatial resolution. The convectively adjusted stable state obtained in all four cases are qualitatively similar; thus the hydrostatic approximation does not eliminate convective adjustment. The details of the simulated convective plumes depend on resolution and whether the hydrostatic approximation is made. The adjusted state has significant stratification which cannot be captured by the conventional instantaneous adjustment or diffusion-based parameterizations. We also compare the results to the case when an instantaneous adjustment parameterization is used.     

Acoustic-gravity waves in a nonadiabatic atmosphere

The effect of a real departure of the atmosphere from the adiabaticity condition on the generation and dissipation of acoustic-gravity waves (AGWs) throughout the entire height of the atmosphere up to the mesopause (≈90 km) is studied. The results of solving the derived dispersion equation can be helpful in the formation of boundary conditions during simulation of the propagation of wave disturbances in the thermosphere and above. Unlike an adiabatic model, in a nonadiabatic model of the atmosphere, the frequencies (the roots of the dispersion equation) are complex and waves attenuate in some atmospheric layers, whereas other layers are unstable with respect to the onset of the corresponding AGW modes. As the height increases, the phase velocities of both acoustic and gravity branches of AGWs decrease and dissipation is enhanced. It is shown that macroscopic flows, along with periodic disturbances, are generated in a nonadiabatic atmosphere.     

Controlling spatial oscillations in bed level update schemes

A frequent problem with process-based coastal morphological models is the appearance of high wave number spatial oscillations in the simulated bed levels with time. After a sufficiently long time, these oscillations become dominant and mask the large-scale features of the bed level evolution.The equation for conservation of sediment mass is used to show that the spatial oscillations are generated by the dependence of the bed celerity (celerity of the bed level oscillations) with bed levels, which is due to the non-linear relationship between sediment transport and bed levels. This breeds higher spatial harmonics of the bed level oscillations with time. In this situation, using a Finite Difference (FD) scheme that does not damp oscillations with high wave numbers leads to the generated harmonics being kept in the solution. These generate further harmonics until the entire solution is dominated by high wave number oscillations.In this paper, a finite difference scheme, in combination with a filtering procedure, is used to dissipate high wave number oscillations. Analysis of the amplification portraits show that the filtering procedure in combination with a Lax–Wendroff scheme does not affect oscillations with lower wave numbers (larger scale features resolved with seven or more grid points). Some examples are also presented to illustrate these features.     

Analysis of Dynamic Characteristics of Submarine Free Spanning Pipelines by Complex Damping Method

Considering the effect of the internal flowing fluid and the external marine environmental condition, the differential equation for the vortex-induced vibration (V1V) of the free spanning pipeline is derived and is discretized by the Hermit interpolation function. The free vibration equation with the damping term is solved by the complex damping method for the natural frequency, and then the effect of fluid damping on the natural frequency of the free spanning pipeline is analyzed.The results show that fluid damping has a significant influence on the damped natural frequency of the free spanning pipeline in the lock-in state, while it has little influence when the pipeline is out of the lock-in state. In the meantime,the change of the free span length has the same effect on the damped natural frequency and the undamped natural frequency.     

On resonant Rossby–Haurwitz triads

The dynamics of non-divergent flow on a rotating sphere are described by the conservation of absolute vorticity. The analytical study of the non-linear barotropic vorticity equation is greatly facilitated by the expansion of the solution in spherical harmonics and truncation at low order. The normal modes are the well-known Rossby–Haurwitz (RH) waves, which represent the natural oscillations of the system. Triads of RH waves, which satisfy conditions for resonance, are of critical importance for the distribution of energy in the atmosphere.
We show how non-linear interactions of resonant RH triads may result in dynamic instability of large-scale components. We also demonstrate a mathematical equivalence between the equations for an orographically forced triad and a simple mechanical system, the forced-damped swinging spring. This equivalence yields insight concerning the bounded response to a constant forcing in the absence of damping. An examination of triad interactions in atmospheric reanalysis data would be of great interest.     

On damping models in free and forced rolling motion

In this paper two different models for the damping moment to introduce in the rolling equation of the ship are proposed. They contain two terms, respectively linear-quadratic and linear-cubic in the angular velocity, and furthermore they foresee a non-linear term representing the dependence of the damping from the heeling angle. These models constitute a generalization of all the models up to now used in the naval literature.With the Bogoliubov-Krilov asymptotic method approximate relations, describing the decay curve of the free oscillations and the maximum roll amplitude in synchronism condition, are obtained. The analysis shows that the choice of the more realistic damping model cannot be based on the simple verification of a good fitting of the free oscillation decay curves. It is necessary to examine also the behaviour of the forced oscillations in synchronism.Finally, a plan of experiments which allows the determination of separate values for the different non-linear damping coefficients is proposed.     

Modelling argon dynamics in first-year sea ice

Focusing on physical processes, we aim at constraining the dynamics of argon (Ar), a biogeochemically inert gas, within first year sea ice, using observation data and a one-dimensional halo-thermodynamic sea ice model, including parameterization of gas physics. The incorporation and transport of dissolved Ar within sea ice and its rejection via gas-enriched brine drainage to the ocean, are modeled following fluid transport equations through sea ice. Gas bubbles nucleate within sea ice when Ar is above saturation and when the total partial pressure of all three major atmospheric gases (N₂, O₂ and Ar) is above the brine hydrostatic pressure. The uplift of gas bubbles due to buoyancy is allowed when the brine network is connected with a brine volume above a given threshold. Ice-atmosphere Ar fluxes are formulated as a diffusive process proportional to the differential partial pressure of Ar between brine inclusions and the atmosphere. Two simulations corresponding to two case studies that took place at Point Barrow (Alaska, 2009) and during an ice-tank experiment (INTERICE IV, Hamburg, Germany, 2009) are presented. Basal entrapment and vertical transport due to brine motion enable a qualitatively sound representation of the vertical profile of the total Ar (i.e. the Ar dissolved in brine inclusions and contained in gas bubbles; TAr). Sensitivity analyses suggest that gas bubble nucleation and rise are of most importance to describe gas dynamics within sea ice. Ice-atmosphere Ar fluxes and the associated parameters do not drastically change the simulated TAr. Ar dynamics are dominated by uptake, transport by brine dynamics and bubble nucleation in winter and early spring; and by an intense and rapid release of gas bubbles to the atmosphere in spring. Important physical processes driving gas dynamics in sea ice are identified, pointing to the need for further field and experimental studies.     

Studies on Stochastic Parametric Roll of Ship with Stochastic Averaging Method

The paper studies the parametric stochastic roll motion in the random waves. The differential equation of the ship parametric roll under random wave is established with considering the nonlinear damping and ship speed. Random sea surface is treated as a narrow-band stochastic process, and the stochastic parametric excitation is studied based on the effective wave theory. The nonlinear restored arm function obtained from the numerical simulation is expressed as the approximate analytic function. By using the stochastic averaging method, the differential equation of motion is transformed into Ito's stochastic differential equation. The steady-state probability density function of roll motion is obtained, and the results are validated with the numerical simulation and model test.     

Altitude-latitude structure of the vertical wind component of the migrating diurnal tide in the range of heights from 80 to 100 km

Based on empirical monthly data on the parameters of oscillations in the horizontal wind component of the diurnal migrating tide, we calculated the altitude-latitude distributions of the parameters of oscillations in the vertical wind component of the diurnal tide in the region of the mesosphere and lower thermosphere (80–100 km). The initial data were obtained from satellite observations of the mesosphere and lower thermosphere at altitudes from 90 to 120 km and from data of ground-based sounding of this region using the radio meteor method and the method of partial reflections in the altitude range from 80 to 100 km. We compare the resulting distributions with the results of numerical modeling for the migrating diurnal tide using a global circulation model for the middle and upper atmosphere. It is shown that, accurate to measurement errors, there is a good agreement between the distributions of parameters of the migrating diurnal tide obtained by the models. One specific feature of the empirical distributions of the amplitude of the vertical wind oscillations is that there are three regions of increased amplitude values—in the vicinity of the equator and at 30° N and 30° S latitudes—which were observed for all seasons. The maximum value of the amplitude of the vertical wind oscillations is approximately 0.1 m/s. The divergence of the Eliassen-Palm flux was estimated to be on the order of 10 m s⁻¹ day⁻¹.     

海洋立管复模态动力特性分析

考虑阻尼的影响,研究海洋立管的动力特性。通过分析管内流体及管外海洋环境荷载的共同作用,建立海洋立管涡激振动偏微分方程,进而得到立管动力特性方程,用复模态分析法求解动力特性方程得到立管考虑阻尼的自振频率。算例计算表明:考虑阻尼的立管自振频率略小于不考虑阻尼的立管自振频率;立管的自振频率随着内流流速的增加而减小,但内流流速不大时,影响较小;管道长度对立管的自振频率影响较大。     

A numerical study of a shallow sea front generated by the buoyancy flux

We numerically investigated the physical process of water exchange caused by fluctuations of the front. This front is formed in a vertically two-dimensional NH-model (non-hydrostatic model) under steady forcing and simulates well the front observed during winter in the Kii Channel, Japan. The velocity field in the model has two kinds of oscillations. The first has a period of 6∼12 hr and is caused by intermittent gravitational convection in the frontal zone. The period and the intensity of intermittent convection are determined by buoyancy flux through the side boundaries as well as surface cooling. The other is associated with large scale circulation driven at the side boundaries and is controlled by the Coriolis force and the bottom stress. Its period of 3∼4 days is determined by the sum of the inertial period and the spin down time for the baroclinic mode of the along-front velocity component. These oscillations make the position of the front fluctuate with the same periods. We next examined water exchange across the fluctuating front by numerically tracking a number of labelled particles. Intermittent convection induces exchange of particles in the frontal zone and large scale circulations transport the exchanged particles toward offshore or onshore through the lower layer. The exchange rate and the dispersion coefficient are calculated in the NH-model as 0.85 and 2.3×10³ cm² sec⁻¹, respectively. On the other hand, in the H-model (hydrostatic model) parameterizing gravitational convections with a convective adjustment method, these values are reduced to 0.68 and 3.2×10² cm² sec⁻¹, respectively. This result implies that intermittent convections in the frontal zone have a large effect on water exchange across the front, and that no little water is exchanged across the fluctuating front in an actual shallow sea, such as observed in the Kii Channel.     

The role of nonhydrostatic dynamics in controlling development of a surface ocean front

Numerical studies of surface ocean fronts forced by inhomogeneous buoyancy loss show nonhydrostatic convective plumes coexisting with baroclinic eddies. The character of the vertical overturning depends sensitively on the treatment of the vertical momentum equation in the model. It is less well known how the frontal evolution over scales of O(10 km) is affected by these dynamics. Here, we compare highly resolved numerical experiments using nonhydrostatic and hydrostatic models and the convective-adjustment parametrization. The impact of nonhydrostatic processes on average cross-frontal transfer is weak compared to the effect of the O(1 km) scale baroclinic motions. For water-mass distribution and formation rate nonhydrostatic dynamics have similar influence to the baroclinic eddies although adequate resolution of the gradients in forcing fluxes is more important. The overall implication is that including nonhydrostatic surface frontal dynamics in ocean general circulation models will have only a minor effect on scales of O(1 km) and greater.     

Comparison between refraction angles measured in the Microlab-1 experiment and calculated on the basis of an atmospheric general circulation model

The differences between the refraction angles measured and calculated for the reanalyses of the European Centre for Medium-Range Weather Forecasts were statistically analyzed on the basis of 64 radio occultation events recorded by the Microlab-1 satellite. It is shown that, for minimum ray heights below 20 km, the main contribution to the differences is made by spatial refractive-index fluctuations neglected by the model. The power spectral density of these fluctuations is mainly concentrated within the vertical wave-number range 0.5–10 rad/km. For heights above 30 km, the deviations are mainly determined by ionospheric disturbances and may vary several times during changes of the site and time of observations. This suggests that the results of satellite radio-occultation sounding of the neutral atmosphere can be used as an indirect quantitative estimate of local discrepancies between the actual field of the refractive index and its values calculated on the basis of a hydrodynamic atmospheric general circulation model.     

Numerical model of nonhydrostatic ocean dynamics based on methods of artificial compressibility and multicomponent splitting

An algorithm is proposed for solving three-dimensional ocean hydrodynamics equations without hydrostatic approximation and traditional simplification of Coriolis acceleration. It is based on multicomponent splitting of the modified model with artificial compressibility. The original system of equations is split into two subsystems describing the transport of three velocity components and adjustment of the density and velocity fields. At the adjustment stage, the horizontal velocity components are represented as a sum of the depth means and deviations; the two corresponding subsystems are derived. For barotropic dynamics, the compressibility effect is represented as the boundary condition at the free surface, while for the baroclinic subsystem, it is introduced as ε-regularization of the continuity equation. Then, the baroclinic equations are split into two subsystems describing the hydrostatic and nonhydrostatic dynamics. The nonhydrostatic dynamics is computed at a separate splitting stage. The algorithm is included into the Institute of Numerical Mathematics of the Russian Academy of Sciences model based on “primitive” equations and verified by solving the hydrodynamics problem for the Sea of Marmara.     

Modeling vertical motion at ocean fronts: Are nonhydrostatic effects relevant at submesoscales?

Through a suite of three-dimensional, high-resolution numerical modeling experiments, we examine the role of nonhydrostatic effects on O(1 km) submesoscale processes at ocean fronts, with particular focus on the vertical velocity field. Several differences between nonhydrostatic and hydrostatic models are pointed out using a framework that enables precise comparison, but it is difficult to identify categorical differences between the model solutions at the grid resolutions afforded. The instantaneous vertical velocity structure is sensitive to the model choice and, even more so, to grid resolution, but the average vertical flux is similar in both hydrostatic and nonhydrostatic cases.When a frontal region with horizontal density gradients is perturbed by wind, a profusion of submesoscale, O(1 km), secondary circulation features develops in the upper 50 m. Narrow, elongated cells of intense up- and down-welling are found to occur close to the surface, overlying broader regions of weaker up- and down-welling associated with the mesoscale meanders of the baroclinically unstable front. The submesoscale down-welling is considerably stronger than up-welling and is concentrated in 1–2 km width filaments within which velocities can attain magnitudes as high as 200 m day⁻¹. The submesoscale features are found to be robust at horizontal grid resolutions varying between 1 and 0.25 km and exist even in the hydrostatic model. Submesoscale circulation is difficult to observe or resolve in coarser resolution circulation models, but is likely to play a significant role in the exchange of energy and properties between the surface ocean and thermocline. Possible mechanisms for the generation of these features are investigated in a follow-on paper.     

Stochastic stability of tethered buoyant platforms

A moment method for analysing the stochastic stability of the surge motion of a tethered buoyant platform (TBP) in a random sea is examined. In the differential equation describing the surge motion the variation of tether tension caused by the vertical component of the wave forces is random-time dependent in form. The asymptotic moment behaviour of the solution is determined and approximated in terms of an integral equation. Under the assumption of a narrow band process imposed upon the random coefficient, the stability results are obtained with the aid of deterministic stability theory. The mean square stability is studied and criteria for stability are obtained in terms of the damping coefficient and the auto-correlation function of the random sea.     

Numerical Wave Tank Based on A Conserved Wave-Absorbing Method

Recently the numerical wave tank has become a widely-used tool to study waves as well as wave-structure interactions, and the wave-absorbing method is very important as its effect on the quality of waves generated. The relaxation method and the derived momentum source method are often utilized, however, the damping weight is constant during calculation and repeated trials are required to obtain an acceptable wave-absorbing effect. To address the above- mentioned issues, a conserved wave-absorbing method is developed. The damping weight is determined by solving the mass conservation equation of the absorbing region at every time step. Based on this method, a two-dimensional numerical wave tank is established by using the VB language to simulate various waves by which the validation of this method is evaluated.     

Frictional influence on sea level oscillations in Otago Harbour,New Zealand

Oscillations in Otago Harbour, (45° 49’ S, 170° 38’ E) produced by the 1960 Chilean Tsunami are found by spectral analysis to have most of their energy at a period of about 80 min. By numerically integrating a one‐dimensional linear momentum equation and the continuity equation for various sections of the harbour, this period is found to correspond to the quarter wavelength oscillation in the main channel between the mouth of the harbour and the Halfway Islands. The large value of the linear frictional coefficient, calculated from the phase of the tide in the harbour, and the resulting excessive damping, indicates why long period non‐tidal oscillations are generally not found in the harbour.     

On several mechanisms of the formation of the compensated thermohaline inhomogeneities in the ocean

The process of the geostrophic adjustment in the stably stratified two-component medium is studied in the framework of a linear approximation. We demonstrate that, at the final stage of that process, a stationary trace is generated by the distribution of the temperature and salinity, whose horizontal inhomogeneities mutually compensate in the field of the density. The compensation level for the stationary thermohaline distributions forming during the geostrophic adjustment is estimated. The origination mechanism of compensated thermohaline inhomogeneities in hydrodynamically stable shear flows is examined. We show that, in such flows, the disturbances of the fields of buoyancy (density), pressure, and velocity damp with time, whereas the compensated disturbances of the fields of the temperature and salinity are carried off by the flow without damping. Based on the explicit solutions of the dynamic equations, it is shown that the evolution of the compensated distribution of the temperature and salinity in the shear flows usually results in the sharpening of the spatial gradients. This feature may be, among others, related to one of the factors of the origination of the fine structure of the ocean: the small-scale thermohaline inhomogeneities, which exist against the background of the smooth vertical distribution of the density.     

Height-season structure of the available potential energy and kinetic energy in the lower and middle atmosphere

The distributions of kinetic energy (KE) and available potential energy (APE) in the lower and middle atmosphere of the Northern and Southern hemispheres over the period 1992–2003 are investigated. Annual mean values of the amplitude and phase of annual and semiannual oscillations in the zonal and eddy forms of KE and APE are calculated in the height range 0–55 km (1000–0.316 hPa) for the 21st layer. A clearly pronounced annual cycle of the zonal and eddy components of KE and APE with maxima in the winter season are observed in the troposphere of both hemispheres. In the lower stratosphere, the annual-cycle maximum is shifted toward the summer season because of the meridional gradient of the zonal mean temperature. In the stratosphere of both hemispheres, along with annual oscillations, semiannual oscillations are present in all forms of energy. The intensity of these oscillations for the zonal KE and APE at the upper-stratosphere heights is comparable to the intensity of annual oscillations. A local structure of the energy regime of the upper mesosphere-lower thermosphere is investigated against the background of the global energy regime from the data of meteor sounding in Kazan. It is shown that, for both the global and regional regimes, specific features of the phase profiles of energy characteristics can be explained by the presence of barriers during the propagation of wave disturbances along the vertical.