Three-dimensional Hydrostatic Model Research Articles

The Effect of the Horizontal Dimensions of Inland Water Bodies on the Thickness of the Upper Mixed Layer

The effect of the horizontal dimensions of inland water bodies (lakes and reservoirs) on the vertical mixing processes is studied. We consider a three-dimensional hydrostatic model and a one-dimensional LAKE model based on the averaging of three-dimensional equations over a horizontal section of the water body. The processes of vertical mixing in both models were simulated with the use of k–e-closure. LAKE model takes into account the seiches through the parameterization of the pressure gradient and horizontal viscosity. The models were verified against the Kato-Phillips experiment data, and a series of numerical experiments was carried out to demonstrate the effect of the horizontal size of the water body on mixed-layer depth. It is shown that the horizontal dimensions of a water body has to be taken into account in the simulation of the vertical temperature distribution in lakes and reservoirs with the size much less than the internal Rossby deformation radius.

Numerical simulation of turbulent mixing and transport of biochemical substances in inland waters

Numerical modeling of inland water objects (lakes and reservoirs) and, in particular, mixing processes and transport of biochemical substances in these basins is considered. A three-dimensional hydrostatic model and a one-dimensional model LAKE based on averaging of three-dimensional equations over a horizontal section of a reservoir are used as tools for the calculations. In the LAKE model, seiche oscillations are taken into account by parameterizing the pressure gradient and horizontal eddy viscosity. A k-ε closure is used to describe the vertical exchange processes in both models. A parameterization of the Prandtl number is implemented in the 3D model which allows turbulence to persist at any values of the gradient Richardson number. The 3D model is also supplemented by equations for calculating biochemical substances by analogy with the one-dimensional biochemistry equations used in the LAKE model, which, in particular, allow us to study the transport of substances such as oxygen (O2) and methane (CH4). Numerical experiments aimed at studying turbulent mixing and transport of substances are carried out.

The life cycle of submesoscale eddies generated by topographic interactions

Abstract. Persian Gulf Water and Red Sea Water are salty and dense waters flowing at intermediate depths in the Gulf of Oman and the Gulf of Aden, respectively. Their spreading pathways are influence by mesoscale eddies that dominate the surface flow in both semi-enclosed basins. In situ measurements combined with altimetry indicate that Persian Gulf Water is stirred in the form of filaments and submesoscale structures by mesoscale eddies. In this paper, we study the formation and the life cycle of intense submesoscale vortices and their potential impact on the spreading of Persian Gulf Water and Red Sea Water. We use a primitive-equation three-dimensional hydrostatic model at a submesoscale-resolving resolution to study the evolution of submesoscale vortices. Our configuration idealistically mimics the dynamics in the Gulf of Oman and the Gulf of Aden: a zonal row of mesoscale vortices interacting with north and south topographic slopes. Intense submesoscale vortices are generated in the simulations along the continental slopes due to two different mechanisms. First, intense vorticity filaments are generated over the continental slope due to frictional interactions of the background flow with the sloping topography. These filaments are shed into the ocean interior and undergo horizontal shear instability that leads to the formation of submesoscale coherent vortices. The second mechanism is inviscid and features baroclinic instabilities arising at depth due to the weak stratification. Submesoscale vortices subsequently drift away, merge and form larger vortices. They can also pair with opposite-signed vortices and travel across the domain. They eventually dissipate their energy via several mechanisms, in particular fusion into the larger eddies or erosion on the topography. Since no submesoscale flow clearly associated with the fragments of Persian Gulf Water was observed in situ, we modeled Persian Gulf Water as Lagrangian particles. Particle patches are advected and sheared by vortices and are entrained into filaments. Their size first grows as the square root of time: a signature of the merging processes. Then, it increases linearly with time, corresponding to their ballistic advection by submesoscale eddies. On the contrary, without intense submesoscale eddies, particles are mainly advected by mesoscale eddies; this implies a weaker dispersion of particles than in the previous case. This shows the potentially important role of submesoscale eddies in spreading Persian Gulf Water and Red Sea Water.

A hybrid hydrostatic and non-hydrostatic numerical model for shallow flow simulations

Hydrodynamics of geophysical flows in oceanic shelves, estuaries, and rivers, are often studied by solving shallow water model equations. Although hydrostatic models are accurate and cost efficient for many natural flows, there are situations where the hydrostatic assumption is invalid, whereby a fully hydrodynamic model is necessary to increase simulation accuracy. There is a growing concern about the decrease of the computational cost of non-hydrostatic pressure models to improve the range of their applications in large-scale flows with complex geometries. This study describes a hybrid hydrostatic and non-hydrostatic model to increase the efficiency of simulating shallow water flows. The basic numerical model is a three-dimensional hydrostatic model solved by the finite volume method (FVM) applied to unstructured grids. Herein, a second-order total variation diminishing (TVD) scheme is adopted. Using a predictor–corrector method to calculate the non-hydrostatic pressure, we extended the hydrostatic model to a fully hydrodynamic model. By localising the computational domain in the corrector step for non-hydrostatic pressure calculations, a hybrid model was developed. There was no prior special treatment on mode switching, and the developed numerical codes were highly efficient and robust. The hybrid model is applicable to the simulation of shallow flows when non-hydrostatic pressure is predominant only in the local domain. Beyond the non-hydrostatic domain, the hydrostatic model is still accurate. The applicability of the hybrid method was validated using several study cases.

The role of diffraction effects in extreme run-up inundation at Okushiri Island due to 1993 tsunami

Abstract. The tsunami generated on 12 July 1993 by the Hokkaido–Nansei–Oki earthquake (Mw = 7.8) brought about a maximum wave run-up of 31.7 m, the highest recorded in Japan during the 20th century, near the Monai Valley on the west coast of Okushiri Island (Hokkaido Tsunami Survey Group, 1993). To reproduce the extreme run-up height, the three-dimensional non-hydrostatic model (Flow Science, 2012), referred to here as the NH-model, has been locally applied with open boundary conditions supplied in an offline manner by the three-dimensional hydrostatic model (Ribeiro et al., 2011), referred to here as the H-model. The area of the H-model is sufficiently large to cover the entire fault region with one-way nested multiple domains. For the initial water deformation, Okada's fault model (1985) using the sub-fault parameters is applied. Three NH-model experiments have been performed, namely without islands, with one island and with two islands. The experiments with one island and with two islands give rise to values close to the observation with maximum run-up heights of about 32.3 and 30.8 m, respectively, while the experiment without islands gives rise to about 25.2 m. The diffraction of the tsunami wave primarily by Muen Island, located in the south, and the southward topographic guiding of the tsunami run-up at the coast are, as in the laboratory simulation (Yoneyama et al., 2002), found to result in the extreme run-up height near Monai Valley. The presence of Hira Island enhances the diffraction of tsunami waves but its contribution to the extreme run-up height is marginal.

Predictability of currents on a mesotidal estuary (Ria de Vigo, NW Iberia)

In this contribution, the implementation, validation and sensitivity analysis of an operational forecasting system (three-dimensional hydrostatic model) in the Ria de Vigo is presented. A set of sensitivity tests for different atmospheric and hydrodynamic typical periods was performed. The goal is to determine the relative importance of forcing mechanisms in order to evaluate the source of errors in predictions. Previously, validations for three periods of about 15 days were compared with measured data. Sea-level evolution reveals low errors and correlation values close to 1. Surface velocities were compared with high-frequency radar and horizontal Acoustic Doppler Current Profiler data, showing acceptable results on radar area, where tidal and wind circulation patterns are well reproduced by the model. Conductivity, temperature, and depth profiles were used to validate simulated temperature and salinity. While modelled temperature profiles show good agreement with measured profiles, eventual errors are detected on salinity. The sensitivity analysis took three variables into account: sea level, currents at open boundary conditions, and winds (two different configurations). The results show that the most important source of errors on simulated surface currents is wind. Errors on open boundary conditions seem to be limited on the outermost part of the Ria. Although the results presented mainly focus on the Ria de Vigo, the method and conclusions may be applied to other mesotidal estuaries. Moreover, this work will allow a more effective operational system focused on coastal management to be performed.

Numerical model of the submarine fresh-water discharge in a karst cavity

We discuss the results of numerical experiments aimed at the reconstruction the structure of hydrophysical fields in a karst cavity (in the region of Cape Aiya on the South Coast of Crimea) observed in the course of the second specialized expedition in September 2008. To describe the process of submarine fresh-water discharge, we use a three-dimensional hydrostatic model with a priori specified boundaries of the layers (σ- and/or Z- levels) in the “rigid-lid” approximation including the procedure of “convective adjustment.” It is shown that only a good vertical resolution enables one to give a quantitatively correct description of a thin upper freshened layer of the sea. It is shown that, in order to get an adequate picture of the influence of bottom topography on the upper layer of the sea, it is reasonable to use a mixed grid along the vertical combining the σ- and Z- coordinates. We also present the results of numerical experiments allowing us to estimate the effects of location, number, and power of fresh-water sources placed on the lateral boundary of the cavity.

A scalable unstructured grid 3-dimensional finite volume model for the shallow water equations

We present an unstructured grid finite volume three-dimensional hydrostatic model. An important aspect in 3D models is the choice of horizontal discretisation. For problems that are governed by complex coastal boundaries an unstructured grid approach seems attractive. This paper focuses on the development of a new unstructured grid three-dimensional hydrostatic model. An efficient and highly scalable implicit solution technique is adopted for the solution of the free surface elevation and an semi-Lagrangian approach is adopted for the advection of momentum and scalars. A number of tests are presented which show that the model is capable of simulating Kelvin waves in a circular basin and the North Sea.

A three-dimensional hydrostatic model for coastal and ocean modelling using a generalised topography following co-ordinate system

A three-dimensional hydrostatic model is presented that combines a generalised vertical co-ordinate system with an efficient implicit solution technique for the free surface. The model is capable of maintaining high resolution in the surface and/or bottom boundary layers as well as dealing with steep topography. Horizontal diffusion is calculated using the Smagorinsky formulation and a k– ε turbulence model is used in the vertical. In addition the model uses higher-order advection routines. An important aspect in three-dimensional models is the choice of vertical discretisation. If one is mostly interested in problems which are governed by boundary layer flows, a terrain following or sigma co-ordinate system seems attractive. This paper focuses on the development of a generalised sigma-type grid in a three-dimensional hydrostatic model. The generalised grid offers a wide range of possibilities including grid refinement toward the bed or surface, a mixed layer transformation, and a constant layer transformation where the lowermost or uppermost grid cells can be specified to have a constant height above the bed or below the surface. A number of tests are presented which show that the model is capable of simulating both shallow nearshore, estuarine flows as well as large-scale geophysical flows. These include an extreme flooding event in the shallow North Sea and the Odden ice tongue formation in the Greenland Sea.

Inland and Offshore Propagation Speeds of a Sea Breeze from Simulations and Measurements

The inland and offshore propagation speeds of a sea breeze circulation cell are simulated using a three-dimensional hydrostatic model within a terrain-following coordinate system. The model includes a third-order semi-Lagrangian advection scheme, which compares well in a one-dimensional stand-alone test with the more complex Bott and Smolarkiewicz advection schemes. Two turbulence schemes are available: a local scheme by Louis (1979) and a modified non-local scheme based on Zhang and Anthes (1982). Both compare well with higher-order closure schemes using the Wangara data set for Day 33–34 (Clark et al., 1971). Two-dimensional cross-sections derived from airborne sea breeze measurements (Finkele et al. 1995) constitute the basis for comparison with two-dimensional numerical model results. The offshore sea breeze propagation speed is defined as the speed at which the seaward extent of the sea breeze grows offshore. On a study day, the offshore sea breeze propagation speed, from both measurements and model, is -3.4 m s-1. The measured inland propagation speed of the sea breeze decreased somewhat during the day. The model results show a fairly uniform inland propagation speed of 1.6 m s-1 which corresponds to the average measured value. The offshore sea breeze propagation speed is about twice the inland propagation speed for this particular case study, from both the model and measurements. The influence of the offshore geostrophic wind on the sea breeze evolution, offshore extent and inland penetration are investigated. For moderate offshore geostrophic winds (-5.0 m s-1), the offshore and inland propagation speeds are non-uniform. The offshore extent in moderate geostrophic wind conditions is similar to the offshore extent in light wind conditions (-2.5 m s-1). The inland extent is greater in light offshore geostrophic winds than in moderate ones. This suggests that the offshore extent of the sea breeze is less sensitive to the offshore geostrophic wind than its inland extent. However, these results hold only if it is possible to define an inland propagation speed. For stronger offshore geostrophic winds (-7.5 m s-1), the sea breeze is completely offshore and the inland propagation speed is ill-defined.

Sensitivity studies on the air flow characteristics In Kharagpur using a meso-scale model


 A three-dimensional hydrostatic model has been employed for the study of sea breeze circulations over south West Bengal with special reference to an inland station Kharagpur (22°.21' N, 87° 19'E). A series of sensitivity experiments have been performed to stress the Importance of differential heating on circulation over south West Bengal during pre-monsoon period. It is found that due to differential heating rate between land and sea surfaces, sea breezes can penetrate to the inland station Kharagpur and beyond even in case of moderate gradient wind. Surface observations at Kharagpur and pilot balloon observation at nearby station Kalaikunda are used to compare the model results. The onset of sea breezes, variation of the air temperature and humidity are In fairly good agreement whereas It over estimates the depth of the circulation and cannot predict the variation of the late morning hours surface wind.

Mean Fields Induced by Local Gravity-Wave Forcing in the Middle Atmosphere

The role of geostrophic adjustment in the middle atmosphere for given wave packet forcing by a three-dimensional hydrostatic model is examined. It is shown that the induced fields consist of two different kinds of modes. One, produced by forcing vorticity only, is steady quasi-geostrophic flow; this is restricted to the forcing region. The other, produced by both forcing vorticity and forcing divergence, is oscillatory, and is in the form of gravity waves propagating out of the forcing region plus inertial oscillations in the forcing region. The scales and amplitudes of the induced gravity waves are determined by the forcing. For a typical example, a 200 km x 200 km gravity wave packet of momentum flux 0.5 N/sq m absorbed in a layer of 5 km thickness centered near 18 km altitude, the gravity waves spread to a larger region about 1000 km x 1000 km at a level 7 km above the forcing region. At that level, the horizontal and vertical wavelengths of the induced waves are about 300 km and 7 km respectively, and the momentum flux is substantially reduced to 0.0004 N/sq m. The results suggest that geostrophic adjustment processes may play an important role in specifying the gravity wave spectrum in the middle atmosphere.

A Numerical Study of Strong Katabatic Winds over Antarctica

Abstract Certain coastal sections of Antarctica, most notably Adelie Land and Terra Nova Bay, experience anomalously intense, persistent katabatic winds. The forcing of such katabatic outflow is believed to originate several hundred kilometers upslope in the interior of the continent where cold air drainage currents from a large area converge into a relatively narrow zone focused on the steeply-sloping ice terrain near the coastline. Numerical simulations with a three-dimensional hydrostatic model incorporating terrain features representative of Adelie Land reveal a significant topographical channeling of the surface airflow. Katabatic wind speeds as depicted by the model are greatly enhanced downslope of the convergence channel. These results emphasize the importance of topography in the continental interior in shaping the character of coastal katabatic flow.