Wake analysis for supersonic decelerator applications. Volume 1 - Theoretical analysis and correlation of wind-tunnel and shallow-water tow channel results
Wake analysis and correlation of wind tunnel and shallow water tow channel data
Lau, R. A.↗
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An energy and potential enstrophy conserving scheme for the shallow water equations
A three-dimensional finite difference scheme for the solution of the shallow water momentum equations which accounts for the conservation of potential enstrophy in the flow of a homogeneous incompressible shallow atmosphere over steep topography as well as for total energy conservation is presented. The scheme is derived to be consistent with a reasonable scheme for potential vorticity advection in a long-term integration for a general flow with divergent mass flux. Numerical comparisons of the characteristics of the present potential enstrophy-conserving scheme with those of a scheme that conserves potential enstrophy only for purely horizontal nondivergent flow are presented which demonstrate the reduction of computational noise in the wind field with the enstrophy-conserving scheme and its convergence even in relatively coarse grids.
Arakawa, A.↗
Using Hough harmonics to validate and assess nonlinear shallow-water models
The implementation of a technique for locating programming errors in shallow-water codes, establishing the correctness of the code, and assessing the performance of the numerical model under various flow conditions is described. The right-hand side of the differential equations is modified in such a way that the exact solution of the nonlinear initial-value problem is known, so that the truncation errors of the numerical scheme can be studied in detail. The exact solution is prescribed to be any linear combination of Hough harmonics which propagate in time according to their natural frequencies.
Dee, Dick P.↗
Solving the shallow water equations on the Cray X-MP/48 and the connection machine 2
The shallow water equations in Cartesian coordinates and 2-D are solved on the Connection Machine 2 (CM-2) using both the spectral and finite difference methods. A description of these implementations is presented together with a brief discussion of the CM-2 as it relates to these specific computations. The finite difference code was written both in C* and *LISP and the spectral code was written in *LISP. The performance of the codes is compared with a FORTRAN version that was optimized for the Cray X-MP/48.
Swarztrauber, Paul N.↗
Theory of the investigation of the atmosphere of binary stars by use of the analogy between gas dynamics and shallow water flow
Theoretical investigation of atmosphere of binary stars based on analogy between gas dynamics and shallow water flow
BINARY STAR↗
Documentation of the Goddard Laboratory for atmospheres fourth-order two-layer shallow water model
The theory and numerical treatment used in the 2-level GLA fourth-order shallow water model are described. This model was designed to emulate the horizontal finite differences used by the GLA Fourth-Order General Circulation Model (Kalnay et al., 1983) in addition to its grid structure, form of high-latitude and global filtering, and time-integration schemes. A user's guide is also provided instructing the user on how to create initial conditions, execute the model, and post-process the data history.
Takacs, L. L.↗
Shallow Water Optical Water Quality Buoy
This NASA grant was funded as a result of an unsolicited proposal submission to Kennedy Space Center. The proposal proposed the development and testing of a shallow water optical water quality buoy. The buoy is meant to work in shallow aquatic systems (ponds, rivers, lagoons, and semi-enclosed water areas where strong wind wave action is not a major environmental During the project period of three years, a demonstration of the buoy was conducted. The last demonstration during the project period was held in November, 1996 when the buoy was demonstrated as being totally operational with no tethered communications line. During the last year of the project the buoy was made to be solar operated by large gel cell batteries. Fund limitations did not permit the batteries in metal enclosures as hoped for higher wind conditions, however the system used to date has worked continuously for in- situ operation of over 18 months continuous deployment. The system needs to have maintenance and somewhat continuous operational attention since various components have limited lifetime ages. For example, within the last six months the onboard computer has had to be repaired as it did approximately 6 months after deployment. The spectrograph had to be repaired and costs for repairs was covered by KB Science since no ftmds were available for this purpose after the grant expired. Most recently the computer web page server failed and it is currently being repaired by KB Science. In addition, the cell phone operation is currently being ftmded by Dr. Bostater in order to maintain the system's operation. The above points need to be made to allow NASA to understand that like any sophisticated measuring system in a lab or in the field, necessary funding and maintenance is needed to insure the system's operational state and to obtain quality factor. The proposal stated that the project was based upon the integration of a proprietary and confidential sensor and probe design that was developed by KB Science and Engineering and is currently patented by KB Science. The buoy's purpose was to collected hyperspectral optical signatures for analysis and resulting estimation of water quality parameters such as chlorophyll-a, seston and dissolved organic matter (DOC). The ultimate goal of the project was to develop a buoy that would integrate a probe to measure upwelling light from a source and thus relate this backscattered light to water quality parameters.
Bostater, Charles↗
Comparison of Damage from Hydrocode Simulations of an Asteroid Airburst or Impact on Land, in Deep, or in Shallow Water
If an asteroid is discovered to be on a collision course with Earth and there is insufficient time for a deflection effort to make it miss Earth completely, should it be redirected to a land or ocean impact? While distance from densely populated areas should obviously be maximized, the differing ability of air blast, seismic waves, and tsunami waves to cause damage at distance does not make the choice between land and ocean impacts an immediately obvious one. More broadly this work is a step towards improving damage models from asteroid impacts. This extended abstract follows the hypothetical scenario of the 2017 IAA Planetary Defense Conference where a 100-250m diameter asteroid is on a potential impact course with Earth. A hydrocode was used to simulate impacts into the most sparsely populated areas along the eastern end of the hypothetical impact corridor- specifically in the Gobi Desert, in the shallow waters of the Sea of Japan, and in the deep waters of the Japan Trench in the Pacific Ocean.
Shallow Water↗
Uncertainties in Simulating Flooding During Hurricane Harvey Using 2D Shallow Water Equations
Abstract Flooding is one of the most impactful weather‐related natural hazards. Numerical models that solve the two dimensional (2D) shallow water equations (SWE) represent the first‐principles approach to simulate all types of spatial flooding, such as pluvial, fluvial, and coastal flooding, and their compound dynamics. High spatial resolution (e.g., () m) is needed in 2D SWE simulations to capture flood dynamics accurately, resulting in formidable computational challenges. Thus, relatively coarser spatial resolutions are used for large‐scale simulations of flooding, which introduce uncertainties in the results. It is unclear how the uncertainty associated with the model resolution compares to the uncertainties in precipitation data sets and assumptions regarding boundary conditions when channelized flows interact with other water bodies. In this study, we compare these three sources of uncertainties in 2D SWE simulations for the 2017 Houston flooding event. Our results show that precipitation uncertainty and mesh resolution have more significant impacts on the simulated streamflow and inundation dynamics than the choice of the downstream boundary condition at the watershed outlet. We point out the viability to confine the uncertainty of coarsening mesh resolution by using the variable resolution mesh (VRM) which refines critical topographic features with far fewer grid cells. Specifically, in simulations with VRM, the simulated inundation depths over the refined region are comparable to that use the finest uniform mesh. This study contributes to understanding the challenges and pathways for applying 2D SWE models to improve the realism of flood simulations over large scales.
54 ENVIRONMENTAL SCIENCES↗
Semi-Lagrangian integration of a gridpoint shallow water model on the sphere
A stable, semi-Lagrangian, semi-implicit, two-time-level, gridpoint integration scheme for the shallow water equations on the sphere is presented. A rotated spherical coordinate system is used to integrate the equations of motion at each gridpoint poleward of a certain latitude, thus overcoming problems associated with the polar singularity. The results of medium term integrations of large scale test patterns using a long time step are presented.
Mcdonald, A.↗
Balanced Central Schemes for the Shallow Water Equations on Unstructured Grids
We present a two-dimensional, well-balanced, central-upwind scheme for approximating solutions of the shallow water equations in the presence of a stationary bottom topography on triangular meshes. Our starting point is the recent central scheme of Kurganov and Petrova (KP) for approximating solutions of conservation laws on triangular meshes. In order to extend this scheme from systems of conservation laws to systems of balance laws one has to find an appropriate discretization of the source terms. We first show that for general triangulations there is no discretization of the source terms that corresponds to a well-balanced form of the KP scheme. We then derive a new variant of a central scheme that can be balanced on triangular meshes. We note in passing that it is straightforward to extend the KP scheme to general unstructured conformal meshes. This extension allows us to recover our previous well-balanced scheme on Cartesian grids. We conclude with several simulations, verifying the second-order accuracy of our scheme as well as its well-balanced properties.
Bryson, Steve↗
A potential enstrophy and energy conserving scheme for the shallow water equations
To improve the simulation of nonlinear aspects of the flow over steep topography, a potential enstrophy and energy conserving scheme for the shallow water equations is derived. It is pointed out that a family of schemes can conserve total energy for general flow and potential enstrophy for flow with no mass flux divergence. The newly derived scheme is a unique member of this family, that conserves both potential enstrophy and energy for general flow. Comparison by means of numerical experiment with a scheme that conserves (potential) enstrophy for purely horizontal nondivergent flow demonstrated the considerable superiority of the newly derived potential enstrophy and energy conserving scheme, not only in suppressing a spurious energy cascade but also in determining the overall flow regime. The potential enstrophy and energy conserving scheme for a spherical grid is also presented.
Arakawa, A.↗
Variational data assimilation with a semi-Lagrangian semi-implicit global shallow-water equation model and its adjoint
An adjoint model is developed for variational data assimilation using the 2D semi-Lagrangian semi-implicit (SLSI) shallow-water equation global model of Bates et al. with special attention being paid to the linearization of the interpolation routines. It is demonstrated that with larger time steps the limit of the validity of the tangent linear model will be curtailed due to the interpolations, especially in regions where sharp gradients in the interpolated variables coupled with strong advective wind occur, a synoptic situation common in the high latitudes. This effect is particularly evident near the pole in the Northern Hemisphere during the winter season. Variational data assimilation experiments of 'identical twin' type with observations available only at the end of the assimilation period perform well with this adjoint model. It is confirmed that the computational efficiency of the semi-Lagrangian scheme is preserved during the minimization process, related to the variational data assimilation procedure.
Li, Y.↗
Comparison of horizontal difference schemes for the shallow water equations on a sphere
The accuracy of horizontal difference schemes used in the hydrodynamics parts of General Circulation Models are compared by means of numerical experiments for the shallow water equations on a sphere. As expected, the phase lag of moving waves decreases as the order of accuracy of a scheme increases or as the grid resolution increases. Overall, Takano and Wurtele's partial fourth order energy and potential enstrophy conserving scheme on the C grid is most accurate. It is clearly superior to the other schemes for the Rossby-Haurwitz wave number 6 initial conditions for coarse grid resolution.
Russell, Gary L.↗
A multigrid solver for semi-implicit global shallow-water models
A multigrid solver is developed for the discretized two-dimensional elliptic equation on the sphere that arises from a semiimplicit time discretization of the global shallow-water equations. Different formulations of the semiimplicit scheme result in variable-coefficient Helmholtz-type equations for which no fast direct solvers are available. The efficiency of the multigrid solver is optimal, in the sense that the total operation count is proportional to the number of unknowns. Numerical experiments using initial data derived from actual 300-mb height and wind velocity fields indicate that the present model has very good accuracy and stability properties.
Barros, Saulo R. M.↗
Shallow water experiments using an improved Kreiss-Oliger 2-4 scheme
The Abarbanel-Gottleib (AG) modification of the Kreiss-Oliger (KO) scheme is applied to a global 1-level shallow water model and the results compared to results obtained using the standard KO scheme. The standard KO scheme consists of the second order leapfrog scheme for time derivatives and fourth order space differencing for spatial derivatives. The AG scheme modifies the KO scheme in a manner similar to that done by Wilson to the multidimensional leapfrog scheme, obtaining a 35-40% improvement of the maximum time step. Application of the AG scheme expands the domain of influence of the KO scheme by including off-axis grid points.
Takacs, L. L.↗
Assimilation of TOPEX Sea Level Measurements with a Reduced-Gravity, Shallow Water Model of the Tropical Pacific Ocean
Sea surface height variability measured by TOPEX is analyzed in the tropical Pacific Ocean by way of assimilation into a wind-driven, reduced-gravity, shallow water model using an approximate Kalman filter and smoother. The analysis results in an optimal fit of the dynamic model to the observations, providing it dynamically consistent interpolation of sea level and estimation of the circulation. Nearly 80% of the expected signal variance is accounted for by the model within 20 deg of the equator, and estimation uncertainty is substantially reduced by the voluminous observation. Notable features resolved by the analysis include seasonal changes associated with the North Equatorial Countercurrent and equatorial Kelvin and Rossby waves. Significant discrepancies are also found between the estimate and TOPEX measurements, especially near the eastern boundary. Improvements in the estimate made by the assimilation are validated by comparisons with independent tide gauge and current meter observations. The employed filter and smoother are based on approximately computed estimation error covariance matrices, utilizing a spatial transformation and an symptotic approximation. The analysis demonstrates the practical utility of a quasi-optimal filter and smoother.
Fukumori, Ichiro↗
Integration of the shallow water equations on the sphere using a vector semi-Lagrangian scheme with a multigrid solver
A vector semi-Lagrangian semi-implicit two-time-level finite-difference integration scheme for the shallow water equations on the sphere is presented. A C-grid is used for the spatial differencing. The trajectory-centered discretization of the momentum equation in vector form eliminates pole problems and, at comparable cost, gives greater accuracy than a previous semi-Lagrangian finite-difference scheme which used a rotated spherical coordinate system. In terms of the insensitivity of the results to increasing timestep, the new scheme is as successful as recent spectral semi-Lagrangian schemes. In addition, the use of a multigrid method for solving the elliptic equation for the geopotential allows efficient integration with an operation count which, at high resolution, is of lower order than in the case of the spectral models. The properties of the new scheme should allow finite-difference models to compete with spectral models more effectively than has previously been possible.
Bates, J. R.↗