The spontaneous generation of inertia–gravity waves during frontogenesis forced by large strain: numerical solutions

2015 ◽  
Vol 772 ◽  
pp. 508-534 ◽  
Author(s):  
Callum J. Shakespeare ◽  
J. R. Taylor
Keyword(s):  
Numerical Model ◽  
Analytical Model ◽  
Strain Field ◽  
Numerical Solutions ◽  
Large Strain ◽  
Spontaneous Generation ◽  
Strain Rates ◽  
Fully Nonlinear ◽  
Order Of Magnitude ◽  
Horizontal Strain

A fully nonlinear numerical model is used to investigate spontaneous wave generation during two-dimensional frontogenesis forced by a horizontal strain field. The model uses the idealised configuration of an infinitely long straight front and uniform potential vorticity, with a uniform imposed convergent strain across the front. Shakespeare & Taylor (J. Fluid Mech., vol. 757, 2014, pp. 817–853) formulated a generalised analytical model (ST14) for this system that extends the classical Hoskins & Bretherton (J. Atmos. Sci., vol. 29, 1972, pp. 11–37) model (HB) to large strain rates (${\it\alpha}\sim f$). Here, we use a numerical model to simulate the fully nonlinear problem and compare the results with the predictions of the analytical model for a variety of strain rates. Even for weak strains (${\it\alpha}=0.2f$), the confinement of the secondary circulation and the spontaneous generation of waves, predicted by ST14, are shown to be important corrections to the HB solution. These inviscid predictions are also robust for an equilibrated front where strain-forced frontogenesis is balanced by diffusion. For strong strains the wavefield becomes of leading-order importance to the solution. In this case the frontal circulation is tightly confined, and the vertical velocity is an order of magnitude larger than in the HB model. The addition of a strain field that weakens with time allows the release and propagation of the spontaneously generated waves. We also consider fronts with both large vorticity and strain rate, beyond the validity of the ST14 model.

scholarly journals Nonhydrostatic Wave Generation at Strained Fronts

2016 ◽  
Vol 73 (7) ◽  
pp. 2837-2850 ◽  
Author(s):  
Callum J. Shakespeare
Keyword(s):  
Numerical Simulations ◽  
Analytical Model ◽  
Strain Field ◽  
Wave Generation ◽  
Vertical Flow ◽  
Simple Analytical Model ◽  
Fully Nonlinear ◽  
Surface Front ◽  
Horizontal Strain ◽  
Hydrostatic Balance

Abstract A simple analytical model is developed to describe wave generation during frontogenesis forced by a horizontal strain field. In contrast to previous models, neither geostrophic nor hydrostatic balance is assumed. The generated waves are trapped in the strain field and form steady bands of enhanced vertical flow on either side of the surface front on scales from 1 to 100 km. The predictions of the analytical model are confirmed by comparison with fully nonlinear numerical simulations.

scholarly journals Spontaneous Wave Generation at Strongly Strained Density Fronts

2016 ◽  
Vol 46 (7) ◽  
pp. 2063-2081 ◽  
Author(s):  
Callum J. Shakespeare ◽  
John R. Taylor
Keyword(s):  
Analytical Model ◽  
Large Strain ◽  
Wave Generation ◽  
Spontaneous Generation ◽  
Strain Rates ◽  
Infinite Domain ◽  
Coriolis Parameter ◽  
Frequency Wave ◽  
Ocean Surface Waves ◽  
Background Strain

AbstractA simple analytical model is presented describing the spontaneous generation of inertia–gravity waves at density fronts subjected to strong horizontal strain rates. The model considers fronts of arbitrary horizontal and vertical structure in a semi-infinite domain, with a single boundary at the ocean surface. Waves are generated because of the acceleration of the steady uniform strain flow around the density front, analogous to the generation of lee waves via flow over a topographic ridge. Significant wave generation only occurs for sufficiently strong strain rates α > 0.2f and sharp fronts H/L > 0.5f/N, where f is the Coriolis parameter, N is the stratification, and H and L are the height and width scales of the front, respectively. The frequencies of the generated waves are entirely determined by the strain rate. The lowest-frequency wave predicted to be generated via this mechanism has a Lagrangian frequency ω = 1.93f as measured in a reference frame moving with the background strain flow. The model is intended as a first-order description of wave generation at submesoscale (1 to 10 km wide) fronts where large strain rates are commonplace. The analytical model compares well with fully nonlinear numerical simulations of the submesoscale regime.

Hysteresis loss of ultra-large off-the-road tire rubber compounds based on operating conditions at mine sites

2021 ◽  
pp. 095440702110155
Author(s):  
Shaosen Ma ◽  
Guangping Huang ◽  
Khaled Obaia ◽  
Soon Won Moon ◽  
Wei Victor Liu
Keyword(s):  
Large Strain ◽  
Tensile Tests ◽  
Operating Conditions ◽  
Hysteresis Loss ◽  
Strain Rates ◽  
Test Results ◽  
Tire Rubber ◽  
The Road ◽  
Rubber Compounds ◽  
Mine Sites

The objective of this study is to investigate the hysteresis loss of ultra-large off-the-road (OTR) tire rubber compounds based on typical operating conditions at mine sites. Cyclic tensile tests were conducted on tread and sidewall compounds at six strain levels ranging from 10% to 100%, eight strain rates from 10% to 500% s−1 and 14 rubber temperatures from −30°C to 100°C. The test results showed that a large strain level (e.g. 100%) increased the hysteresis loss of tire rubber compounds considerably. Hysteresis loss of tire rubber compounds increased with a rise of strain rates, and the increasing rates became greater at large strain levels (e.g. 100%). Moreover, a rise of rubber temperatures caused a decrease in hysteresis loss; however, the decrease became less significant when the rubber temperatures were above 10°C. Compared with tread compounds, sidewall compounds showed greater hysteresis loss values and more rapid increases in hysteresis loss with the rising strain rate.

Analytical Model to Predict Nonhomogeneous Soil Temperature Variation

1995 ◽  
Vol 117 (2) ◽  
pp. 100-107 ◽  
Author(s):  
M. Krarti ◽  
D. E. Claridge ◽  
J. F. Kreider
Keyword(s):  
Thermal Properties ◽  
Soil Temperature ◽  
Temperature Variation ◽  
Analytical Model ◽  
Soil Surface ◽  
Deep Soil ◽  
Soil Thermal Properties ◽  
Order Of Magnitude ◽  
Soil Surface Temperature ◽  
Annual Time

This paper presents an analytical model to predict the temperature variation within a multilayered soil. The soil surface temperature is assumed to have a sinusoidal time variation for both daily and annual time scales. The soil thermal properties in each layer are assumed to be uniform. The model is applied to two-layered, three-layered, and to nonhomogeneous soils. In case of two-layered soil, a detailed analysis of the thermal behavior of each layer is presented. It was found that as long as the order of magnitude of the thermal diffusivity of soil surface does not exceed three times that of deep soil; the soil temperature variation with depth can be predicted accurately by a simplified model that assumes that the soil has constant thermal properties.

Dense GPS derived deformation and rotation of intraplate blocks in Central Europe - comparison to seismicity and volcanism

2021 ◽  
Author(s):  
Zhiguo Deng ◽  
Torsten Dahm
Keyword(s):  
High Precision ◽  
Velocity Fields ◽  
Shear Stresses ◽  
Intraplate Seismicity ◽  
Strain Rates ◽  
Horizontal Shear ◽  
Regional Patterns ◽  
Quaternary Volcanism ◽  
Intraplate Deformation ◽  
Horizontal Strain

<p>Intraplate deformation is often small but can nowdays be resolved from high precision GNSS velocity fields derived from decade-long time series and high precision network or point wise  solutions if uncertainties are smaller than ~0.2 mm/a.</p><p>If local effects are discarded, dense velocity fields may resolve regional patterns of intraplate deformation and motion, which are related to the bending of lithospheric plates, to mantle upwelling, the diffuse or zoned deformation along structural weaknesses or faults, and the rotation of rigid blocks within a plate. </p><p>We derive for the first time, dense high precision network solutions at 323 GNSS stations in Germany and adjacent areas and resolve regions experiencing uplift with velocities of up to ~2 mm/a, rotational relative motions with angular velocities of ~0.7±0.3 mas/a, and horizontal shear along an extended,  NS trending zone with strain rates in the range of 10-8 1/a. </p><p>We integrate European dense velocity solutions into our dataset to discuss the geodynamic context to European microplate motions, the Alpine collision, the structure of the European mantle, Quaternary volcanism and historical seismicity. </p><p>Unexpectedly, the zones of high horizontal strain rates only partly correlate to seismicity. Such a non-correlation between ongoing horizontal strain and seismicity has been recognized before. We discuss possible reasons for the absence of intraplate seismicity in regions experiencing recent strain, including the stress shadow effects if the strain buildup is reducing shear stresses from plate tectonics. The combination of GNSS derived dense velocity fields with time dependent seismicity models may change our current understanding of intraplate seismicity and impact the assessment of intraplate seismic hazard in future. </p>

An Improved Assembling Algorithm in Boundary Elements With Galerkin Weighting Applied to Three-Dimensional Stokes Flows

2017 ◽  
Vol 140 (1) ◽  
Author(s):  
Sofia Sarraf ◽  
Ezequiel López ◽  
Laura Battaglia ◽  
Gustavo Ríos Rodríguez ◽  
Jorge D'Elía
Keyword(s):  
Boundary Element Method ◽  
Linear System ◽  
Boundary Element ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Boundary Integral ◽  
Computational Time ◽  
Creeping Flows ◽  
Order Of Magnitude ◽  
Element Method

In the boundary element method (BEM), the Galerkin weighting technique allows to obtain numerical solutions of a boundary integral equation (BIE), giving the Galerkin boundary element method (GBEM). In three-dimensional (3D) spatial domains, the nested double surface integration of GBEM leads to a significantly larger computational time for assembling the linear system than with the standard collocation method. In practice, the computational time is roughly an order of magnitude larger, thus limiting the use of GBEM in 3D engineering problems. The standard approach for reducing the computational time of the linear system assembling is to skip integrations whenever possible. In this work, a modified assembling algorithm for the element matrices in GBEM is proposed for solving integral kernels that depend on the exterior unit normal. This algorithm is based on kernels symmetries at the element level and not on the flow nor in the mesh. It is applied to a BIE that models external creeping flows around 3D closed bodies using second-order kernels, and it is implemented using OpenMP. For these BIEs, the modified algorithm is on average 32% faster than the original one.

An Approach to Approximate the Full Strain Field of Turbofan Blades During Operation

2018 ◽  
Author(s):  
Gen Fu ◽  
Alexandrina Untaroiu ◽  
Walter O’Brien
Keyword(s):  
Numerical Model ◽  
Cantilever Beam ◽  
Strain Field ◽  
Measured Data ◽  
Mode Shapes ◽  
Beam Model ◽  
Reference Solution ◽  
Full Field ◽  
Field Response ◽  
Critical Locations

The measurement of the aeromechanical response of the fan blades is important to quantifying their integrity. The accurate knowledge of the response at critical locations of the structure is crucial when assessing the structural condition. A reliable and low cost measuring technique is necessary. Currently, sensors can only provide the measured data at several discrete points. A significant number of sensors may be required to fully characterize the aeromechanical response of the blades. However, the amount of instrumentation that can be placed on the structure is limited due to data acquisition system limitations, instrumentation accessibility, and the effect of the instrumentation on the measured response. From a practical stand point, it is not possible to place sensors at all the critical locations for different excitations. Therefore, development of an approach that derives the full strain field response based on a limited set of measured data is required. In this study, the traditional model reduction method is used to expand the full strain field response of the structure by using a set of discrete measured data. Two computational models are developed and used to verify the expansion approach. The solution of the numerical model is chosen as the reference solution. In addition, the numerical model also provides the mode shapes of the structure. In the expansion approach, this information is used to develop the algorithm. First, a cantilever beam model is created. The influences of the sensor location, number of sensors and the number of modes included are analyzed using this cantilever beam model. The expanded full field response data is compared with the reference solution to evaluate the expansion procedure. The rotor 67 blade model is then used to test the expansion method. The results show that the expanded full field data is in good agreement with the calculated data. The expansion algorithm can be used for the full field strain by using the limited sets of strain data.

scholarly journals NUMERICAL MODEL INVESTIGATION OF SELECTED TIDAL INLET-BAY SYSTEM CHARACTERISTICS

1978 ◽  
Vol 1 (16) ◽  
pp. 76
Author(s):  
William N. Seelig ◽  
Robert M. Sorensen
Keyword(s):  
Sediment Transport ◽  
Numerical Model ◽  
Transport Model ◽  
Tidal Inlet ◽  
Inlet Channel ◽  
Astronomical Tide ◽  
Order Of Magnitude ◽  
Flow And Sediment Transport ◽  
Transport Factors ◽  
System Characteristics

A spatially integrated one-dimensional numerical model of inlet bay hydraulics has been combined with a simple sediment transport model to investigate selected tidal inlet-bay system characteristics. A parametric study has been performed using the models to determine the effect of various factors on the net direction and order of magnitude of inlet channel flow and sediment transport. Factors considered include astronomical tide type, storm surge height and duration, variation in bay surface area, time-dependent channel friction factor, and the addition of a second inlet connecting the bay and sea.

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