EXPERIMENTAL STUDY ON COHERENT VORTEX STRUCTURES IN DIFFERENTIALLY ROTATING QUASI TWO DIMENSIONAL ZONAL FLOW

An experimental system for forming a rotating paraboloid shaped shallow water with a free surface was conducted to study coherent vortex structures in a differentially rotating quasi two dimensional zonal flow.Flow visualization and laser light scattering techniques were used to obtain the information of spatial flow patterns.Experimental results show that the coexistence of Coriolis effect and strong shear in latitudinal zones may lead to formation of coherent vortices.Power spectra analysis and photographs which were taken in a reference frame rotating with the observed vortices also justified the emergence,drift and evolution of persistent vortices on the large scale.Locked vortex state manifests the cyclone and anticyclone asymmetry.

Effect of potassium on soil conservation and productivity of maize/cowpea based crop rotations in the north-west Indian Himalayas

Plots under conservation tillage may require higher amount of potassium(K) application for augmenting productivity due to its stratification in upper soil layers, thereby reducing K supplying capacity in a medium or long-term period. To test this hypothesis, a field experiment was performed in 2002-2003 and 2006-2007 to study the effect of K and several crop rotations on yield, water productivity, carbon sequestration, grain quality, soil K status and economic benefits derived in maize(Zea mays L)/cowpea(Vigna sinensis L.) based cropping system under minimum tillage(MT). All crops recorded higher grain yield with a higher dose of K(120 kg K2 O ha-1) than recommended K(40 kg K2 O ha-1). The five years' average yield data showed that higher K application(120 kg K2 O ha-1) produced 16.4%(P<0.05)more maize equivalent yield. Cowpea based rotation yielded 14.2%(P<0.05) higher production than maize based rotation. The maximum enhancement was found in cowpea-mustard rotation. Relationship between yield and sustainable indices revealed that only agronomic efficiency of fertilizer input was significantly correlated with yield. Similarly, higherdoses of K application not only increased the water use efficiency(WUE) of all crops, but also reduced runoff and soil loss by 16.5% and 15.8% under maize and 23.3% and 19.7% under cowpea cover, respectively. This study also revealed that on an average 16.5% of left over carbon input contributed to soil organic carbon(SOC). Here, cowpea based rotation with the higher K application increased carbon sequestration in soil. Potassium fertilization also significantly improved the nutritional value of harvested grain by increasing the protein content for maize(by 9.5%) and cowpea(by 10.6%). The oil content in mustard increased by 5.0% and 6.0% after maize and cowpea, respectively. Net return also increased with the application of the higher K than recommended K and the trend was similar to yield. Hence, the present study demonstrated the potential yield and profit gains along with resource conservation in the Indian Himalayas due to annual additions of higher amount of K than the recommended dose. The impact of high K application was maximum in the cowpea-mustard rotation.

Flux Globalization Based Well-Balanced Path-Conservative Central-Upwind Scheme for the Thermal Rotating Shallow Water Equations

We present an extension of the flux globalization based well-balanced pathconservative central-upwind scheme to the one-and two-dimensional thermal rotating shallow water equations.The scheme is well-balanced in the sense that it can exactly preserve a variety of physically relevant steady states.In the one-dimensional case,it can preserve different“lake-at-rest”equilibria,thermo-geostrophic equilibria,as well as general moving-water steady states.In the two-dimensional case,preserving general moving-water steady states is difficult,and to the best of our knowledge,none of existing schemes can achieve this ultimate goal.The proposed scheme can exactly preserve the x-and y-directional jets in the rotational frame as well as certain genuinely two-dimensional equilibria.Furthermore,our approach employs a path-conservative technique for discretizing nonconservative product terms,which are incorporated into the global fluxes.This allows the developed scheme to exactly preserve some of the discontinuous steady states as well.We provide a number of numerical examples to demonstrate the advantages of the proposed scheme over some alternative finitevolume methods.

Localized Exponential Time Differencing Method for Shallow Water Equations: Algorithms and Numerical Study

In this paper,we investigate the performance of the exponential time differencing(ETD)method applied to the rotating shallow water equations.Comparing with explicit time stepping of the same order accuracy in time,the ETD algorithms could reduce the computational time in many cases by allowing the use of large time step sizes while still maintaining numerical stability.To accelerate the ETD simulations,we propose a localized approach that synthesizes the ETD method and overlapping domain decomposition.By dividing the original problem into many subdomain problems of smaller sizes and solving them locally,the proposed approach could speed up the calculation of matrix exponential vector products.Several standard test cases for shallow water equations of one or multiple layers are considered.The results show great potential of the localized ETD method for high-performance computing because each subdomain problem can be naturally solved in parallel at every time step.