SUMMARYThe propagation, runup and rundown of long surface waves are numerically investigated, initially in one dimension, using a well-balanced high-resolution finite volume scheme. A conservative form of the nonlinear shallow water equations with source terms is solved numerically using a high-resolution Godunov-type explicit scheme coupled with Roe's approximate Riemann solver. The scheme is also extended to handle two-dimensional complex domains. The numerical difficulties related to the presence of the topography source terms in the model equations along with the appearance of the wet/dry fronts are properly treated and extended. The resulting numerical model accurately describes breaking waves as bores or hydraulic jumps and conserves volume across flow discontinuities. Numerical results show very good agreement with previously presented analytical or asymptotic solutions as well as with experimental benchmark data.
BackgroundCareful review of published evidence has led to the postulate that the degree of lumbar lordosis may possibly influence the development and progression of spinal osteoarthritis, just as misalignment does in other joints. Spinal degeneration can ensue from the asymmetrical distribution of loads. The resultant lesions lead to a domino- like breakdown of the normal morphology, degenerative instability and deviation from the correct configuration. The aim of this study is to investigate whether a relationship exists between the sagittal alignment of the lumbar spine, as it is expressed by lordosis, and the presence of radiographic osteoarthritis.Methods112 female subjects, aged 40-72 years, were examined in the Outpatients Department of the Orthopedics' Clinic, University Hospital of Heraklion, Crete. Lumbar radiographs were examined on two separate occasions, independently, by two of the authors for the presence of osteoarthritis. Lordosis was measured from the top of L1 to the bottom of L5 as well as from the top of L1 to the top of S1. Furthermore, the angle between the bottom of L5 to the top of S1was also measured.Results and discussion49 women were diagnosed with radiographic osteoarthritis of the lumbar spine, while 63 women had no evidence of osteoarthritis and served as controls. The two groups were matched for age and body build, as it is expressed by BMI. No statistically significant differences were found in the lordotic angles between the two groupsConclusionsThere is no difference in lordosis between those affected with lumbar spine osteoarthritis and those who are disease free. It appears that osteoarthritis is not associated with the degree of lumbar lordosis.
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