Skimming impacts and rebounds of smoothly shaped bodies on shallow liquid layers

Investigated in this paper is the coupled fluid–body motion of a thin solid body undergoing a skimming impact on a shallow-water layer. The underbody shape (the region that makes contact with the liquid layer) is described by a smooth polynomic curve for which the magnitude of underbody thickness is represented by the scale parameter C. The body undergoes an oblique impact (where the horizontal speed of the body is much greater than its vertical speed) onto a liquid layer with the underbody’s trailing edge making the initial contact. This downstream contact point of the wetted region is modelled as fixed (relative to the body) throughout the skimming motion with the liquid layer assumed to detach smoothly from this sharp trailing edge. There are two geometrical scenarios of interest: the concave case (C < 0 producing a hooked underbody) and the convex case (C < 0producing a rounded underbody). As C is varied the rebound dynamics of the motion are predicted. Analyses of small-time water entry and of water exit are presented and are shown to be broadly in agreement with the computational results of the shallow-water model. Reduced analysis and physical insights are also presented in each case alongside numerical investigations and comparisons as C is varied, indicating qualitative analytical/numerical agreement. Increased body thickness substantially changes the interaction structure and accentuates inertial forces in the fluid flow

A body in nonlinear near-wall shear flow:impacts, analysis and comparisons

Interaction between body motion and fluid motion is considered inside a nonlinear viscous wall layer, with this unsteady two-way coupling leading to impact of the body on the wall. The present paper involves a reduced system analysis which is shown to be consistent with computational solutions from direct numerical simulations for a basic flat-plate shape presented in an allied paper (Palmer & Smith, J. Fluid Mech., 2020). The occurrence of impact depends mainly on fluid parameters and initial conditions. The body considered is translating upstream or downstream relative to the wall. Subsequent analysis focusses on the unusual nature of the impact at the leading edge. The impacting flow structure is found to have two nonlinear viscous–inviscid regions lying on either side of a small viscous region. The flow properties in the regions dictate the lift and torque which drive the body towards the wall. Pronounced flow separations are common as the impact then cuts off the mass flux in the gap between the body and the wall; here, a nonlinear similarity solution sheds extra light on the separations. Comparisons are made between results from direct simulations and asymptotics at increased flow rate

The role of body shape and mass in skimming on water

Over many years, there has been great practical interest in how solid bodies interact with and skim on liquid layers. In the present investigation, the focus is on the important role of body mass and shape in such skimming motions. Considering a thin two-dimensional solid body that impacts obliquely and then rebounds on a shallow inviscid water layer, we develop a mathematical model to predict quantitatively the duration and evolution of the body and fluid motions and indeed the success or failure of the whole skim. In the current setting, the shallow water layer thickness is small relative to the representative body length. The combined roles of increased mass and shape are found to be crucial, governed by a similarity solution. The relationship C ∼ M2/3 between scaled body curvature and mass is identified and highlighted. In particular, increased convex curvature of the underbody is found to alter the interactive pressure in such a way that it inhibits the occurrence of a super-elastic response in the exit vertical velocity and height of the body, and in effect enables a much heavier body to skim successfully provided the above relationship is maintained

When a small thin two-dimensional body enters a viscous wall layer

If a body enters a viscous-inviscid fluid layer near a wall, then significant effects can be felt from the presence of incident vorticity, viscous forces and nonlinear forces. The focus here is on the response in the outer edge of such a wall layer. Nonlinear two-dimensional unsteady behaviour is examined through modelling, computation and analysis applied for a thin body travelling streamwise upstream or downstream or staying still relative to the wall. The wall layer with its balance between inviscid and viscous effects interacts freely with the body movement, causing relatively high magnitudes of pressure on top of the body and nonlinear responses in the gap between the body and the wall. The study finds explicit solutions for the motion of the body, separation of the flow arising near the wall and possible instabilities occurring over the length scale of any short body

Skimming impact of a thin heavy body on a shallow liquid layer

This study addresses the question of whether a thin, relatively heavy solid body with a smooth under-surface can skim on a shallow layer of liquid (for example water), i.e. impact on the layer and rebound from it. The body impacts obliquely onto the liquid layer with the trailing edge of the underbody making the initial contact. The wetted region then spreads along the underbody and eventually either retracts, generating a rebound, or continues to the leading edge of the body and possibly leads to the body sinking. The present inviscid study involves numerical investigations for increased mass ( M , in scaled terms) and moment of inertia ( I , proportional to the mass) together with an asymptotic analysis of the influential parameters and dynamics at different stages of the skimming motion. Comparisons between the asymptotic analysis and numerical results show close agreement as the body mass becomes large. A major finding is that, for a given impact angle of the underbody relative to the liquid surface, only a narrow band of initial conditions is found to allow the heavy-body skim to take place. This band includes reduced impact velocities of the body vertically and rotationally, both decreasing like M−2/3 , while the associated total time of the skim from entry to exit is found to increase like M1/3 typically. Increased mass thereby enhances the super-elastic behaviour of the skim

Historical reconstruction of the Atlantic Meridional Overturning Circulation from the ECMWF operational ocean reanalysis

A reconstruction of the Atlantic Meridional Overturning Circulation (MOC) for the period 1959–2006 has been derived from the ECMWF operational ocean reanalysis. The reconstruction shows a wide range of time-variability, including a downward trend. At 26N, both the MOC intensity and changes in its vertical structure are in good agreement with previous estimates based on trans-Atlantic surveys. At 50N, the MOC and strength of the subpolar gyre are correlated at interannual time scales, but show opposite secular trends. Heat transport variability is highly correlated with the MOC but shows a smaller trend due to the warming of the upper ocean, which partially compensates for the weakening of the circulation. Results from sensitivity experiments show that although the time-varying upper boundary forcing provides useful MOC information, the sequential assimilation of ocean data further improves the MOC estimation by increasing both the mean and the time variability

Particle movement in a boundary layer

The study here is concerned with a thin solid body passing through a boundary layer or channel flow and interacting with the flow. Relevant new features from modelling, analysis and computation are presented along with comparisons. Three scenarios of such fluid-body interactive evolution in two-dimensional settings are considered in turn, namely a long body translating upstream or downstream, a long body with little or no translation and a short body with or without translation. The main progress and findings concern predictions of the time taken by the body to traverse the flow and impact upon the underlying wall, the delicate behaviour at the onset of impact, the dependence on parameters such as the initial conditions and the mass and shape of the body, and the influence of streamwise translation of the body in the surrounding fluid flow

Parameter inference in mechanistic models of cellular regulation and signalling pathways using gradient matching

A challenging problem in systems biology is parameter inference in mechanistic models of signalling pathways. In the present article, we investigate an approach based on gradient matching and nonparametric Bayesian modelling with Gaussian processes. We evaluate the method on two biological systems, related to the regulation of PIF4/5 in Arabidopsis thaliana, and the JAK/STAT signal transduction pathway

Association of plasma uric acid with ischaemic heart disease and blood pressure: mendelian randomisation analysis of two large cohorts

Objectives: To assess the associations between both uric acid levels and hyperuricaemia, with ischaemic heart disease and blood pressure, and to explore the potentially confounding role of body mass index. Design: Mendelian randomisation analysis, using variation at specific genes (SLC2A9 (rs7442295) as an instrument for uric acid; and FTO (rs9939609), MC4R (rs17782313), and TMEM18 (rs6548238) for body mass index). Setting: Two large, prospective cohort studies in Denmark. Participants: We measured levels of uric acid and related covariables in 58 072 participants from the Copenhagen General Population Study and 10 602 from the Copenhagen City Heart Study, comprising 4890 and 2282 cases of ischaemic heart disease, respectively. Main outcome: Blood pressure and prospectively assessed ischaemic heart disease. Results: Estimates confirmed known observational associations between plasma uric acid and hyperuricaemia with risk of ischaemic heart disease and diastolic and systolic blood pressure. However, when using genotypic instruments for uric acid and hyperuricaemia, we saw no evidence for causal associations between uric acid, ischaemic heart disease, and blood pressure. We used genetic instruments to investigate body mass index as a potentially confounding factor in observational associations, and saw a causal effect on uric acid levels. Every four unit increase of body mass index saw a rise in uric acid of 0.03 mmol/L (95% confidence interval 0.02 to 0.04), and an increase in risk of hyperuricaemia of 7.5% (3.9% to 11.1%). Conclusion: By contrast with observational findings, there is no strong evidence for causal associations between uric acid and ischaemic heart disease or blood pressure. However, evidence supports a causal effect between body mass index and uric acid level and hyperuricaemia. This finding strongly suggests body mass index as a confounder in observational associations, and suggests a role for elevated body mass index or obesity in the development of uric acid related conditions

A genome-wide association study suggests an association of Chr8p21.3 (GFRA2) with diabetic neuropathic pain

BACKGROUND: Neuropathic pain, caused by a lesion or a disease affecting the somatosensory system, is one of the most common complications in diabetic patients. The purpose of this study is to identify genetic factors contributing to this type of pain in a general diabetic population. METHOD: We accessed the Genetics of Diabetes Audit and Research Tayside (GoDARTS) datasets that contain prescription information and monofilament test results for 9439 diabetic patients, among which 6927 diabetic individuals were genotyped by Affymetrix SNP6.0 or Illumina OmniExpress chips. Cases of neuropathic pain were defined as diabetic patients with a prescription history of at least one of five drugs specifically indicated for the treatment of neuropathic pain and in whom monofilament test result was positive for sensory neuropathy in at least one foot. Controls were individuals who did not have a record of receiving any opioid analgesics. Imputation of non‐genotyped SNPs was performed by IMPUTE2, with reference files from 1000 Genomes Phase I datasets. RESULTS: After data cleaning and relevant exclusions, imputed genotypes of 572 diabetic neuropathic pain cases and 2491 diabetic controls were used in the Fisher's exact test. We identified a cluster in the Chr8p21.3, next to GFRA2 with a lowest p‐value of 1.77 × 10(−7) at rs17428041. The narrow‐sense heritability of this phenotype was 11.00%. CONCLUSION: This genome‐wide association study on diabetic neuropathic pain suggests new evidence for the involvement of variants near GFRA2 with the disorder, which needs to be verified in an independent cohort and at the molecular level