Balance, gravity waves and jets in turbulent shallow water flows

• Main Author: Shipton, Jemma
• Format: Dissertation
• Language: English
• Published: University of St Andrews 2009; The University of St Andrews
• Subjects: Jets > Fluid dynamics; QA925.S5; Rotating masses of fluid; Turbulence; vi, 149

This thesis contains a thorough investigation of the properties of freely decaying turbulence in a rotating shallow water layer on a sphere. A large numberof simulations, covering an extensive range of Froude and Rossby numbers, havebeen carried out using a novel numerical algorithm that exploits the underly-ing properties of the flow. In general these flows develop coherent structures;vortices interact, merge and migrate polewards or equatorwards depending ortheir sign, leaving behind regions of homogenized potential vorticity separatedby sharp zonal jets. In the first half of the thesis we investigate new ways of looking at these structures. In the second half of the thesis we examine the propertiesof the potential vorticity (PV) induced, balanced component and the residual,unbalanced component of the flows.Cyclone-anticyclone asymmetry has long been observed in atmospheric andoceanic data, laboratory experiments and numerical simulations. This asymmetry is usually seen to favour anticyclonic vorticity with the asymmetry becoming more pronounced at higher Froude numbers (e.g. Polvani et al. [1994a]). We find a similar result but note that the cyclones, although fewer, are significantlymore intense and coherent. We present several ways of quantifying this acrossthe parameter space.Potential vorticity homogenization is an important geophysical mechanismresponsible for sharpening jets through the expulsion of PV gradients to the edge of flow structures or domains. Sharp gradients of PV are obvious in contour plotsof this field as areas where the contours are bunched together. This suggests thatwe can estimate the number of zonal jets by performing a cluster analysis onthe mean latitude of PV contours (this diagnostic is also examined by Dritscheland McIntyre [2007]). This provides an estimate rather than an exact count ofthe number of jets because the jets meander signficantly. We investigate theaccuracy of the estimates provided by different clustering techniques. We findthat the properties of the jets defy such simple classification and instead demanda more local examination. We achieve this by examining the palinstrophy field.This field, calculated by taking the gradient of the PV, highlights the regionswhere PV contours come closer together, exactly what we would expect in regionsof strong jets. Plots of the palinstrophy field reveal the complex structure of thesefeatures.The potential vorticity field is even more central to the flow evolution thanthe strong link with jets suggests. From a knowledge of the spatial distributionof PV, it is possible to diagnose the balanced components of all other fields.These components will not contain inertia-gravity waves but will contain thedominant, large scale features of the flow. This inversion, or decomposition intobalanced (vortical) and unbalanced (wave) components, is not unique and can bedefined to varying orders of accuracy. We examine the results of four dfferentdefinitions of this decomposition, two based on truncations of the full equationsand two based on an iterative procedure applied to the full equations. We find theiterative procedure to be more accurate in that it attributes more of the flow tothe PV controlled, balanced motion. However, the truncated equations performsurprisingly well and do not appear to suffer in accuracy at the equator, despitethe fact that the scaling on which they are based has been thought to break downthere.We round off this study by considering the impact of the unbalanced motion on the flow. This is accomplished by splitting the integration time of the model intointervals τ < t < τ+dτ and comparing, at the end of each interval, the balancedcomponents of the flow obtained by a) integrating the model from t = 0 and b)integrating the full equations, initialised at t = τ with the balanced componentsfrom a) at t = τ. We find that any impact of the unbalanced component of theflow is less than the numerical noise of the model.