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Abstract Himalayan lakes represent critical water resources, culturally important waterbodies, and potential hazards. Some of these lakes experience dramatic water-level changes, responding to seasonal monsoon rains and post-monsoonal draining. To address the paucity of direct observations of hydrology in retreating mountain glacial systems, we describe a field program in a series of high altitude lakes in Sagarmatha National Park, adjacent to Ngozumba, the largest glacier in Nepal. In situ observations find extreme (>12 m) seasonal water-level changes in a 60-m deep lateral-moraine-dammed lake (lacking surface outflow), during a 16-month period, equivalent to a 5$$\times 10^6$$ $\times {10}^6$m$$^3$$ ${}^3$volume change annually. The water column thermal structure was also monitored over the same period. A hydraulic model is constructed, validated against observed water levels, and used to estimate hydraulic conductivities of the moraine soils damming the lake and improves our understanding of this complex hydrological system. Our findings indicate that lake level compared to the damming glacier surface height is the key criterion for large lake fluctuations, while lakes lying below the glacier surface, regulated by surface outflow, possess only minor seasonal water-level fluctuations. Thus, lakes adjacent to glaciers may exhibit very different filling/draining dynamics based on presence/absence of surface outflows and elevation relative to retreating glaciers, and consequently may have very different fates in the next few decades as the climate warms. 

Abstract Wave front propagation with nontrivial bottom topography is studied within the formalism of hyperbolic long wave models. Evolution of nonsmooth initial data is examined, and, in particular, the splitting of singular points and their short time behavior is described. In the opposite limit of longer times, the local analysis of wave fronts is used to estimate the gradient catastrophe formation and how this is influenced by the topography. The limiting cases when the free surface intersects the bottom boundary, belonging to the so‐called “physical” and “nonphysical” vacuum classes, are examined. Solutions expressed by power series in the spatial variable lead to a hierarchy of ordinary differential equations for the time‐dependent series coefficients, which are shown to reveal basic differences between the two vacuum cases: for nonphysical vacuums, the equations of the hierarchy are recursive and linear past the first two pairs, whereas for physical vacuums, the hierarchy is nonrecursive, fully coupled, and nonlinear. The former case may admit solutions that are free of singularities for nonzero time intervals, whereas the latter is shown to develop nonstandard velocity shocks instantaneously. Polynomial bottom topographies simplify the hierarchy, as they contribute only a finite number of inhomogeneous forcing terms to the equations in the recursion relations. However, we show that truncation to finite‐dimensional systems and polynomial solutions is in general only possible for the case of a quadratic bottom profile. In this case, the system's evolution can reduce to, and is completely described by, a low‐dimensional dynamical system for the time‐dependent coefficients. This system encapsulates all the nonlinear properties of the solution for general power series initial data, and, in particular, governs the loss of regularity in finite times at the dry point. For the special case of parabolic bottom topographies, an exact, self‐similar solution class is introduced and studied to illustrate via closed‐form expressions the general results. 

Abstract An extremely broad and important class of phenomena in nature involves the settling and aggregation of matter under gravitation in fluid systems. Here, we observe and model mathematically an unexpected fundamental mechanism by which particles suspended within stratification may self-assemble and form large aggregates without adhesion. This phenomenon arises through a complex interplay involving solute diffusion, impermeable boundaries, and aggregate geometry, which produces toroidal flows. We show that these flows yield attractive horizontal forces between particles at the same heights. We observe that many particles demonstrate a collective motion revealing a system which appears to solve jigsaw-like puzzles on its way to organizing into a large-scale disc-like shape, with the effective force increasing as the collective disc radius grows. Control experiments isolate the individual dynamics, which are quantitatively predicted by simulations. Numerical force calculations with two spheres are used to build many-body simulations which capture observed features of self-assembly. 

In this paper we study the self-induced low-Reynolds-number flow generated by a cylinder immersed in a stratified fluid. In the low Péclet limit, where the Péclet number is the ratio of the radius of the cylinder and the Phillips length scale, the flow is captured by a set of linear equations obtained by linearising the governing equations with respect to the prescribed far field conditions. We specifically focus on the low Péclet regime and develop a Green's function approach to solve the linearised equations governing the flow over the cylinder. We cross check our analytical solution against numerical solution of the nonlinear equations to obtain the range of the Péclet numbers for which the linear solution is valid. We then take advantage of the analytical solution to find explicit far-field decay rates of the flow. Our detailed analysis points out that the streamfunction and the velocity field decays algebraically in the far field. Intriguingly, this algebraic decay of the flow is much slower when compared with the exponential decay of the flow generated by a slow moving cylinder in the homogeneous Stokes regime, in the absence of stratification. Consequently, the flow generated by a cylinder in the stratified Stokes regime will have a larger domain of influence when compared with the flow generated by a cylinder in the homogeneous Stokes regime.