Asymptotic expansions of the probability functions of sums of independent random vectors. I

An estimate of the speed of convergence in the multidmensional central limit theorem without moment hypotheses

“…In the present note we will obtain a series of estimates of the quantity An(A) = [Pn(A) --~(A) I, strengthening some results of Petrov, Osipov, Rotar', Bikyalis, and the author [1][2][3][4][5].…”

“…Precisely the result required by us is proved perfectly analogously, with the only difference that in Lemma 2 of [4], used in the proof, we apply the estimate This is quite inconsequential.…”

Hydrodynamics of Meander Bends in Intertidal Mudflats: A Field Study From the Macrotidal Yangkou Coast, China

“…Previous studies have demonstrated that secondary circulation cells do not necessarily occupy the whole channel cross‐section (e.g., Blanckaert, 2009, 2011; Finotello, Ghinassi, et al., 2020). Particularly, hydrodynamic nonlinearities can arise in sharp bends characterized by radius‐to‐width ratios $$R/\overline{W}$$ lower than 2–3, and flow separation may occur either at the inner or outer bank, respectively, immediately upstream or downstream of the bend apex (Blanckaert et al., 2013; Finotello, Ghinassi, et al., 2020; Hickin, 1978; Hickin & Nanson, 1975; Hooke, 2013; Parsons et al., 2004; Rozovskiĭ, 1957). Flow separation, which is common in tidal meanders owing to the high curvature values that they typically attain (Ferguson et al., 2003; Finotello, D’Alpaos, et al., 2019), can effectively reduce the portion of the channel that is hydrodynamically active and confine curvature‐induced secondary circulations to the nonrecirculating portion of the primary flow (Finotello, Ghinassi, et al., 2020; Leeder & Bridges, 1975; Parsons et al., 2004).…”

“…These differences in landforming hydrodynamic processes are also likely to affect the development of curvature‐induced helical flows that are typically related to the growth of meander bends in both rivers and salt‐marsh tidal channels (Azpiroz‐Zabala et al., 2017; Finotello, Ghinassi, et al., 2020; Keevil et al., 2015; Kranenburg et al., 2019; Nidzieko et al., 2009; Thorne et al., 1985). Such helical flow forms as a consequence of secondary (i.e., cross‐sectional) circulations, oriented toward the inner and outer bank in the near‐bed and near‐surface zone, respectively, which result from the imbalance between the upward‐increasing centrifugal forces and the lateral pressure gradients created by the curvature‐induced superelevation of the water surface at the outer bank (Engelund, 1974; Prandtl, 1926; Rozovskiĭ, 1957; Solari et al., 2002). The downstream advection of secondary circulations operated by the main streamwise flow produces a helical flow, as extensively documented in a variety of field (Dietrich & Smith, 1983; Dinehart & Burau, 2005; Frothingham & Rhoads, 2003), laboratory (Blanckaert, 2011; Liaghat et al., 2014), and numerical studies (Blanckaert & de Vriend, 2003; Bridge & Jarvis, 1982; Ferguson et al., 2003).…”

Curvature‐ and Wind‐Driven Cross‐Channel Flows at an Unstratified Tidal Bend

“…Cross‐channel flows laterally redistribute water properties and momentum, affecting along‐channel dynamics (Lerczak & Geyer, ), longitudinal dispersion (Lacy & Monismith, ; Seim & Gregg, ), and bay‐ocean exchange (Smith, ). Thus, curvature‐driven cross‐channel flows (e.g., at a bend or headland) have been studied for many years (Boussinesq ; Geyer ; Kalkwijk & Booij, ; Rozovskii, ; Thomson ).…”