Computational Simulations of Wide-Beam Air-Cavity Hull in Waves

An effective method to reduce ship drag is to supply air under specially profiled bottom with the purpose to decrease wetted surface area of the hull and thus its water resistance. Although such systems have been installed on some vessels, the broad implementation of this technique has not yet occurred. A major problem is how to sustain air lubrication in rough water. Modeling of air-ventilated flows is challenging, but modern computational fluid dynamics tools can provide valuable insight. In this study, a wide-beam, shallow-draft hull with a bottom air cavity is considered. This hull imitates a semi-planing boat that can be used for fast transportation of cargo from large marine vessels to shallow shores. To simulate fluid flow around this hull in calm water and head waves, as well as heave and pitch motions of the boat, CFD software Star-CCM+ has been employed. It is found that the air cavity effectiveness decreases in waves; vertical accelerations exhibit high-frequency oscillations; and heave, pitch and vertical accelerations increase, while time-averaged heave, pitch and added drag show non-monotonic behavior with increasing wave amplitude. The air-cavity hull also demonstrates substantially lower vertical accelerations in waves in comparison with a similar solid hull without bottom recess. Time histories of kinematic parameters and distributions of flow field variables presented in this paper can be insightful for developers of air-cavity hulls.

CHARACTERISATIONS OF HARDY GROWTH SPACES WITH DOUBLING WEIGHTS

Let $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}H(\mathbb{D})$ denote the space of holomorphic functions on the unit disc $\mathbb{D}$. Given $p>0$ and a weight $\omega $, the Hardy growth space $H(p, \omega )$ consists of those $f\in H(\mathbb{D})$ for which the integral means $M_p(f,r)$ are estimated by $C\omega (r)$, $0<r<1$. Assuming that $p>1$ and $\omega $ satisfies a doubling condition, we characterise $H(p, \omega )$ in terms of associated Fourier blocks. As an application, extending a result by Bennett et al. [‘Coefficients of Bloch and Lipschitz functions’, Illinois J. Math. 25 (1981), 520–531], we compute the solid hull of $H(p, \omega )$ for $p\ge 2$.

On the solid hull of the Hardy-Lorentz space

The solid hulls of the Hardy-Lorentz spaces Hp,q,0 < p < 1, 0 < q ? ? and Hp,? 0, 0 < p < 1, as well as of the mixed norm space H p,?,? 0,0 < p ? 1, 0 < ? < ?, are determined.

An unpleasant set in a non-locally-convex vector lattice

In a linear topological space E one often carries out various “ smoothing ” operations on a subset A, such as taking the convex hull co A and the closure A-. If E is also a (real) vector lattice, the solid hullis also a natural “ smoothing out ” of A. If sol A = A then A is called solid, and if E has a base of solid neighbourhoods of 0 as do all the common topological vector lattices such as C(X), Lp, Köthe spaces and so on—then E is called a locally solid space.

The order-bound topology on Riesz spaces

1. Introduction. Let (X, C) be a Riesz space (or vector lattice) with positive cone C. A subset B of X is said to be solid if it follows from |x| ≤ |b| with b in B that x is in B (where |x| denotes the supremum of x and − x). The solid hull of B (absolute envelope of B in the terminology of Roberts (2)) is denoted to be the smallest solid set containing B, and is denoted by SB. A locally convex Hausdorff topology on (X, C) is called a locally solid topology if admits a neighbourhood-base of 0 consisting of solid and convex sets in X; and (X, C, ), where is a locally solid topology, is called a locally convex Riesz space.

Abstract Köthe Spaces. I

The purpose of this paper and the next is to demonstrate that the ‘perfect Riesz spaces’ of (1) are an effective abstraction of the ‘espaces de Köthe’ of (2). I shall follow the ideas of (1), with certain changes in notation:If L is a Riesz space and x, y ∈ L, let us denote sup (x, y) by x ∧ y and inf (x, y) by x ∧ y. I shall use the convenient if informal notation xr↓ ((1), section 16·1) and shall in this usage assume that 0 ∈ {r} and that x0 ≥ xτ for all τ. A set A ⊆ L is solid if x ∈ A and |y| ≤ |x| together imply that y ∈ A; A is then balanced. The solid hull of A is the set {y: ∃ x ∈ A, |y| ≤ |x|}; this is the smallest solid set containing A. An ‘ideal’ ((1), section 17) is then a solid subspace.