Search

Let x → ϕ s , t ( x ) be a R d -valued stochastic homeomorphic flow produced by non-Lipschitz stochastic differential equation ϕ s , t ( x ) = x + ∫ s t σ ( ϕ s , u ( x ) ) ⋅ d W u + ∫ s t b ( ϕ s , u ( x ) ) d u , where W = ( W 1 , W 2 , … ) is an infinite sequence of independent standard Brownian motions. We first give some estimates of modulus of continuity of { ϕ s , t ( ⋅ ) } , then prove that the flow ϕ s , t ( x ) , when x nears infinity, grows slower than Z exp { c ln ln | x | } for some constant c > 0 and integrable random variable Z via lemma of Garsia–Rodemich–Rumsey Lemma (abbreviated as GRR Lemma) improved by Arnold and Imkeller [L. Arnold, P. Imkeller, Stratonovich calculus with spatial parameters and anticipative problems in multiplicative ergodic theory, Stochastic Process. Appl. 62 (1996) 19–54] and moment estimates for one- and two-point motions.

航空宇宙技術研究所 27-29 Sept.2000 東京 日本, National Aerospace Laboratory 27-29 Sept.2000 Tokyo Japan, e(exp N)法を使用した遷移位置の予測には、空間成長速度Nに及ぼす外部擾乱の定量的評価が強く求められるため、2次元翼流れ内の層流-乱流遷移に及ぼす音響騒音の影響を実験的に検討した。最初に、同一モデルに対する自然遷移を異なる5風洞中で調べた。各因子の貢献度は分離不可能であるが、大音響騒音および/または大残留主流乱れを用いた風洞では早期遷移を観測した。そこで、測定胴内に設置したスピーカを使って人工音響騒音を導入した。大きな励起が遷移過程を促進することを確認した。Nと音圧レベル(SPL)間の経験的関係N=-0.6×SPL+74を提案した。, Influence of acoustic noise on laminar-to-turbulent transition in 2-D wing flow is investigated experimentally, since the quantitative evaluation of external disturbances on spatial growth rate N is intensively required to predict the transition location by the use of the e(exp N) method. At first, natural transition on an identical model is examined in five different wind tunnels. Early transition is observed in the wind tunnels with large acoustic noise and/or large residual free-stream turbulence, although the contribution of each factor is not separable. Therefore artificial acoustic noise is introduced by means of a loud speaker installed in the settling chamber. Larger excitation is confirmed to facilitate the transition process. An empirical relation between N and Sound Pressure Level (SPL) is proposed as N = -0.6 x SPL + 74., 資料番号: AA0028637014, レポート番号: NAL SP-48T

層流制御とよばれる、翼上の層流・乱流遷移を遅らせる技術は、超音速で巡航する高速民間輸送機における抗力低減にとって重要である。境界層流の計算、流れの線形安定解析および解析で求めた空間増幅率の積分によって遷移の開始を数値的に予測する。遷移の予測に用いる境界層流は、一般に境界層コードにより計算されてきた。本論文では計算用のナビエ・ストークスコードを構築した。無限後退円柱周りの超音速流を密度の異なる3つの型の格子を用いて計算した。3つの格子で求めた境界層の速度-温度プロファイルの比較によって、ナビエ・ストークスコードの精度をテストした。さらに、付着線境界層を線形安定解析した。解析で求めた不安定領域はMalik(1988)の結果と良く一致し、ここで用いたナビエ・ストークスコードの精度の良さを確認した。, Techniques to delay laminar-turbulent transition on the wing, called laminar-flow control, are important for drag reduction of high-speed civil transports cruising at supersonic speeds. The onset of transition is numerically predicted by computation of a boundary-layer flow, linear stability analysis for the flow, and integration of the spatial growth rates obtained by the analysis. Boundary-layer flows used to predict the transition have been generally computed with boundary-layer codes. In this paper, a Navier-Stokes code is constructed for the computation. The supersonic flow around an infinite swept cylinder is computed with three types of grids, which have different resolutions. The accuracy of the Navier-Stokes code is tested by comparing velocity, and temperature profiles in the boundary layer obtained with these three grids. Furthermore, linear stability analysis for the attachment-line boundary layer is performed. The unstable ranges obtained by the analysis agree well with the results of Malik (1988), which confirm the accuracy of the present Navier-Stokes code., 資料番号: AA0001142000, レポート番号: NAL TR-1321

We study asymptotic growth rates of stochastic flows on $\mathbf{R}^d$ and their derivatives with respect to the spatial parameter under Lipschitz conditions on the local characteristics of the generating semimartingales. In a first step these conditions are seen to imply moment inequalities for the flow $\phi$ of the form $$E \sup_{0 \le t \le T}|\phi_{0t} (x) - \phi_{0t} (y)|^p\le|x-y|^p\exp(cp^2)\quad\text{for all $p\ge 1$.}$$ In a second step we deduce the growth rates from an integrated version of these moment inequalities, using the continuity lemma of Garsia, Rodemich and Rumsey. We provide two examples to show that our results are sharp.