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The complexity or randomness was examined with the aid of Kolmogorov complexity for the flow about a turbulence wedge developed from a single roughness element on a flat plate. Velocity data obtained from a hot-wire anemometer and its time derivative data were compressed using a compression program running on a Windows PC. Approximated Kolmogorov complexity, AK, and normalized compression distance, NCD, were obtained. Although the AK variation of fluctuating velocity and that of its time derivative do not completely agree with that of the fluctuating velocity and the intermittency factor, they do roughly. Therefore, the objective judgment of the laminar-turbulent transition progress based on the Kolmogorov complexity mostly supports the judgment by the conventional intermittency factor. With the aid of the AK we can distinguish the complexity within the turbulent region; on the other hand, the intermittency factor cannot. The AK distribution of fluctuating velocity and that of time derivative are similar, and this suggests the similarity in the differentiation of complexity. The AK in the turbulent flow is larger than that in the non-turbulent flow. The AK decreases when the coherent structure has occurred in the turbulent flow. This means that the length of the algorithm is short if a computer expresses the coherent structure detected by the conventional method. Although the hot-wire signal within the coherent structure is random in appearance, it is coherent in the algorithm view. The difference in NCD on the time derivative of the fluctuating velocity between the turbulent and non-turbulent flow is larger than the NCD on the fluctuating velocity itself. That is, the difference in complexity appears in the fluctuating vorticity more than in the fluctuating velocity. : Transition, Turbulence, Boundary layer, Randomness, Kolmogorov complexity, Normalized compression distance, Single roughness element, Turbulence wedge 1. 緒 論 乱流の代表的特徴の一つは,流れの諸量が時空間に亘って複雑にランダムに変化することとされている(Hinze, 1975)(Pope, 2000).事物,現象の複雑さ,ランダムさの程度の問題,これは逆に見れば対象から我々が読み取れる 意味の大小の問題,は非常に広範囲に顕われており,まず通信に関係してその定量化が考えられてきた.その最 初でかつ最重要な量が,Shannon の情報エントロピーである(Shannon, 1948).これに触発されて Kolmogorov(1983) は計算機を用いて複雑さを定量化することを考え,複雑度の概念を定式化してその性質を明らかにした.これは コルモゴロフ複雑度による乱流のランダムさ表現 (平板上単一突起下流の乱流くさびの場合) *1, *3 The University of Tokushima, Institute of Technology and Science 2-1 Minami-Josanjima-cho, Tokushima-shi, Tokushima 770-8506, Japan *2 Emeritus Professor, Nagoya University Furo-cho, Chikusa-ku, Nagoya-shi, Aichi 464-8601, Japan Received 10 March 2014

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Randomness representation in turbulent flows with Kolmogorov complexity (In turbulence wedge developed from a single roughness element on a flat plate)