Coastal processes include various aspects of surface wave and bottom sediment movement together with the interaction between them. Among them, sand transport is an essential link in the coastal morphodynamics related to the change of bottom topography. The present study is motivated by the increase in beach instabilities corresponding to the erosion and accretion courses around the world, and focuses on the cross-shore sand transport under various wave and current flow conditions in the sheetflow regime. Sheetflow transport develops under storm conditions when the Shields parameter becomes large （0.8-1.0） enough to wash out sand ripples and the bed turns to plane again. A thin layer （〜1 cm） with high sand concentration is moving in a sheet along the bed.

The primary aim of the present study is twofold. The first objective is to increase insight in cross-shore sand transport processes under sheetflow conditions through physical experiments. The second objective is to apply the insight from experiments to develop a new theoretical model for numerical simulation through a two-phase flow conception on describing the cross-shore sediment movement.

Experimental approach

Sheetflow experiments were performed in the oscillatory flow water tunnel applying the pure sinusoidal wave condition. Two series of experiments were carried out with mobile sand beds consisting of well-sorted sand with different medium grain sizes: 0.21 mm and 0.3 mm. By using image analysis, which overcomes the demerits introduced by intrusive measurements, the time-dependent as well as the maximum erosion depths for different flow conditions were estimated. In addition, one specified experiment was carried out in order to investigate the sediment concentration distribution and grain velocity variation. The experimental processes were recorded using a high-speed video camera.

From the experimental measurements, the erosion depth in the sheetflow transport varies significantly and never returns back to zero during one wave period. Temporal variation of the erosion depth is significant under the conditions of large velocity amplitude and short wave period. The relative maximum erosion depth is found related to the maximum Shield parameter linearly with a large linearity coefficient for fine sand.

Although the free-stream velocity is sinusoidal, the suspended concentration is asymmetric with large concentration values in the deceleration phase. The duration of the suspension is generally longer than sedimentation process reflecting the asymmetry in turbulence. The phase lag between concentration and free stream velocity is important for sediment movement and increases with the elevation.

The sediment velocity is determined using a PIV technique on the successive images. A sudden decrease in the bottom horizontal sediment velocity profile is observed at the beginning of acceleration phases corresponding to the sedimentation of a large amount of sand particles. Turbulence intensity is strong around maximum velocities and weak around flow reversals, which is consistent with the suspension and deposition processes.

Numerical simulation

Taking into account the sediment movement mechanism observed from the experimental study, a new two-phase flow model for fluid phase and sediment phase, was set up based on the conservation of mass and momentum in horizontal and vertical directions.

Compared with the practical quasi-steady and semi-unsteady models as well as traditional one-dimensional vertical models, the two-phase flow models are sophisticated models and circumstantiate the interactions between fluid and grain, the collision among grain particles, and can describe the sediment movement from the stationary sand bed, into the high-concentration sheetflow layer, and then upwards into the dilute suspended layer. Various forces, like the interaction force between the fluid and water, the intergranular stress among the sand particles, the turbulent stress in the fluid, the sediment diffusivity and pressure gradient are specified in the two-phase flow model. Reasonable numerical integrations together with the suitable boundary and initial conditions for simulation were proposed. The two-phase flow model proposed in the present study includes six governing equations with six unknown variables. The finite difference method is employed to solve these coupled nonlinear differential equations.

Preliminary descriptions on the model's results show the capability of the two-phase flow model for sediment movement simulation under the sheetflow conditions. It was found that anti-phase behaviour for concentration profiles together with large vertical concentration gradient was estimated in the sheetflow layer. Horizontal velocity difference between the fluid and sand is small with the largest discrepancy appearing in the sheetflow layer. At the bottom layer, the vertical instantaneous sediment velocity profile presents an upwardly convex "o a" shape in the low region and downwardly convex "e o" tendency in the above region within one wave period. In the suspended layer, the magnitude of fluid velocity is always larger than that of sand velocity in the acceleration phase, and smaller in the deceleration phase. As for vertical velocity distribution, the upward flow is simulated around the initial bed level for fluid phase where significant decrease on the sand falling velocity can be observed. In the suspended layer, the sand falling velocity approaches to the free settling velocity of a single sand particle. Further discussions on the force terms governing the sand movement demonstrate that in the bottom sheetflow layer the intergranular stress gradient plays an important role for sand movement, whilst the pressure gradient affects the sediment dynamics significantly in the upper sheetflow region due to the counteraction between intergranular stress gradient and drag force. In the suspended layer, the drag force and pressure gradient are more crucial for sand movement.

The model's validation was carried out by comprehensive comparison between numerical simulation and experimental measurement. This included the verification on a large amount of up to date experimental data: Horikawa et al. （1982） for pure sinusoidal flows, Ribberink and Al-Salem （1995） for pure sinusoidal and asymmetric waves, Dohmen-Janssen （1999） for combined wave/current flows, O'Donoghue and Wright （2004a, 2004b） for asymmetric wave conditions and Liu and Sato （2005） for pure sinusoidal flows.

The comparison was carried out based on four aspects: the temporal and spatial sediment concentration configurations together with the mean concentration profiles, the detailed fluid and sand velocities profiles together with the mean velocity profile for combined wave/ current flows, the information on sediment flux structure and the net transport rate for combined wave/current flows and asymmetric wave conditions. The simulated solutions represent the main characteristics of sediment movement satisfactorily for most of the experimental cases. Overestimation on the net transport rate for combined wave/current flows is found, especially for fine sand with large current/wave velocity ratio cases. After some suitable modification on the expressions for eddy viscosity and sand diffusivity, the simulated net transport rate for asymmetric wave conditions is rather well compared with several previous empirical formulae. Both the magnitude and direction of the net transport rate can be estimated from the present model with an agreement by a factor of 2, especially for fine sand cases with an offshore directional net transport.

現地海岸では砕波帯内で短期的かつ大規模な地形変化を引き起こすシートフロー形式の砂移動が重要となる．シートフロー条件は主として高波浪時に発生し，底面流速振幅が大きくなるため，砂漣が消滅し底面上で極めて高濃度の移動砂層が形成される．本研究では，シートフロー移動層の力学的挙動を，振動流装置を用いた実験と新たに開発した二相流モデルによる数値実験により解明したものである．二相流モデルは，連続式および運動方程式を満足する固相（底質）と液相（流体）の運動を質量保存則および運動量保存則の観点から記述し，圧力だけでなく固液間力・粒子間力・乱流応力・乱流拡散も同様に考慮することにより，水と砂粒子の運動を相互干渉を考慮しながら同時に解くものである．

本論文は，振動流装置を用いた実験，波・流れ共存場での数値実験，非対称振動流場での数値実験で構成される．第1部ではシートフロー現象について既往の研究を整理し，室内実験を実施した．室内実験では，底質に細砂を用い振動流境界層において，漂砂特性の把握や漂砂量の測定，またハイスピードカメラで得られた輝度分布を基に時空間的な漂砂濃度分布が示されている．室内実験では，移動機構を計測することを目的として改良PIV法が適用された．改良PIV手法では，相互相関手法に比べて優れていることが確認された自乗誤差最小化手法が採用された．また，底面近傍でも精度の高い流速・濃度推定手法を開発することに成功した．PIV手法で計測された砂粒子の移動速度や浮遊砂濃度の特性に関する知見は，後半の数値モデル構築の見通しを良くするのに活用するとともに，移動床条件での乱流計測や固液混相流の固相濃度変化など，計測が困難な条件における新しい知見が数多く得られた．

第2部では，まず，二相流の概念に基づく数学モデルを構築した．連続式および運動方程式を固液相へ適用することで物理現象を数学的に表現した．流体の単位体積当りの固液間力，粒子間力成分，乱流応力，乱流拡散過程を数学的に記述した．初期条件および境界条件についても数学的に記述している．構築したモデルを，差分法を用いて数値的に解くアルゴリズムを開発し，実験データが比較的豊富な正弦振動流，および，波・流れ共存条件に適用し，数値モデルの精度と適用性を検証した．

第3部では，海浜変形問題で極めて重要になる非対称振動流条件への適用性を検討した．非対称振動流では岸向きと沖向きで境界層の乱流構造が異なるため，これらを合理的に表現できるように渦粘性係数と乱流拡散係数を修正し，底質の移動速度や浮遊砂濃度に関して最新の実験データと比較することによりモデルの精度を検証した．本研究で提案したモデルは，底質の粒径，振動流の流速，周期のさまざまな条件において，シートフロー漂砂の移動方向を正しく予測し，漂砂量の予測精度も従来のモデルに比べて格段に向上していることが確認できた．また，近年発表された二相流モデルと比較しても，流速，浮遊砂濃度，底質の輸送フラックスのいずれにおいても，本研究のモデルの予測精度が最も優れていることが確認できた．

以上，要するに，本研究は計測が困難なシートフロー漂砂現象について，画像解析に基づく実験と二相流理論による数値モデルを開発し，シートフロー条件での底質の総輸送量に対して精度の高いモデルを提案することに成功した．開発したモデルの妥当性は，最新の実験データに対して網羅的に検証されており，現時点では本モデルが世界中で最も高精度なモデルであることが定量的に示されている．本研究で開発したモデルは，縮尺効果の影響を受ける経験定数を含まないため，現地海岸条件にも適用可能なものであり，広い適用範囲を持つもので実用性が高い．よって本論文は博士（工学）の学位請求論文として合格と認められる．