The boundary layer equations for plane, incompressible, and steady flow are 

$$\matrix{ {u{{\partial u} \over {\partial x}} + v{{\partial u} \over {\partial y}} = - {1 \over \varrho }{{\partial p} \over {\partial x}} + v{{{\partial ^2}u} \over {\partial {y^2}}},} \cr {0 = {{\partial p} \over {\partial y}},} \cr {{{\partial u} \over {\partial x}} + {{\partial v} \over {\partial y}} = 0.} \cr }$$

Boundary Layer Theory

Although uncertainty about structures of environmental models (conceptual uncertainty) is often acknowledged to be the main source of uncertainty in model predictions, it is rarely considered in environmental modelling. Rather, formal uncertainty analyses have traditionally focused on model parameters and input data as the principal source of uncertainty in model predictions. The traditional approach to model uncertainty analysis, which considers only a single conceptual model, may fail to adequately sample the relevant space of plausible conceptual models. As such, it is prone to modelling bias and underestimation of predictive uncertainty. In this paper we review a range of strategies for assessing structural uncertainties in models. The existing strategies fall into two categories depending on whether field data are available for the predicted variable of interest. To date, most research has focussed on situations where inferences on the accuracy of a model structure can be made directly on the basis of field data. This corresponds to a situation of ‘interpolation’. However, in many cases environmental models are used for ‘extrapolation’; that is, beyond the situation and the field data available for calibration. In the present paper, a framework is presented for assessing the predictive uncertainties of environmental models used for extrapolation. It involves the use of multiple conceptual models, assessment of their pedigree and reflection on the extent to which the sampled models adequately represent the space of plausible models. � 2005 Elsevier Ltd. All rights reserved.

A Framework for Dealing With Uncertainty due to Model Structure Error

Velocity measurements are presented for turbulent oscillatory flow over rough beds. Two components of velocity were measured with a laser-Doppler anemometer and the rough beds consisted of a single layer of sand, gravel or pebbles on a flat surface. Turbulence intensities showed significant variation during the course of the cycle. Maximum turbulence intensity propagated out from the bed at a more or less constant velocity for all beds. Variation of time-mean turbulence intensity with height was qualitatively similar to that observed in steady flows. Reynolds stress showed several interesting features. Near the bed, maximum Reynolds stress was in phase with one of the two peaks of turbulence intensity but further out it was in phase with the other, i.e. the phase of maximum Reynolds stress showed a 180° phase shift at a certain height above the bed. A related effect was seen in the time-mean eddy viscosity which was negative near the bed but positive further out. It is suggested that these effects are caused by the jets of fluid associated with vortex formation and ejection in oscillatory flow over rough beds. Maximum Reynolds stress was also significantly less than the horizontal force per unit area of bed obtained from the momentum integral. Eddy viscosity and mixing length were found to vary significantly during the course of the cycle. Variation with height of time-mean values of these variables showed similar trends, except in the near-bed region, to those observed in steady flow but derived values of the Karman constant were significantly lower. Non-dimensional defect velocity appeared to show dependence on a/ks as well as on y/δ in the outer layer away from the bed, even at high Reynolds numbers.

Turbulent oscillatory flow over rough beds

At 14:46 local time on March 11, 2011, a magnitude 9.0 earthquake occurred off the coast of northeast Japan. This earthquake generated a tsunami that struck Japan as well as various locations around the Pacific Ocean. With the participation of about 300 researchers from throughout Japan, joint research groups conducted a tsunami survey along a 2,000 km stretch of the Japanese coast. More than 5,200 locations have been surveyed to date, generating the largest tsunami survey dataset in the world. The inundation height and run-up height were surveyed by laser, GPS, and other instruments, and the tidal correction has been accurately adjusted using a tidal database and a numerical simulation for Tohoku, an area where tide gauges were destroyed by the tsunami. Based on the survey dataset, the regional and local scale analyses were conducted to understand the basic characteristics of this event. Maximum run-up heights greater than 10 m are distributed along 500 km of coast in direct distance. The affected area o...

https://www.tandfonline.com/doi/pdf/10.1142/S0578563412500015

Nationwide post event survey and analysis of the 2011 tohoku earthquake tsunami

Wave-current interaction within and outside the bottom boundary layer

The 2011 Great East Japan Earthquake that occurred on March 11, 2011, had magnitude of 9.0 on the Richter Scale with the epicenter approximately 70 km east of the Oshika Peninsula in Miyagi Prefect...

Coastal and estuarine morphology changes induced by the 2011 great east japan earthquake tsunami

At 14:46 JST on March 11, 2011 a magnitude 90 earthquake (2011 Tohoku Earthquake and Tsunami) occurred off the Pacific Coast of Miyagi Prefecture This study investigated the extensive changes in 

Impact of the 2011 tohoku earthquake and tsunami on beach morphology along the northern sendai coast

Characteristics of turbulent boundary layers over a rough bed under saw-tooth waves and its application to sediment transport

Full-range equation of friction coefficient and phase difference in a wave-current boundary layer

A friction coefficient f cw is derived for a wave-current coexistent system, by assuming a time-invariant eddy viscosity. It is found that f cw is a function of four parameters, Zn/Z0, ūc/uw, ϕ and...

Hitoshi Tanaka

Papers

Coastal and estuarine morphology changes induced by the 2011 great east japan earthquake tsunami

Impact of the 2011 tohoku earthquake and tsunami on beach morphology along the northern sendai coast

Characteristics of turbulent boundary layers over a rough bed under saw-tooth waves and its application to sediment transport

Full-range equation of friction coefficient and phase difference in a wave-current boundary layer

Friction Coefficient for a Wave-Current Coexistent System