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An analysis is made of the formation of a thermoerosional niche into a frozen bluff due to a storm surge on the Beaufort Sea coast. As a first attempt, the problem is treated as a one‐dimensional unsteady problem in which the vertical melting front of the thermoerosional niche migrates into the frozen bluff under the thermoerosional action of breaking waves inside the surf zone during a storm. The analysis examines the temporal and shore‐normal variations of the temperature and salinity of the seawater and the concentration of suspended sediment resulting from the migration of the melting front into the frozen bluff. A simple analytical solution is obtained for the case where the mean water depth during a storm is approximately constant in the neighborhood of the frozen bluff. An example computation based on the simple analytical solution indicates that the thermal driving of the ambient seawater, the mechanical driving represented by the water depth, and the duration of the storm surge are important in determining the degree of the thermoerosional niche formation into the frozen bluff. The computed results are also shown to be in qualitative agreement with available field observations.

Abstract. Laboratory measurements of the instantaneous horizontal and vertical turbulent velocities, u' and w', induced by regular waves spilling on a rough, impermeable slope were analyzed to elucidate the nature of turbulence generated in the bottom boundary layer and by wave breaking. The analyses focused on the instantaneous turbulent events such as the absolute shear stress I,'l = I-u'w'l and turbulent kinetic energy k' = (u '2 + w'2)/2. Below trough level inside the surf zone, the horizontal and vertical velocity records showed intense, intermittent turbulent events that did not occur with the passing of each wave, and the instantaneous quantities of Ir'[ and k' could not be explained in terms of the phase-averaged quantities. The intermittent turbulent events extended into the bottom boundary layer inside the surf zone, and in this region the infrequent but intense turbulence generated by wave breaking was an order of magnitude larger than the turbulence generated locally at the boundary. Two techniques were used to analyze the turbulent motions. A quadrant analysis technique showed that although the large turbulent motions did not occur with each wave, they were phase-dependent near trough level and less so near the bottom. A conditional sampling technique quantified the intensity and duration of the turbulent motions, indicating that coherent events (intense events) occurred for -10% (2%) of the record and accounted for approximately 50% (20%) of the turbulent motion. It is likely that the exactitude of these statistics will differ depending on breaker type. Nevertheless, these statistics indicated that large turbulent motions are infrequent but contribute significantly to the turbulence intensity and possibly the suspension of bottom sediments. In the studies mentioned above, the instantaneous velocitieswere measured with electromagnetic current meters which precluded a detailed analysis of the turbulent flow. Further, these sensors were typically deployed to measure horizontal fluctuations (longshore and cross-shore velocity components) and 14,223

Abstract. A time-dependent cross-shore sediment transport model in the surf and swash zones on beaches is developed to predict both beach accretion and erosion under the assumptions of alongshore uniformity and normally incident waves. The model is based on the depth-integrated sediment continuity equation, which includes sediment suspension by turbulence generated by wave breaking and bottom friction, sediment storage in the entire water column, sediment advection by waves and wave-induced return current, and sediment settling on the movable bottom. The hydrodynamic input required for this sediment transport model is predicted using the finite-amplitude shallow-water equations including bottom friction. The developed model is compared with three large-scale laboratory tests with accretional, neutral (little), and erosional beach profile changes under regular waves. The model predicts sediment suspension under the steep front of breaking waves and due to bottom friction in the swash zone. The computed depth-averaged sediment concentration does not respond to local sediment suspension instantaneously because of the sediment storage and advection. The mean sediment concentration becomes large in comparison to the oscillatory concentration with the decrease of the normalized sediment fall velocity. The net cross-shore sediment transport rate is shown to be the small difference between the onshore transport rate due to the positively correlated oscillatory components of the suspended sediment volume per unit area and the horizontal sediment velocity and the offshore transport rate due to the product of the mean suspended sediment volume and the mean horizontal sediment velocity. Relatedly, the net accretion or erosion rate of the movable bottom is determined by the small difference between the mean sediment settling rate and the mean suspension rate caused by wave breaking and bottom friction. The present computation is limited to the initial beach profile change, but the numerical model is capable of predicting the accretional, erosional, and neutral profile changes.

The numerical model developed previously for coastal structures is slightly modified and applied to predict the wave transformation in the surf and swash zones on gentle slopes as well as the wave reflection and swash oscillation on relatively steep beaches. The numerical model is one‐dimensional in the cross‐shore direction and is based on the finite amplitude, shallow water equations, including the effect of bottom friction, which are solved in the time domain for the incident wave train specified as input at the seaward boundary of the computation located outside the breakpoint. The slight modification is related to the effect of the time‐averaged current on the seaward boundary condition and improves the agreement between the computed and measured mean water levels on gentle slopes. The modified numerical model is compared with available small‐scale test data for monochromatic waves spilling on gentle slopes as well as for monochromatic waves plunging and surging on a relatively steep slope. Additional comparisons are made with small‐scale tests conducted using transient monochromatic and grouped waves on a 1:8 smooth slope with and without an idealized nearshore bar at the toe of the 1:8 slope. As a whole, the numerical model is shown to be capable of predicting both time‐varying and time‐averaged hydrodynamic quantities in the surf and swash zones on gentle as well as steep slopes.

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[1] Laboratory experiments were performed to examine the cross-shore sediment transport processes under breaking solitary waves on a fine sand beach. The initial beach slope of 1/12 was exposed to a positive solitary wave eight times. The beach was rebuilt and exposed to a negative solitary wave eight times. The wave motion and sediment transport were not affected much by the beach profile change from the initial profile. The positive solitary wave plunged violently near the shoreline and suspended a considerable volume of sand. The plunging wave with no seaward flow impeding its run-up caused large run-up on the foreshore. The strong downrush following the large run-up resulted in erosion on the foreshore and deposition seaward of wave run-down. On the other hand, the negative solitary wave collapsed against the seaward flow induced by the free surface slope of the negative wave and caused less sediment suspension. The wave run-up against the seaward flow was much smaller. The weak downrush following the small run-up resulted in deposition on the foreshore and erosion near the wave collapsing point. These limited laboratory experiments indicate the importance of the initial wave profile for swash sediment dynamics and the capacity of a single wave in causing noticeable beach profile changes.

[1] Three tests were conducted in a wave flume to investigate time-averaged suspended sediment transport processes under irregular breaking waves on equilibrium beaches consisting of fine sand. Free surface elevations were measured at ten locations for each test. Velocities and concentrations were measured in the vicinity of the bottom at 94 elevations along 17 vertical lines. The relations among the three turbulent velocity variances are found to be similar to those for the boundary layer flow. The vertical variation of the mean velocity, which causes offshore transport, is fitted by a parabolic profile fairly well. The vertical variation of the mean concentration C is fitted by the exponential and power-form distributions equally well. The ratio between the concentration standard deviation s C and the mean C varies little vertically. The correlation coefficient g UC between the horizontal velocity and concentration, which results in onshore transport, is of the order of 0.1 and decreases upward linearly. The offshore and onshore transport rates of suspended sediment are estimated and expressed in terms of the suspended sediment volume V per unit area. A time-averaged numerical model is developed to predict V as well as the mean and standard deviation of the free surface elevation and horizontal velocity. The bottom slope effect on the wave energy dissipation rate D B due to wave breaking is included in the model. The computation can be made well above the still water shoreline with no numerical difficulty. Reflected waves from the shoreline are estimated from the wave energy flux remaining at the shoreline. The numerical model is in agreement with the statistical data except that the undertow current is difficult to predict accurately. The measured turbulent velocities are found to be more related to the turbulent velocity estimated from the energy dissipation rate D f due to bottom friction. The suspended sediment volume V expressed in terms of D B and D f can be predicted only within a factor of about 2. The roller effect represented by the roller volume flux does not necessarily improve the agreement for the three tests.