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1.
The nonhydrostatic pressure effects on the generation and propagation of wind-forced internal waves are studied with a two-dimensional
numerical ocean model. A one-way directed wind pulse over a stratified ocean initiates surface and internal waves in a closed
basin. The studies are performed with horizontal grid sizes in the range from 1 km to 62.5 m. The experiments are performed
with both a hydrostatic and a nonhydrostatic model, facilitating systematic studies of the sensitivity of the numerical model
results to the grid size and to the nonhydrostatic pressure adjustments. The results show that the nonhydrostatic pressure
effects are highly dependent on the grid size and grow with increased resolution. In the internal depression wave, the horizontal
nonhydrostatic pressure gradients reach the same order of magnitude as the hydrostatic gradients in the high-resolution nonhydrostatic
studies. In these studies, the nonhydrostatic pressure gradients approximately balance the corresponding hydrostatic pressure
gradients in the internal depression wave, and the wave degenerates into a train of soliton waves. The time for the soliton
form to develop agrees with the steepening timescale calculated from Korteweg-de Vries theory. In the high-resolution hydrostatic
model, the internal depression wave takes the form of a single wave front. When the internal waves are generated in the boundary
layers, the nonhydrostatic pressure gradients are much smaller than the hydrostatic gradients and the generation processes
are not effected by the nonhydrostatic pressure with the present range of grid sizes. 相似文献
2.
A three-dimensional non-linear, non-hydrostatic model in cross-sectional form is used to determine the factors influencing
the relative importance of the linear, non-hydrostatic and non-linear contributions to the internal wave energy flux in sill
regions due to tidal forcing. The importance of the free surface elevation term is also considered. Idealised topography representing
the sill at the entrance to Loch Etive, the site of a recent measurement programme, is used. Calculations show that the non-linear
terms in the energy flux become increasingly important as the sill Froude Number (F
s) increases and the sill aspect ratio is increased. The vertical profile of the stratification, in particular its value close
to the sill crest where internal waves are generated, has a significant influence on unsteady lee wave and mixed tidal–lee
wave generation and the non-linear contribution to the energy flux. Calculations show that as F
s increases, the energy flux due to the non-linear and non-hydrostatic terms increases more rapidly than the linear term. The
importance of the non-linear terms in the energy flux also increases as the sill aspect ratio is increased. Increasing the
buoyancy frequency reduces the contribution of the non-hydrostatic and non-linear terms to the total energy flux. Also, as
the buoyancy frequency is increased, this reduces unsteady lee wave and mixed tidal–lee wave generation. In essence, these
calculations show that the energy flux due to the non-hydrostatic and non-linear terms is appreciable in sill regions. 相似文献
3.
On the importance of non-hydrostatic processes in determining tidally induced mixing in sill regions
The importance of using a non-hydrostatic model to compute tidally induced mixing and flow in the region of a sill is examined using idealized topography representing the sill at the entrance to Loch Etive. This site is chosen since detailed measurements were recently made there. Calculations are performed with and without the inclusion of non-hydrostatic dynamics using a vertical slice model for a range of sill widths corresponding to typical sill regions. Initial non-hydrostatic calculations showed that the model could reproduce the observed flow characteristics in the region. However, when calculations were performed using the model in hydrostatic form, the significant artificial convective mixing that occurred in order to remove density inversions led to excessively high vertical mixing. This influenced the computed temperature field and the intensity of the current jet that separated from the sill on its lee side. In addition it affected the magnitude and spatial characteristics of the lee waves generated on the lee side of the sill. Calculations with a range of sill widths, showed that as the sill width decreased the difference between the solution computed with the non-hydrostatic and hydrostatic model increased. 相似文献
4.
Field observations of tidally driven stratified flow in the sill area of Knight Inlet (British Columbia) revealed a very complicated structure, which includes solitary waves, upstream bifurcation, hydraulic jump and mixing processes. Recent observations suggest that the flow instabilities on the plunging pycnocline at the lee side of the sill may contribute to solitary wave generation through a subharmonic interaction. The present study reports on a series of numerical experiments of stratified tidal flow in Knight Inlet performed with the help of a fine resolution fully non-linear non-hydrostatic numerical model. The model reproduces all important stages of the baroclinic tidal dynamics observed in Knight Inlet. Results demonstrate that solitary waves are generated apart from the area of hydrodynamic instability. Accelerating tidal flux forms a baroclinic hydraulic jump just above the top of the sill, whereas the bifurcations and zones of shear instabilities are formed downstream of the sill. The first baroclinic mode having the largest velocity escapes from the generation area and propagates upstream, disintegrating further into a packet of solitary waves reviling the classical “non-subharmonic” mechanism of generation. The remaining part of the disturbance (slow baroclinic modes) is arrested by tidal flow and carried away to the lee side of the obstacle, where shear instability, billows and mixing processes are developed. Some sensitivity runs were performed for different value of tidal velocity. 相似文献
5.
A cross-sectional non-hydrostatic model with idealized topography was used to examine the processes influencing tidal mixing
in the region of sills. Initial calculations with appropriate parameters for the sill at the entrance to Loch Etive showed
that the model could reproduce the main features of the observed mixing in the region. In particular, the hydraulic jump in
the sill region was reproduced, as was an intense mid-water jet that was observed to separate from the lee side of the sill.
Shear instabilities associated with the jet appeared to be a source of mixing within the thermocline. In addition, internal
lee waves were generated on the lee side of the sill, with the observed amplification because of trapping during the flood
stage. Their magnitude and hence the mixing increased with increasing Froude number (F
r). In the case of vertically varying buoyancy frequency, its value near the sill top determined the F
r number, with its value below influencing internal waves magnitude at depth. At high F
r values particularly with strong currents, short waves and overturning occurred. 相似文献
6.
A 3D non-hydrostatic model is developed to compute internal waves. A novel grid arrangement is incorporated in the model. This not only ensures the homogenous Dirichlet boundary condition for the non-hydrostatic pressure can be precisely and easily imposed but also renders the model relatively simple in its discretized form. The Perot scheme is employed to discretize horizontal advection terms in the horizontal momentum equations, which is based on staggered grids and has the conservative property. Based on previous water wave models, the main works of the present paper are to (1) utilize a semi-implicit, fractional step algorithm to solve the Navier-Stokes equations (NSE); (2) develop a second-order flux-limiter method satisfying the max–min property; (3) incorporate a density equation, which is solved by a high-resolution finite volume method ensuring mass conservation and max–min property based on a vertical boundary-fitted coordinate system; and (4) validate the developed model by using four tests including two internal seiche waves, lock-exchange flow, and internal solitary wave breaking. Comparisons of numerical results with analytical solutions or experimental data or other model results show reasonably good agreement, demonstrating the model’s capability to resolve internal waves relating to complex non-hydrostatic phenomena. 相似文献
7.
A non-hydrostatic model in cross-sectional form with an idealized sill is used to examine the influence of sill depth (h
s) and aspect ratio upon internal motion. The model is forced with a barotropic tide and internal waves and mixing occurs at
the sill. Calculations using a wide sill and quantifying the response using power spectra show that for a given tidal forcing
namely Froude number F
r as the sill depth (h
s) increases the lee wave response and vertical mixing decrease. This is because of a reduction in across sill velocity U
s due to increased depth. Calculations show that the sill Froude number F
s based on sill depth and across sill velocity is one parameter that controls the response at the sill. At low F
s (namely F
s ≪ 1) in the wide sill case, there is little lee wave production, and the response is in terms of internal tides. At high
F
s, calculations with a narrow sill show that for a given F
s value, the lee wave response and internal mixing increase with increasing aspect ratio. Calculations using a narrow sill
with constant U
s show that for small values of h
s, a near surface mixed layer can occur on the downstream side of the sill. For large values of h
s, a thick well-mixed bottom boundary layer occurs due to turbulence produced by the lee waves at the seabed. For intermediate
values of h
s, “internal mixing” dominates the solution and controls across thermocline mixing. 相似文献
8.
The role of water depth and bottom boundary layer turbulence upon lee-wave generation in sill regions is examined. Their effect
upon vertical mixing is also considered. Calculations are performed using a non-hydrostatic model in cross-section form with
a specified tidal forcing. Initial calculations in deeper water and a sill height such that the sill top is well removed from
the surrounding bed region showed that downstream lee-wave generation and associated mixing increased as bottom friction coefficient
k increased. This was associated with an increase in current shear across the sill. However, for a given k, increasing vertical eddy viscosity A
v reduced vertical shear in the across sill velocity, leading to a reduction in lee-wave amplitude and associated mixing. Subsequent
calculations using shallower water showed that for a given k and A
v, lee-wave generation was reduced due to the shallower water depth and changes in the bottom boundary layer. However, in this
case (unlike in the deepwater case), there is an appreciable bottom current. This gives rise to bottom mixing which in shallow
water extends to mid-depth and enhances the mid-water mixing that is found on the lee side of the sill. Final calculations
with deeper water but small sill height showed that lee waves could propagate over the sill, thereby reducing their contribution
to mixing. In this case, bottom mixing was the major source of mixing which was mainly confined to the near bed region, with
little mid-water mixing. 相似文献
9.
A cross-sectional nonhydrostatic model using idealized sill topography is used to examine the influence of bottom friction
upon unsteady lee wave generation and flow in the region of a sill. The implications of changes in shear and lee wave intensity
in terms of local mixing are also considered. Motion is induced by a barotropic tidal flow which produces a hydraulic transition,
associated with which are convective overturning cells, wave breaking, and unsteady lee waves that give rise to mixing on
the lee side of the sill. Calculations show that, as bottom friction is increased, current profiles on the shallow sill crest
develop a highly sheared bottom boundary layer. This enhanced current shear changes the downwelling of isotherms downstream
of the sill with an associated increase in the hydraulic transition, wave breaking, and convective mixing in the upper part
of the water column. Both short and longer time calculations with wide and narrow sills for a number of sill depths and buoyancy
frequencies confirm that increasing bottom friction modifies the flow and unsteady lee wave distribution on the downstream
side of a sill. Associated with this increase in bottom friction coefficient, there is increased mixing in the upper part
of the water column with an associated decrease in the vertical temperature gradient. However, this increase in mixing and
decrease in temperature gradient in the upper part of the water column is very different from the conventional change in near-bed
temperature gradient produced by increased bottom mixing that occurs in shallow sea regions as the bottom drag coefficient
is increased. 相似文献
10.
The flow of a stratified fluid over small-scale topographic features in an estuary may generate significant internal wave activity. Lee waves and upstream influence generated at isolated topographic features have received considerable attention during the past few decades. Field surveys of a partially mixed estuary, the Rotterdam Waterway, in 1987, also showed a plethora of internal wave activity generated by isolated topography, banks and groynes. Additionally it revealed a spectacular series of resonant internal waves trapped above low-amplitude bed waves. The internal waves reached amplitudes of 3–4 m in an estuary with a mean depth of 16 m. The waves were observed during the decreasing flood tide and are thought to make a significant contribution to turbulence production and mixing. However, while stationary linear and finite amplitude theories can be used to explain the presence of these waves, it is important to further investigate their time-dependent and non-linear behaviour. With the development of advanced non-hydrostatic models it now becomes possible to further investigate these waves through numerical experimentation. This is the focus of the work presented here. The non-hydrostatic finite element numerical model FINEL3D developed by Labeur was used in the experiments presented here. The model has been shown to work well in a number of stratified flow investigations. Here, we first show that the model reproduces the field data and for idealised stationary flow scenarios that the results are in agreement with the resonant response predicted by linear theory. Then we explore the effects of non-linearity and time dependence and consider the importance of resonant internal waves for turbulence production in stratified coastal environments.Responsible Editior: Hans Burchard 相似文献
11.
Cai Shuqun Wu Yuqi Xu Jiexin Chen Zhiwu Xie Jieshuo He Yinghui 《中国科学:地球科学(英文版)》2021,64(10):1674-1686
Numerous internal solitary waves(ISWs) have been observed in the southern Andaman Sea. In this study, the two-dimensional Massachusetts Institute of Technology general circulation model is applied to investigate the dynamics of ISWs and explore the effects of the bottom topography and tidal forcing on the generation and propagation of ISWs in the southern Andaman Sea. The results show that the large-amplitude depression ISWs are mainly generated via the oscillating tidal flow over the sill of the Great Channel, and the generation of ISWs is subject to the lee wave regime. The Dreadnought Bank cannot generate ISWs itself; however, it can enhance the amplitudes of eastward-propagating ISWs generated from sill A, owing to constructive interference of internal tide generation between the sill of the Great Channel and the Dreadnought Bank. The eastward-propagating ISWs generated by the eastern shallow sill near the continental shelf can propagate to the shelf, where they evolve into elevation waves because of the shallow water. Sensitivity runs show that both the semidiurnal and diurnal tides over the sill of the Great Channel can generate ISWs in this area. However, the ISWs generated by diurnal tides are much weaker than those generated by semidiurnal tides. Mixed tidal forcing has no significant effect on the generation of ISWs. 相似文献
12.
A free surface non-hydrostatic model in a cross-sectional form, namely, two-dimensional, in the vertical is used to examine
the role of larger-scale topography, namely, sill width, and smaller scale topography, namely, ripples on the sill upon internal
wave generation and mixing in sill regions. The present work is set in the context of earlier work and the wider literature
in order to emphasise the problems of simulating mixing in hydrographic models. Highlights from previous calculations and
references to the literature for detail, together with new results presented here with smooth and “ripple” topography, are
used to show that an idealised cross-sectional model can reproduce the dominant features found in observations at the Loch
Etive sill. Calculations show that on both the short and long time scales, the presence of small-scale “ripple” topography
influence the mixing and associated Richardson number distribution in the sill region. Subsequent calculations in which the
position and form of the small-scale sill topography is varied show for the first time that it is the small-scale topography
near the sill crest that is particularly important in enhancing mid-water mixing on the lee side of the sill. Both short-term
and longer-term calculations with a reduced sill width and associated time series show that as the sill width is reduced,
the non-linear response of the system increases. In addition, Richardson number plots show that the region of critical Richardson
number, and hence enhanced mixing, increases with time and a reduction in sill width. Calculations in which buoyancy frequency
N varies through the vertical show that buoyancy frequency close to the top of the sill is primarily controlling mixing rather
than its mean value. Hence, a Froude number based on sill depth and local N is the critical parameter rather than one based on total depth and mean N. 相似文献
13.
A three-dimensional non-hydrostatic numerical model for simulation of the free-surface stratified flows is presented. The model is a non-hydrostatic extension of free-surface primitive equation model with a general vertical coordinate and horizontal orthogonal curvilinear coordinates. The model equations are integrated with mode-splitting technique and decomposition of pressure and velocity fields on hydrostatic and non-hydrostatic components. The model was tested against laboratory experiments on the steep wave transformation over the longshore bar, solitary wave impact on the vertical wall, the collapse of the mixed region in the thin pycnocline, mixing in the lock-exchange flows and water exchange through the sea strait. The agreement is generally fair.Responsible Editor: Hans Burchard 相似文献
14.
《Continental Shelf Research》2006,26(12-13):1416-1432
A nonhydrostatic model for simulating small-scale processes in the ocean is described. The model is developed using the object-oriented approach. The system is modeled as a set of cooperating objects to manage both the behavioral and information complexity associated with modeling oceanic processes. Objects are storage variables that are created based on classes. A class defines the variables and routines that are members of all objects of that class. The program accesses data stored in these objects using the defined interfaces. Because both data and function are accessed through objects, the model is better organized than one written in a procedural language. The program is easier to understand, debug, maintain, and evolve. Abstraction of the data in the nonhydrostatic model is implemented in both C++ and Matlab. Three examples obtained from the Matlab version of the code illustrate the capabilities of the model in cases where nonhydrostatic effects are important. The model successfully simulates nonhydrostatic atmospheric lee waves, internal waves at a discharge plume, and internal solitary waves generated by tidal flow over a sill. These examples show that the model is capable of studying strongly nonlinear, nonhydrostatic flow processes. 相似文献
15.
《Continental Shelf Research》2006,26(12-13):1469-1480
The generation of internal waves in the partially mixed estuaries is examined. The numerical experiments consider the barotropic tidal currents interacting with isolated obstacles in an open channel. The bottom boundary layer and longitudinal salinity gradient are included. Internal lee (arrested) waves are excited when the accelerating barotropic tidal current approaches the first-mode internal wave speed. The arrested waves are amplified, and are subsequently released when the decelerating tidal current falls below the first-mode internal wave speed. The power input from the barotropic tidal energy into internal wave energy is calculated. It is on the order of 10−2 W/m2, and is comparable to the estimated interior dissipation rate. This suggests that the tidally generated internal waves could be a significant energy source for mixing in the halocline. 相似文献
16.
《Advances in water resources》1998,22(3):239-245
In this paper, we examine the behavior of internal Kelvin waves on an f-plane in finite-difference models using the Arakawa C-grid. The dependence of Kelvin wave phase speed on offshore grid resolution and propagation direction relative to the numerical grid is illustrated by numerical experiments for three different geometries: (1) Kelvin wave propagating along a straight coastline; (2) Kelvin wave propagating at a 45° angle to the numerical grid along a stairstep coastline with stairstep size equal to the grid spacing; (3) Kelvin wave propagating at a 45° angle to the numerical grid along a coarse resolution stairstep coastline with stairstep size greater than the grid spacing. It can be shown theoretically that the phase speed of a Kelvin wave propagating along a straight coastline on an Arakawa C-grid is equal to the analytical inviscid wave speed and is not dependent on offshore grid resolution. However, we found that finite-difference models considerably underestimate the Kelvin wave phase speed when the wave is propagating at an angle to the grid and the grid spacing is comparable with the Rossby deformation radius. In this case, the phase speed converges toward the correct value only as grid spacing decreases well below the Rossby radius. A grid spacing of one-fifth the Rossby radius was required to produce results for the stairstep boundary case comparable with the straight coast case. This effect does not appear to depend on the resolution of the coastline, but rather on the direction of wave propagation relative to the grid. This behavior is important for modeling internal Kelvin waves in realistic geometries where the Rossby radius is often comparable with the grid spacing, and the waves propagate along irregular coastlines.©1998 Published by Elsevier Science Limited. All rights reserved 相似文献
17.
Reservoir topography has significant effects on mechanism of selective withdrawal. We study selective withdrawal of a linearly stratified fluid through a point sink in a long rectangular reservoir with a sill at the bed experimentally and analytically. Experiments were conducted for various flow rates and sill heights to evaluate their effects on withdrawal layer in the inertial-buoyancy regime. Transition to the steady state is discussed in terms of dynamics of shear waves over the sill. The results show that in presence of a sill the withdrawal layer is thicker and higher in elevation. For flows controlled at the sill crest, the withdrawal layer thickness in the point-sink flow is almost equal to that in the similar line-sink flow. We propose an analytical relation for the withdrawal layer thickness in presence of a sill and confirm it by experiments. 相似文献
18.
Toward very high horizontal resolution NWP over the alps: Influence of increasing model resolution on the flow pattern 总被引：1，自引：0，他引：1
Michał Z. Ziemiański Marcin J. Kurowski Zbigniew P. Piotrowski Bogdan Rosa Oliver Fuhrer 《Acta Geophysica》2011,59(6):1205-1235
The increasing resolution of contemporary regional numerical weather prediction (NWP) models, reaching horizontal grid sizes
of O(1 km), requires robust and reliable dynamical cores, working well beyond the approximation of quasi-horizontal flows. That
stimulates an interest in an application for NWP purposes of dynamical cores based on the anelastic, or — more generally —
sound-proof flow equations, and characterized by appropriate robustness and reliability. The paper presents results from testing
the dynamical core of EULAG, the anelastic research model for multi-scale flows, as a prospective NWP dynamical core. The
model simulates the semi-realistic frictionless and adiabatic flow over realistic steep Alpine topographies, employing horizontal
grid sizes of 2.2, 1.1, and 0.55 km. The paper demonstrates not only the numerical robustness of EULAG, but also studies the
influence of the varying horizontal resolution on the simulated flow. Results show that the increased horizontal resolution
increases orographic drag on the flow. While the general flow pattern remains the same, increased resolution influences the
flow on scales from hundreds of kilometers to meso-gamma scales. The differences are especially apparent in the near-surface
layer of 1.5 to 3 km deep, and in the distribution and amplitudes of the orographically-induced gravity waves. 相似文献
19.
Hans van Haren 《Ocean Dynamics》2012,62(8):1123-1137
During a period of 3?days, an accurate bottom-pressure sensor and a four-beam acoustic Doppler current profiler (ADCP) were mounted in a bottom frame at 23?m in a narrow sea strait with dominant near-rectilinear tidal currents exceeding 1?m?s?1 in magnitude. The pressure record distinguishes small and short surface waves, wind- and ferry-induced near-surface turbulence and waves, large turbulent overturns and high-frequency internal waves. Typical low-frequency turbulent motions have amplitudes of 50?N?m?2 and periods of about 50?s. Such amplitudes are also found in independent estimates of non-hydrostatic pressure using ADCP data, but phase relationships between these data sets are ambiguous probably due to the averaging over the spread of the slanted acoustic beams. ADCP's echo amplitudes that are observed in individual beams show much better phase correspondence with near-bottom pressure, whether they are generated near the surface (mainly air bubbles) or near the bottom (mainly suspended sediment). These 50-s motions are a mix of turbulence and internal waves, but they are not due to surface wave interactions, and they are not directly related to the main tidal flow. Internal waves are supported by stratification varying between extremely strong thin layer and very weak near-homogeneous stratification. They are driven by the main flow over 2-m amplitude sand-wave topography, with typical wavelengths of 150?m. 相似文献
20.
Generation of cyclonic vortices in the middle layer of flow around a large mountain like Tibet and Rocky was investigated by means of a 3-D nonhydrostatic meteorological prognostic model. Special attention was paid to the effects of the earth’s rotation and stratification on the vortices detached successively from the slope of a high and large horizontal scale mountain. It was found the successive formation and detachment of such ‘von Karman-like vortices’ occurred in the flow regime at high Rossby numbers Ro and low Froude numbers Fr. It was successfully divided by the criterion of baroclinic instability. This means that if the condition is unstable baroclinically, a lee vortex is destabilized into a three-dimensional one, while under baroclinically stable conditions the lee vortex with vertical axis retains its standing structure and remains long lasting in the middle layer. 相似文献